Dynamos and MHD theory of turbulence suppression
Yoshizawa, Akira [Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, 87, Kasuga 810- 8580 (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan); Yokoi, Nobumitsu [Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505 (Japan)
2004-03-01
Characteristics of electrically conducting media are reviewed from the macroscopic viewpoint based on mean-field magnetohydrodynamics, while being compared using the methodology and knowledge in fluid mechanics. The themes covered in this review range from the mechanism of generating stellar magnetic fields (dynamo) to transport properties in fusion. The primary concern here is to see the characteristics common to these apparently different phenomena, within the framework of the mean-field theory. Owing to the intrinsic limitation of the approach, the present discussions are limited more or less to specific aspects of phenomena. They are supplemented with reference to theoretical, numerical, and observational approaches intrinsic to each theme. In the description of dynamo phenomena, emphasis is laid on the cross helicity dynamo. Features common to stellar magnetic-field generation and the rotational-motion drive in toroidal plasmas are illustrated on this basis. (topical review)
MHD Turbulence and Magnetic Dynamos
Shebalin, John V
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
MHD Turbulence, Turbulent Dynamo and Applications
Beresnyak, Andrey
2014-01-01
MHD Turbulence is common in many space physics and astrophysics environments. We first discuss the properties of incompressible MHD turbulence. A well-conductive fluid amplifies initial magnetic fields in a process called small-scale dynamo. Below equipartition scale for kinetic and magnetic energies the spectrum is steep (Kolmogorov -5/3) and is represented by critically balanced strong MHD turbulence. In this paper we report the basic reasoning behind universal nonlinear small-scale dynamo and the inertial range of MHD turbulence. We measured the efficiency of the small-scale dynamo $C_E=0.05$, Kolmogorov constant $C_K=4.2$ and anisotropy constant $C_A=0.63$ for MHD turbulence in high-resolution direct numerical simulations. We also discuss so-called imbalanced or cross-helical MHD turbulence which is relevant for in many objects, most prominently in the solar wind. We show that properties of incompressible MHD turbulence are similar to the properties of Alfv\\'enic part of MHD cascade in compressible turbul...
Dipole Alignment in Rotating MHD Turbulence
Shebalin, John V.; Fu, Terry; Morin, Lee
2012-01-01
We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.
Observational Tests of Recent MHD Turbulence Perspectives
Ghosh, Sanjoy
2001-06-01
This grant seeks to analyze the Heliospheric Missions data to test current theories on the angular dependence (with respect to mean magnetic field direction) of magnetohydrodynamic (MHD) turbulence in the solar wind. Solar wind turbulence may be composed of two or more dynamically independent components. Such components include magnetic pressure-balanced structures, velocity shears, quasi-2D turbulence, and slab (Alfven) waves. We use a method, developed during the first two years of this grant, for extracting the individual reduced spectra of up to three separate turbulence components from a single spacecraft time series. The method has been used on ISEE-3 data, Pioneer Venus Orbiter, Ulysses, and Voyager data samples. The correlation of fluctuations as a function of angle between flow direction and magnetic-field direction is the focus of study during the third year.
Electron MHD: dynamics and turbulence
Lyutikov, Maxim
2013-01-01
(Abridged) We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact non-linear solutions; (ii) co-linear whistlers do not interact (including counter-propagating); (iii) waves with the same value of the wave vector, $k_1=k_2$, do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero-mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfven turbulence cannot be transferred to the E...
Achieving Fast Reconnection in Resistive MHD Models via Turbulent Means
Lapenta, Giovanni
2011-01-01
Astrophysical fluids are generally turbulent and this preexisting turbulence must be taken into account for the models of magnetic reconnection which are attepmted to be applied to astrophysical, solar or heliospheric environments. In addition, reconnection itself induces turbulence which provides an important feedback on the reconnection process. In this paper we discuss both theoretical model and numerical evidence that magnetic reconnection gets fast in the approximation of resistive MHD. We consider the relation between the Lazarian & Vishniac turbulent reconnection theory and Lapenta's numerical experiments testifying of the spontaneous onset of turbulent reconnection in systems which are initially laminar.
Eigenanalysis of Ideal Hall MHD Turbulence
Fu, T.; Shebalin, J. V.
2011-12-01
Ideal, incompressible, homogeneous, Hall magnetohydrodynamic (HMHD) turbulence may be investigated through a Fourier spectral method. In three-dimensional periodic geometry, the independent Fourier coefficients represent a canonical ensemble described by a Gaussian probability density. The canonical ensemble is based on the conservation of three invariants: total energy, generalized helicity, and magnetic helicity. Generalized helicity in HMHD takes the place of cross helicity in MHD. The invariants determine the modal probability density giving the spectral structure and equilibrium statistics of ideal HMHD, which are compared to known MHD results. New results in absolute equilibrium ensemble theory are derived using a novel approach that involves finding the eigenvalues of a Hermitian covariance matrix for each modal probability density. The associated eigenvectors transform the original phase space variables into eigenvariables through a special unitary transformation. These are the normal modes which facilitate the analysis of ideal HMHD non-linear dynamics. The eigenanalysis predicts that the low wavenumber modes with very small eigenvalues may have mean values that are large compared to their standard deviations, contrary to the ideal ensemble prediction of zero mean values. (Expectation values may also be relatively large at the highest wave numbers, but the addition of even small levels of dissipation removes any relevance this may have for real-world turbulence.) This behavior is non-ergodic over very long times for a numerical simulation and is termed 'broken ergodicity'. For fixed values of the ideal invariants, the effect is seen to be enhanced with increased numerical grid size. Broken ergodicity at low wave number modes gives rise to large-scale, quasi-stationary, coherent structure. Physically, this corresponds to plasma relaxation to force-free states. For real HMHD turbulence with dissipation, broken ergodicity and coherent structure are still
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
Type I Planetary Migration with MHD Turbulence
Laughlin, G; Adams, F; Laughlin, Gregory; Steinacker, Adriane; Adams, Fred
2004-01-01
This paper examines how type I planet migration is affected by the presence of turbulent density fluctuations in the circumstellar disk. For type I migration, the planet does not clear a gap in the disk and its secular motion is driven by torques generated by the wakes it creates in the surrounding disk fluid. MHD turbulence creates additional density perturbations that gravitationally interact with the planet and can dominate the torques produced by the migration mechanism itself. This paper shows that conventional type I migration can be readily overwhelmed by turbulent perturbations and hence the usual description of type I migration should be modified in locations where the magnetorotational instability is active. In general, the migrating planet does not follow a smooth inward trned, but rather exhibits a random walk through phase space. Our main conclusion is that MHD turbulence will alter the time scales for type I planet migration and -- because of chaos -- requires the time scales to be described by ...
Turbulence evolution in MHD plasmas
Wisniewski, M; Spanier, F
2013-01-01
Turbulence in the interstellar medium has been an active field of research in the last decade. Numerical simulations are the tool of choice in most cases. But while there are a number of simulations on the market some questions have not been answered finally. In this paper we are going to examine the influence of compressible and incompressible driving on the evolution of turbulent spectra in a number of possible interstellar medium scenarios. We conclude that the driving not only has an influence on the ratio of compressible to incompressible component but also on the anisotropy of turbulence.
Statistical Theory of the Ideal MHD Geodynamo
Shebalin, J. V.
2012-01-01
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the
Quasi-isotropic cascade in MHD turbulence with mean field
Grappin, Roland; Gürcan, Özgür
2012-01-01
We propose a phenomenological theory of incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale magnetic field, which establishes a link between the known anisotropic models of strong and weak MHD turbulence We argue that the Iroshnikov-Kraichnan isotropic cascade develops naturally within the plane perpendicular to the mean field, while oblique-parallel cascades with weaker amplitudes can develop, triggered by the perpendicular cascade, with a reduced flux resulting from a quasi-resonance condition. The resulting energy spectrum $E(k_\\parallel,k_\\bot)$ has the same slope in all directions. The ratio between the extents of the inertial range in the parallel and perpendicular directions is equal to $b_{rms}/B_0$. These properties match those found in recent 3D MHD simulations with isotropic forcing reported in [R. Grappin and W.-C. M\\"uller, Phys. Rev. E \\textbf{82}, 26406 (2010)].
Cosmic ray transport in MHD turbulence
Yan, Huirong
2007-01-01
Numerical simulations shed light onto earlier not trackable problem of magnetohydrodynamic (MHD) turbulence. They allowed to test the predictions of different models and choose the correct ones. Inevitably, this progress calls for revisions in the picture of cosmic ray (CR) transport. It also shed light on the problems with the present day numerical modeling of CR. In this paper we focus on the analytical way of describing CR propagation and scattering, which should be used in synergy with the numerical studies. In particular, we use recently established scaling laws for MHD modes to obtain the transport properties for CRs. We include nonlinear effects arising from large scale trapping, to remove the 90 degree divergence. We determine how the efficiency of the scattering and CR mean free path depend on the characteristics of ionized media, e.g. plasma $\\beta$, Coulomb collisional mean free path. Implications for particle transport in interstellar medium and solar corona are discussed. We also examine the perp...
MHD Turbulence in Accretion Disk Boundary Layers
Chan, Chi-kwan
2012-01-01
The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations...
Cosmic-ray pitch-angle scattering in imbalanced MHD turbulence simulations
Weidl, Martin S; Teaca, Bogdan; Schlickeiser, Reinhard
2015-01-01
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.
Drag reduction in turbulent MHD pipe flows
Orlandi, P.
1996-01-01
This is a preliminary study devoted to verifying whether or not direct simulations of turbulent Magneto-Hydro-Dynamic (MHD) flows in liquid metals reproduce experimental observations of drag reduction. Two different cases have been simulated by a finite difference scheme which is second order accurate in space and time. In the first case, an external azimuthal magnetic field is imposed. In this case, the magnetic field acts on the mean axial velocity and complete laminarization of the flow at N(sub a) = 30 has been achieved. In the second case, an axial magnetic field is imposed which affects only fluctuating velocities, and thus the action is less efficient. This second case is more practical, but comparison between numerical and experimental results is only qualitative.
Dynamo action in dissipative, forced, rotating MHD turbulence
Shebalin, John V.
2016-06-01
Magnetohydrodynamic (MHD) turbulence is an inherent feature of large-scale, energetic astrophysical and geophysical magnetofluids. In general, these are rotating and are energized through buoyancy and shear, while viscosity and resistivity provide a means of dissipation of kinetic and magnetic energy. Studies of unforced, rotating, ideal (i.e., non-dissipative) MHD turbulence have produced interesting results, but it is important to determine how these results are affected by dissipation and forcing. Here, we extend our previous work and examine dissipative, forced, and rotating MHD turbulence. Incompressibility is assumed, and finite Fourier series represent turbulent velocity and magnetic field on a 643 grid. Forcing occurs at an intermediate wave number by a method that keeps total energy relatively constant and allows for injection of kinetic and magnetic helicity. We find that 3-D energy spectra are asymmetric when forcing is present. We also find that dynamo action occurs when forcing has either kinetic or magnetic helicity, with magnetic helicity injection being more important. In forced, dissipative MHD turbulence, the dynamo manifests itself as a large-scale coherent structure that is similar to that seen in the ideal case. These results imply that MHD turbulence, per se, may play a fundamental role in the creation and maintenance of large-scale (i.e., dipolar) stellar and planetary magnetic fields.
Numerical study of Cosmic Ray Diffusion in MHD turbulence
Beresnyak, A.; Yan, H.; Lazarian, A.
2010-01-01
We study diffusion of Cosmic Rays (CRs) in turbulent magnetic fields using test particle simulations. Electromagnetic fields are produced in direct numerical MHD simulations of turbulence and used as an input for particle tracing, particle feedback on turbulence being ignored. Statistical transport coefficients from the test particle runs are compared with earlier analytical predictions. We find qualitative correspondence between them in various aspects of CR diffusion. In the incompressible ...
Transition from weak to strong cascade in MHD turbulence.
Verdini, Andrea; Grappin, Roland
2012-07-13
The transition from weak to strong turbulence when passing from large to small scales in magnetohydrodynamic (MHD) turbulence with guide field is a cornerstone of anisotropic turbulence theory. We present the first check of this transition, using the Shell-RMHD, which combines a shell model of perpendicular nonlinear coupling and linear propagation along the guide field. This model allows us to reach Reynolds numbers around 10(6). We obtain surprisingly good agreement with the theoretical predictions, with a reduced perpendicular energy spectrum scaling as k(⊥)(-2) at large scales and as k(⊥)(-5/3) at small scales, where critical balance between nonlinear and propagation time is reached. However, even in the strong regime, a high level of excitation is found in the weak coupling region of Fourier space, which is due to the rich frequency spectrum of large eddies. A corollary is that the reduced parallel spectral slope is not a definite test of the spectral anisotropy, contrary to standard belief.
Bershadskii, A.G.
1985-06-01
An exact solution for the nonlinear problem of the spectral energy function of a homogeneous turbulence is derived under the assumption that energy transfer under the effect of inertial forces is determined mainly by the interactions among vortices whose wavenumbers are only slightly different from each other. The results are experimentally verified for turbulence behind grids. Similar problems are solved for MHD turbulence and for a nonstationary spectral energy function. It is shown that at the initial stage of degeneration, the spectral energy function is little influenced by the Stewart number; this agrees with experimental data for the damping of longitudinal velocity pulsations behind a grid in a longitudinal magnetic field. 15 references.
MHD-effects in a turbulent medium of nonuniform density
Vaynshteyn, S.I.
1978-01-01
Turbulence in a medium of nonuniform density, such as the convective solar layer, is analyzed with the assumption that Del rho = rho lambda (exponential stratification). Considered are first the simplest case of a quasi-isotropic turbulence, then addition of a scalar factor such as the temperature, and finally anisotropic turbulence. The magnetic field and MHD-effects are then calculated without diffusion, and with two-dimensional turbulence as a special case. Also the values of the essential parameters in this problem are estimated. 7 references.
Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas
G. G. Howes
2009-03-01
Full Text Available The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range of the solar wind must be one, or a mixture, of three electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic Alfvén waves. These modes are generally well described by Hall MHD. Determining the applicability of linear kinetic damping rates in turbulent plasmas requires a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid and kinetic simulations will also shed light on whether the presence of spurious wave modes alters the nonlinear couplings inherent in turbulence and will illuminate the turbulent dynamics and energy transfer in the regime of the characteristic ion kinetic scales.
Dissipation and Heating in Supersonic Hydrodynamic and MHD Turbulence
Lemaster, M Nicole
2008-01-01
We study energy dissipation and heating by supersonic MHD turbulence in molecular clouds using Athena, a new higher-order Godunov code. We analyze the dependence of the saturation amplitude, energy dissipation characteristics, power spectra, sonic scaling, and indicators of intermittency in the turbulence on factors such as the magnetic field strength, driving scale, energy injection rate, and numerical resolution. While convergence in the energies is reached at moderate resolutions, we find that the power spectra require much higher resolutions that are difficult to obtain. In a 1024^3 hydro run, we find a power law relationship between the velocity dispersion and the spatial scale on which it is measured, while for an MHD run at the same resolution we find no such power law. The time-variability and temperature intermittency in the turbulence both show a dependence on the driving scale, indicating that numerically driving turbulence by an arbitrary mechanism may not allow a realistic representation of these...
Role of Cross Helicity in Cascade Processes of MHD turbulence
Mizeva, Irina; Frick, Peter; 10.1134/S1028335809020128
2009-01-01
The purpose of this work is to investigate the spectral properties of the developed isotropic (non-Alfven) MHD turbulence stationary excited by an external force, which injects the cross helicity into the flow simultaneously with the energy. It is shown that the cross helicity blocks the spectral energy transfer in MHD turbulence and results in energy accumulation in the system. This accumulation proceeds until the vortex intensification compensates the decreasing efficiency of nonlinear interactions. The formula for estimating the average turbulence energy is obtained for the set ratio between the injected helicity and energy. It is remarkable that the turbulence accumulates the injected cross helicity at its low rate injection -- the integral correlation coefficient significantly exceeds the ratio between the injected helicity and the energy. It is shown that the spectrum slope gradually increases from "5/3" to "2" with the cross helicity level.
Turning the resistive MHD into a stochastic field theory
M. Materassi
2008-08-01
Full Text Available Classical systems stirred by random forces of given statistics may be described via a path integral formulation in which their degrees of freedom are stochastic variables themselves, undergoing a multiple-history probabilistic evolution. This framework seems to be easily applicable to resistive Magneto-Hydro-Dynamics (MHD. Indeed, MHD equations form a dynamic system of classical variables in which the terms representing the density, the pressure and the conductivity of the plasma are irregular functions of space and time when turbulence occurs. By treating those irregular terms as random stirring forces, it is possible to introduce a Stochastic Field Theory which should represent correctly the impulsive phenomena caused by the spece- and time-irregularity of plasma turbulence. This work is motivated by the recent observational evidences of the crucial role played by stochastic fluctuations in space plasmas.
Turning the resistive MHD into a stochastic field theory
Materassi, M.; Consolini, G.
2008-08-01
Classical systems stirred by random forces of given statistics may be described via a path integral formulation in which their degrees of freedom are stochastic variables themselves, undergoing a multiple-history probabilistic evolution. This framework seems to be easily applicable to resistive Magneto-Hydro-Dynamics (MHD). Indeed, MHD equations form a dynamic system of classical variables in which the terms representing the density, the pressure and the conductivity of the plasma are irregular functions of space and time when turbulence occurs. By treating those irregular terms as random stirring forces, it is possible to introduce a Stochastic Field Theory which should represent correctly the impulsive phenomena caused by the spece- and time-irregularity of plasma turbulence. This work is motivated by the recent observational evidences of the crucial role played by stochastic fluctuations in space plasmas.
Spectral slope and Kolmogorov constant of MHD turbulence.
Beresnyak, A
2011-02-18
The spectral slope of strong MHD turbulence has recently been a matter of controversy. While the Goldreich-Sridhar model predicts a -5/3 slope, shallower slopes have been observed in numerics. We argue that earlier numerics were affected by driving due to a diffuse locality of energy transfer. Our highest-resolution simulation (3072(2)×1024) exhibited the asymptotic -5/3 scaling. We also discover that the dynamic alignment, proposed in models with -3/2 slope, saturates and cannot modify the asymptotic, high Reynolds number slope. From the observed -5/3 scaling we measure the Kolmogorov constant C(KA)=3.27±0.07 for Alfvénic turbulence and C(K)=4.2±0.2 for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger C(K) indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.
Turbulent MHD transport coefficients - An attempt at self-consistency
Chen, H.; Montgomery, D.
1987-01-01
In this paper, some multiple scale perturbation calculations of turbulent MHD transport coefficients begun in earlier papers are first completed. These generalize 'alpha effect' calculations by treating the velocity field and magnetic field on the same footing. Then the problem of rendering such calculations self-consistent is addressed, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous 'alpha effect' and 'beta effect' coefficients emerge as limiting cases. A treatment of the inertial range can also be given, consistent with a -5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.
Alignment of Velocity and Magnetic Fluctuations in Simulations of Anisotropic MHD Turbulence
Ng, C. S.; Bhattacharjee, A.
2007-11-01
There has been recent theoretical interest in the effect of the alignment of velocity and magnetic fluctuations in three-dimensional (3D) MHD turbulence with a large-scale magnetic field [Boldyrev 2005, 2006]. This theory predicts that the angle θ between the velocity and magnetic fluctuation vectors has a scaling of θ&1/4circ;, where λ is the spatial scale of the fluctuations. There have also been simulations on 3D forced MHD turbulence that supports this prediction [Mason et al. 2006, 2007]. The scaling has also been tested against observations of solar wind turbulence [Podesta et al. 2007]. We report here simulation results based on decaying 2D turbulence. The scaling of θ&1/4circ; and Iroshnikov-Kraichnan scaling has also been observed within a range of time interval and spatial scales, despite the fact that Boldyrev's theory was developed for fully 3D turbulence in the presence of a strong external field. As the external field is reduced in magnitude and becomes comparable to the magnitude of magnetic fluctuations or lower, the scale-dependent alignment is weakened. Implications for observations of solar wind turbulence will be discussed.
Intermittency in MHD turbulence and coronal nanoflares modelling
P. Veltri
2005-01-01
Full Text Available High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD. The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis.
MHD Turbulent Mixing Layers: Equilibrium Cooling Models
Esquivel, A; Cho, J; Lazarian, A; Leitner, S N
2006-01-01
We present models of turbulent mixing at the boundaries between hot (T~10^{6-7} K) and warm material (T~10^4 K) in the interstellar medium, using a three-dimensional magnetohydrodynamical code, with radiative cooling. The source of turbulence in our simulations is a Kelvin-Helmholtz instability, produced by shear between the two media. We found, that because the growth rate of the large scale modes in the instability is rather slow, it takes a significant amount of time (~1 Myr) for turbulence to produce effective mixing. We find that the total column densities of the highly ionized species (C IV, N V, and O VI) per interface (assuming ionization equilibrium) are similar to previous steady-state non-equilibrium ionization models, but grow slowly from log N ~10^{11} to a few 10^{12} cm^{-2} as the interface evolves. However, the column density ratios can differ significantly from previous estimates, with an order of magnitude variation in N(C IV)/N(O VI) as the mixing develops.
Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence
Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.
2017-02-01
The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.
MHD turbulence-Star Formation Connection: from pc to kpc scales
Pino, E M de Gouveia Dal; Lazarian, A; Leão, M R M; Falceta-Gonçalves, D; Kowal, G
2011-01-01
The transport of magnetic flux to outside of collapsing molecular clouds is a required step to allow the formation of stars. Although ambipolar diffusion is often regarded as a key mechanism for that, it has been recently argued that it may not be efficient enough. In this review, we discuss the role that MHD turbulence plays in the transport of magnetic flux in star forming flows. In particular, based on recent advances in the theory of fast magnetic reconnection in turbulent flows, we will show results of three-dimensional numerical simulations that indicate that the diffusion of magnetic field induced by turbulent reconnection can be a very efficient mechanism, especially in the early stages of cloud collapse and star formation. To conclude, we will also briefly discuss the turbulence-star formation connection and feedback in different astrophysical environments: from galactic to cluster of galaxy scales.
The mathematical theory of reduced MHD models for fusion plasmas
Guillard, Hervé
2015-01-01
The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of this theory and to prove rigorously that reduced MHD models are valid approximations of the full MHD equations. In particular, it is proven that the solutions of the full MHD system converge to the solutions of an appropriate reduced model.
Final Report: "Large-Eddy Simulation of Anisotropic MHD Turbulence"
Zikanov, Oleg
2008-06-23
To acquire better understanding of turbulence in flows of liquid metals and other electrically conducting fluids in the presence of steady magnetic fields and to develop an accurate and physically adequate LES (large-eddy simulation) model for such flows. The scientific objectives formulated in the project proposal have been fully completed. Several new directions were initiated and advanced in the course of work. Particular achievements include a detailed study of transformation of turbulence caused by the imposed magnetic field, development of an LES model that accurately reproduces this transformation, and solution of several fundamental questions of the interaction between the magnetic field and fluid flows. Eight papers have been published in respected peer-reviewed journals, with two more papers currently undergoing review, and one in preparation for submission. A post-doctoral researcher and a graduate student have been trained in the areas of MHD, turbulence research, and computational methods. Close collaboration ties have been established with the MHD research centers in Germany and Belgium.
Statistical turbulence theory and turbulence phenomenology
Herring, J. R.
1973-01-01
The application of deductive turbulence theory for validity determination of turbulence phenomenology at the level of second-order, single-point moments is considered. Particular emphasis is placed on the phenomenological formula relating the dissipation to the turbulence energy and the Rotta-type formula for the return to isotropy. Methods which deal directly with most or all the scales of motion explicitly are reviewed briefly. The statistical theory of turbulence is presented as an expansion about randomness. Two concepts are involved: (1) a modeling of the turbulence as nearly multipoint Gaussian, and (2) a simultaneous introduction of a generalized eddy viscosity operator.
Magnetosheath Turbulence at MHD Scales: A Statistical Study
Huang, Shiyong; Sahraoui, Fouad; Hadid, Lina; Yuan, Zhigang
2015-04-01
Turbulence is ubiquitous in space plasmas, such as terrestrial magnetotail and magnetosheath, solar wind, or the interstellar medium. In the solar wind, it is well established that at MHD scales, the magnetic energy spectra generally follow the so-called Kolmogorov's spectrum f-5/3. In the magnetosheath, Alexandrova et al. [2006] observed a Kolmogorov-like inertial range in the frequency range f < fci. In this study, we used three years data from the Cluster mission to statistically investigate the existence of the Kolmogorov inertial range in the whole magnetosheath, including flanks and subsolar regions. Statistical results show that most spectra are shallower than the Kolmogorov one, and have a scaling ~ f-1recalling the energy containing scales of solarwind turbulence. These spectra were found to be populated by uncorrelated fluctuations. The Kolmogorov scaling is observed only away from the bock shock and in the flanks region. These results suggest that random-like fluctuations are generated behind the shock, which reach a fully developed turbulence state only after some time corresponding to their propagation (or advection) away from the shock. At kinetic scales no dependence of the turbulence scaling on the location in the magnetosheath was found.
Non-ideal MHD turbulent decay in molecular clouds
Downes, T P
2009-01-01
It is well known that non-ideal magnetohydrodynamic effects are important in the dynamics of molecular clouds: both ambipolar diffusion and possibly the Hall effect have been identified as significant. We present the results of a suite of simulations with a resolution of 512-cubed of turbulent decay in molecular clouds incorporating a simplified form of both ambipolar diffusion and the Hall effect simultaneously. The initial velocity field in the turbulence is varied from being super-Alfv\\'enic and hypersonic, through to trans-Alfv\\'enic but still supersonic. We find that ambipolar diffusion increases the rate of decay of the turbulence increasing the decay from $t^{-1.25}$ to $t^{-1.4}$. The Hall effect has virtually no impact in this regard. The power spectra of density, velocity and the magnetic field are all affected by the non-ideal terms, being steepened significantly when compared with ideal MHD turbulence with exponents. The density power spectra components change from about 1.4 to about 2.1 for the i...
Damping of MHD turbulence in partially ionized plasma: implications for cosmic ray propagation
Xu, Siyao; Lazarian, A
2015-01-01
We study the damping from neutral-ion collisions of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium. We start from the linear analysis of MHD waves applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and cutoff boundary of linear MHD waves is investigated. Our analytical results are shown to be applicable in a variety of partially ionized interstellar medium (ISM) phases and solar chromosphere. As a significant astrophysical utility, we introduce damping effects to propagation of cosmic rays in partially ionized ISM. The important role of turbulence damping in both transit-time damping and gyroresonance is identified.
Toward the Theory of Turbulence in Magnetized Plasmas
Boldyrev, Stanislav [University of Wisconsin - Madison
2013-07-26
The goal of the project was to develop a theory of turbulence in magnetized plasmas at large scales, that is, scales larger than the characteristic plasma microscales (ion gyroscale, ion inertial scale, etc.). Collisions of counter-propagating Alfven packets govern the turbulent cascade of energy toward small scales. It has been established that such an energy cascade is intrinsically anisotropic, in that it predominantly supplies energy to the modes with mostly field-perpendicular wave numbers. The resulting energy spectrum of MHD turbulence, and the structure of the fluctuations were studied both analytically and numerically. A new parallel numerical code was developed for simulating reduced MHD equations driven by an external force. The numerical setting was proposed, where the spectral properties of the force could be varied in order to simulate either strong or weak turbulent regimes. It has been found both analytically and numerically that weak MHD turbulence spontaneously generates a “condensate”, that is, concentration of magnetic and kinetic energy at small k{sub {parallel}}. A related topic that was addressed in the project is turbulent dynamo action, that is, generation of magnetic field in a turbulent flow. We were specifically concentrated on the generation of large-scale magnetic field compared to the scales of the turbulent velocity field. We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model.
Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics
Klein, R I; Li, P S; McKee, C F; Fisher, R
2008-04-10
Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256{sup 3} and 512{sup 3} simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li et al. (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.
A heuristic model for MRI turbulent stresses in Hall MHD
Lingam, M
2016-01-01
Although the Shakura-Sunyaev $\\alpha$ viscosity prescription has been highly successful in characterizing myriad astrophysical environments, it has proven to be partly inadequate in modelling turbulent stresses driven by the MRI. Hence, we adopt the approach employed by \\citet{GIO03}, but in the context of Hall magnetohydrodynamics (MHD), to study MRI turbulence. We utilize the exact evolution equations for the stresses, and the non-linear terms are closed through the invocation of dimensional analysis and physical considerations. We demonstrate that the inclusion of the Hall term leads to non-trivial results, including the modification of the Reynolds and Maxwell stresses, as well as the (asymptotic) non-equipartition between the kinetic and magnetic energies; the latter issue is also addressed via the analysis of non-linear waves. The asymptotic ratio of the kinetic and magnetic energies is shown to be \\emph{independent} of the choice of initial conditions, but it is governed by the \\emph{Hall parameter}. W...
Impact of observational uncertainties on universal scaling of MHD turbulence
Gogoberidze, G; Hnat, B; Dunlop, M W
2011-01-01
Scaling exponents are the central quantitative prediction of theories of turbulence and in-situ satellite observations of the high Reynolds number solar wind flow have provided an extensive testbed of these. We propose a general, instrument independent method to estimate the uncertainty of velocity field fluctuations. We obtain the systematic shift that this uncertainty introduces into the observed spectral exponent. This shift is essential for the correct interpretation of observed scaling exponents. It is sufficient to explain the contradiction between spectral features of the Elsasser fields observed in the solar wind with both theoretical models and numerical simulations of Magnetohydrodynamic turbulence.
Hall MHD Stability and Turbulence in Magnetically Accelerated Plasmas
H. R. Strauss
2012-11-27
The object of the research was to develop theory and carry out simulations of the Z pinch and plasma opening switch (POS), and compare with experimental results. In the case of the Z pinch, there was experimental evidence of ion kinetic energy greatly in excess of the ion thermal energy. It was thought that this was perhaps due to fine scale turbulence. The simulations showed that the ion energy was predominantly laminar, not turbulent. Preliminary studies of a new Z pinch experiment with an axial magnetic field were carried out. The axial magnetic is relevant to magneto - inertial fusion. These studies indicate the axial magnetic field makes the Z pinch more turbulent. Results were also obtained on Hall magnetohydrodynamic instability of the POS.
A MHD-turbulence model for solar corona
Romeou, Z.; Velli, M.; Einaudi, G.
2009-02-01
The disposition of energy in the solar corona has always been a problem of great interest. It remains an open question how the low temperature photosphere supports the occurence of solar extreme phenomena. In this work, a turbulent heating mechanism for the solar corona through the framework of reduced magnetohydrodynamics (RMHD) is proposed. Two-dimensional incompressible long time simulations of the average energy disposition have been carried out with the aim to reveal the characteristics of the long time statistical behavior of a two-dimensional cross-section of a coronal loop and the importance of the photospheric time scales in the understanding of the underlying mechanisms. It was found that for a slow, shear type photospheric driving the magnetic field in the loop self-organizes at large scales via an inverse MHD cascade. The system undergoes three distinct evolutionary phases. The initial forcing conditions are quickly “forgotten” giving way to an inverse cascade accompanied with and ending up to electric current dissipation. Scaling laws are being proposed in order to quantify the nonlinearity of the system response which seems to become more impulsive for decreasing resistivity. It is also shown that few, if any, qualitative changes in the above results occur by increasing spatial resolution.
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Farge, Marie
2015-01-01
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.
Applications of continuous and orthogonal wavelet transforms to MHD and plasma turbulence
Farge, Marie; Schneider, Kai
2016-10-01
Wavelet analysis and compression tools are presented and different applications to study MHD and plasma turbulence are illustrated. We use the continuous and the orthogonal wavelet transform to develop several statistical diagnostics based on the wavelet coefficients. We show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising and describe multiscale numerical simulation schemes using wavelets. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented. Details can be found in M. Farge and K. Schneider. Wavelet transforms and their applications to MHD and plasma turbulence: A review. Support by the French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement (EFDA) is thankfully acknowledged.
Local 4/5-law and energy dissipation anomaly in turbulence of incompressible MHD Equations
Guo, Shanshan; Tan, Zhong
2016-12-01
In this paper, we establish the longitudinal and transverse local energy balance equation of distributional solutions of the incompressible three-dimensional MHD equations. In particular, we find that the functions D_L^ɛ (u,B) and D_T^ɛ (u,B) appeared in the energy balance, all converging to the defect distribution (in the sense of distributions) D(u,B) which has been defined in Gao et al. (Acta Math Sci 33:865-871, 2013). Furthermore, we give a simpler form of defect distribution term, which is similar to the relation in turbulence theory, called the "4 / 3-law." As a corollary, we give the analogous "4 / 5-law" holds in the local sense.
Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: I. Turbulence Statistics
Li, Pak Shing; Klein, Richard I; Fisher, Robert T
2008-01-01
Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectr...
Cascades and Spectra of Elastic Turbulence in 2D: Spinodal Decomposition & MHD
Fan, Xiang; Diamond, Patrick; Chacon, Luis
2016-10-01
We report on studies of turbulence in 2D spinodal decompositions of symmetric binary mixtures. This study emphasizes a comparison and contrast of the physics of spinodal turbulence with that of 2D MHD turbulence. The important similarities include basic equations, ideal quadratic conserved quantities, cascade directions and elastic waves. Turbulence in spinodal decomposition exhibits an elastic range when the Hinze scale is sufficiently larger than the dissipation scale, i.e. LH k (analogous to HkA ≡k in MHD) scales as k - 7 / 3. This suggests an inverse cascade of Hψ, corresponding to the case in MHD. However, we also show that, the kinetic energy spectrum scales as k-3, as in the direct enstrophy cascade range for a 2D fluid (not MHD!). The resolution of this dilemma is that capillarity acts only at blob boundaries. This is in contrast to B in MHD. Thus, as blob merger progresses, the packing fraction of interfaces decreases, thus explaining the outcome for the kinetic energy spectrum. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award Number DE-FG02-04ER54738.
New aspects of plasma sheet dynamics - MHD and kinetic theory
H. Wiechen
Full Text Available Magnetic reconnection is a process of fundamental importance for the dynamics of the Earth's plasma sheet. In this context, the development of thin current sheets in the near-Earth plasma sheet is a topic of special interest because they could be a possible cause of microscopic fluctuations acting as collective non-idealness from a macroscopic point of view. Simulations of the near-Earth plasma sheet including boundary perturbations due to localized inflow through the northern (or southern plasma sheet boundary show developing thin current sheets in the near-Earth plasma sheet about 810 R_{E} tailwards of the Earth. This location is largely independent from the localization of the perturbation. The second part of the paper deals with the problem of the macroscopic non-ideal consequences of microscopic fluctuations. A new model is presented that allows the quantitative calculation of macroscopic non-idealness without considering details of microscopic instabilities or turbulence. This model is only based on the assumption of a strongly fluctuating, mixing dynamics on microscopic scales in phase space. The result of this approach is an expression for anomalous non-idealness formally similar to the Krook resistivity but now describing the macroscopic consequences of collective microscopic fluctuations, not of collisions.
Key words. Magnetospheric physics (plasma sheet · Space plasma physics (kinetic and MHD theory; magnetic reconnection
Generalized Heisenberg theory of turbulence
Uberoi, M. S.; Narain, J. P.
1974-01-01
Solutions of the generalized theory are obtained which are consistent with the previous work on energy transfer measurements. They also agree with the measurements of turbulent energy spectrum for wave numbers in the universal equilibrium range.
Temporal and Spatial Turbulent Spectra of MHD Plasma and an Observation of Variance Anisotropy
Schaffner, D A; Lukin, V S
2014-01-01
The nature of MHD turbulence is analyzed through both temporal and spatial magnetic fluctuation spectra. A magnetically turbulent plasma is produced in the MHD wind-tunnel configuration of the Swarthmore Spheromak Experiment (SSX). The power of magnetic fluctuations is projected into directions perpendicular and parallel to a local mean field; the ratio of these quantities shows the presence of variance anisotropy which varies as a function of frequency. Comparison amongst magnetic, velocity, and density spectra are also made, demonstrating that the energy of the turbulence observed is primarily seeded by magnetic fields created during plasma production. Direct spatial spectra are constructed using multi-channel diagnostics and are used to compare to frequency spectra converted to spatial scales using the Taylor Hypothesis. Evidence for the observation of dissipation due to ion inertial length scale physics is also discussed as well as the role laboratory experiment can play in understanding turbulence typica...
Alexakis, A.
2009-04-01
Most astrophysical and planetary systems e.g., solar convection and stellar winds, are in a turbulent state and coupled to magnetic fields. Understanding and quantifying the statistical properties of magneto-hydro-dynamic (MHD) turbulence is crucial to explain the involved physical processes. Although the phenomenological theory of hydro-dynamic (HD) turbulence has been verified up to small corrections, a similar statement cannot be made for MHD turbulence. Since the phenomenological description of Hydrodynamic turbulence by Kolmogorov in 1941 there have been many attempts to derive a similar description for turbulence in conducting fluids (i.e Magneto-Hydrodynamic turbulence). However such a description is going to be based inevitably on strong assumptions (typically borrowed from hydrodynamics) that do not however necessarily apply to the MHD case. In this talk I will discuss some of the properties and differences of the energy and helicity cascades in turbulent MHD and HD flows. The investigation is going to be based on the analysis of direct numerical simulations. The cascades in MHD turbulence appear to be a more non-local process (in scale space) than in Hydrodynamics. Some implications of these results to turbulent modeling will be discussed
Turbulent thermal diffusion in strongly stratified turbulence: theory and experiments
Amir, G; Eidelman, A; Elperin, T; Kleeorin, N; Rogachevskii, I
2016-01-01
Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic ve...
Wave damping by MHD turbulence and its effect upon cosmic ray propagation in the ISM
Farmer, A J; Farmer, Alison J.; Goldreich, Peter
2004-01-01
Cosmic rays scatter off magnetic irregularities (Alfven waves) with which they are resonant, that is waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfven speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering efficiency of MHD turbulence is severely diminished by its anisotropy. We show that MHD turbulence has an indirect effect on cosmic ray propagation by acting as a damping mechanism for cosmic ray generated waves. The hot (``coronal'') phase of the interstellar medium is the best candidate location for cosmic ray confinement by scattering from self-generated waves. We relate the streaming velocity of cosmic rays to the rate of turbulent dissipation in this medium, for the case in which turbulent damping is the dominant damping mechanism. We conclude that cosmic rays with up to 10^2 GeV could not stream much faster than the ...
Enhanced MHD transport in astrophysical accretion flows: turbulence, winds and jets
Dobbie, Peter B; Bicknell, Geoffrey V; Salmeron, Raquel
2009-01-01
Astrophysical accretion is arguably the most prevalent physical process in the Universe; it occurs during the birth and death of individual stars and plays a pivotal role in the evolution of entire galaxies. Accretion onto a black hole, in particular, is also the most efficient mechanism known in nature, converting up to 40% of accreting rest mass energy into spectacular forms such as high-energy (X-ray and gamma-ray) emission and relativistic jets. Whilst magnetic fields are thought to be ultimately responsible for these phenomena, our understanding of the microphysics of MHD turbulence in accretion flows as well as large-scale MHD outflows remains far from complete. We present a new theoretical model for astrophysical disk accretion which considers enhanced vertical transport of momentum and energy by MHD winds and jets, as well as transport resulting from MHD turbulence. We also describe new global, 3D simulations that we are currently developing to investigate the extent to which non-ideal MHD effects may...
Nanoflares and MHD turbulence in coronal loops: a hybrid shell model.
Nigro, Giuseppina; Malara, Francesco; Carbone, Vincenzo; Veltri, Pierluigi
2004-05-14
A model to describe injection, due to footpoint motions, storage, and dissipation of MHD turbulence in coronal loops, is presented. The model is based on the use of the shell technique in the wave vector space applied to the set of reduced MHD equations. Numerical simulation showed that the energy injected is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions among these fluctuations give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. The statistical analysis performed on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics.
Exploring reconnection, current sheets, and dissipation in a laboratory MHD turbulence experiment
Schaffner, D. A.
2015-12-01
The Swarthmore Spheromak Experiment (SSX) can serve as a testbed for studying MHD turbulence in a controllable laboratory setting, and in particular, explore the phenomena of reconnection, current sheets and dissipation in MHD turbulence. Plasma with turbulently fluctuating magnetic and velocity fields can be generated using a plasma gun source and launched into a flux-conserving cylindrical tunnel. No background magnetic field is applied so internal fields are allowed to evolve dynamically. Point measurements of magnetic and velocity fluctuations yield broadband power-law spectra with a steepening breakpoint indicative of the onset of a dissipation scale. The frequency range at which this steepening occurs can be correlated to the ion inertial scale of the plasma, a length which is characteristic of the size of current sheets in MHD plasmas and suggests a connection to dissipation. Observation of non-Gaussian intermittent jumps in magnetic field magnitude and angle along with measurements of ion temperature bursts suggests the presence of current sheets embedded within the turbulent plasma, and possibly even active reconnection sites. Additionally, structure function analysis coupled with appeals to fractal scaling models support the hypothesis that current sheets are associated with dissipation in this system.
Intermittent heating of the solar corona by MHD turbulence
É. Buchlin
2007-10-01
Full Text Available As the dissipation mechanisms considered for the heating of the solar corona would be sufficiently efficient only in the presence of small scales, turbulence is thought to be a key player in the coronal heating processes: it allows indeed to transfer energy from the large scales to these small scales. While Direct numerical simulations which have been performed to investigate the properties of magnetohydrodynamic turbulence in the corona have provided interesting results, they are limited to small Reynolds numbers. We present here a model of coronal loop turbulence involving shell-models and Alfvén waves propagation, allowing the much faster computation of spectra and turbulence statistics at higher Reynolds numbers. We also present first results of the forward-modelling of spectroscopic observables in the UV.
Numerical Simulations of Driven Supersonic Relativistic MHD Turbulence
Zrake, Jonathan; 10.1063/1.3621748
2011-01-01
Models for GRB outflows invoke turbulence in relativistically hot magnetized fluids. In order to investigate these conditions we have performed high-resolution three-dimensional numerical simulations of relativistic magneto-hydrodynamical (RMHD) turbulence. We find that magnetic energy is amplified to several percent of the total energy density by turbulent twisting and folding of magnetic field lines. Values of epsilon_B near 1% are thus naturally expected. We study the dependence of saturated magnetic field energy fraction as a function of Mach number and relativistic temperature. We then present power spectra of the turbulent kinetic and magnetic energies. We also present solenoidal (curl-like) and dilatational (divergence-like) power spectra of kinetic energy. We propose that relativistic effects introduce novel couplings between these spectral components. The case we explore in most detail is for equal amounts of thermal and rest mass energy, corresponding to conditions after collisions of shells with re...
DNS of MHD turbulent flow via the HELIOS supercomputer system at IFERC-CSC
Satake, Shin-ichi; Kimura, Masato; Yoshimori, Hajime; Kunugi, Tomoaki; Takase, Kazuyuki
2014-06-01
The simulation plays an important role to estimate characteristics of cooling in a blanket for such high heating plasma in ITER-BA. An objective of this study is to perform large -scale direct numerical simulation (DNS) on heat transfer of magneto hydro dynamic (MHD) turbulent flow on coolant materials assumed from Flibe to lithium. The coolant flow conditions in ITER-BA are assumed to be Reynolds number and Hartmann number of a higher order. The maximum target of the DNS assumed by this study based on the result of the benchmark of Helios at IFERC-CSC for Project cycle 1 is 116 TB (2048 nodes). Moreover, we tested visualization by ParaView to visualize directly the large-scale computational result. If this large-scale DNS becomes possible, an essential understanding and modelling of a MHD turbulent flow and a design of nuclear fusion reactor contributes greatly.
SOLAR WIND TURBULENCE FROM MHD TO SUB-ION SCALES: HIGH-RESOLUTION HYBRID SIMULATIONS
Franci, Luca; Verdini, Andrea; Landi, Simone [Dipartimento di Fisica e Astronomia, Università di Firenze, Largo E. Fermi 2, I-50125 Firenze (Italy); Matteini, Lorenzo [Department of Physics, Imperial College London, London SW7 2AZ (United Kingdom); Hellinger, Petr [Astronomical Institute, AS CR, Bocni II/1401, CZ-14100 Prague (Czech Republic)
2015-05-10
We present results from a high-resolution and large-scale hybrid (fluid electrons and particle-in-cell protons) two-dimensional numerical simulation of decaying turbulence. Two distinct spectral regions (separated by a smooth break at proton scales) develop with clear power-law scaling, each one occupying about a decade in wavenumbers. The simulation results simultaneously exhibit several properties of the observed solar wind fluctuations: spectral indices of the magnetic, kinetic, and residual energy spectra in the magnetohydrodynamic (MHD) inertial range along with a flattening of the electric field spectrum, an increase in magnetic compressibility, and a strong coupling of the cascade with the density and the parallel component of the magnetic fluctuations at sub-proton scales. Our findings support the interpretation that in the solar wind, large-scale MHD fluctuations naturally evolve beyond proton scales into a turbulent regime that is governed by the generalized Ohm’s law.
Hadid, L.; Sahraoui, F.; Kiyani, K. H.; Retino, A.; Modolo, R.; Masters, A.; Dougherty, M.
2015-10-01
Low frequency turbulence in Saturn's magnetosheath is investigated using in-situ measurements of the Cassini spacecraft. We focus on the magnetic energy spectra computed in the frequency range # [10-4, 1]Hz. Three main results are reported: 1) The magnetic energy spectra showed a # f-1 scaling at MHD scales followed by an # f-2.6 scaling at the sub-ion scales without forming the so-called inertial range, breaking the universality of the Kolmogorov spectrum in the magnetosheath; 2) The magnetic compressibility and the cross-correlation between the parallel component of the magnetic field and density fluctuations C(#n, #B||) indicate the dominance of the compressible magnetosonic slow modes at MHD scales rather than the Alfvén mode [3] ; 3) Higher order statistics revealed a monofractal (resp. multifractal) behaviour of the turbulent flow behind a quasiperpendicular (resp. quasi-parallel) shock at the subion scales.
MAGNETOHYDRODYNAMIC WAVES AND CORONAL HEATING: UNIFYING EMPIRICAL AND MHD TURBULENCE MODELS
Sokolov, Igor V.; Van der Holst, Bart; Oran, Rona; Jin, Meng; Manchester, Ward B. IV; Gombosi, Tamas I. [Department of AOSS, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States); Downs, Cooper [Predictive Science Inc., 9990 Mesa Rim Road, Suite 170, San Diego, CA 92121 (United States); Roussev, Ilia I. [Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States); Evans, Rebekah M., E-mail: igorsok@umich.edu [NASA Goddard Space Flight Center, Space Weather Lab, 8800 Greenbelt Road, Greenbelt, MD 20771 (United States)
2013-02-10
We present a new global model of the solar corona, including the low corona, the transition region, and the top of the chromosphere. The realistic three-dimensional magnetic field is simulated using the data from the photospheric magnetic field measurements. The distinctive feature of the new model is incorporating MHD Alfven wave turbulence. We assume this turbulence and its nonlinear dissipation to be the only momentum and energy source for heating the coronal plasma and driving the solar wind. The difference between the turbulence dissipation efficiency in coronal holes and that in closed field regions is because the nonlinear cascade rate degrades in strongly anisotropic (imbalanced) turbulence in coronal holes (no inward propagating wave), thus resulting in colder coronal holes, from which the fast solar wind originates. The detailed presentation of the theoretical model is illustrated with the synthetic images for multi-wavelength EUV emission compared with the observations from SDO AIA and STEREO EUVI instruments for the Carrington rotation 2107.
JOINT INVERSE CASCADE OF MAGNETIC ENERGY AND MAGNETIC HELICITY IN MHD TURBULENCE
Stepanov, R.; Frick, P.; Mizeva, I. [Institute of Continuous Media Mechanics, Korolyov str. 1, 614013 Perm (Russian Federation)
2015-01-10
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number MHD turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy is related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to –3/2. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.
Turbulence introduction to theory and applications of turbulent flows
Westerweel, Jerry; Nieuwstadt, Frans T M
2016-01-01
This book provides a general introduction to the topic of turbulent flows. Apart from classical topics in turbulence, attention is also paid to modern topics. After studying this work, the reader will have the basic knowledge to follow current topics on turbulence in scientific literature. The theory is illustrated with a number of examples of applications, such as closure models, numerical simulations and turbulent diffusion, and experimental findings. The work also contains a number of illustrative exercises.
From Weakly to Strongly Magnetized Isotropic MHD Turbulence
Alexakis, Alexandros
2012-01-01
High Reynolds number isotropic magneto-hydro-dynamic turbulence in the presence of large scale magnetic fields is investigated as a function of the magnetic field strength. For a variety of flow configurations the energy dissipation rate \\epsilon, follows the Kolmogorov scaling \\epsilon ~ U^3/L even when the large scale magnetic field energy is twenty times larger than the kinetic. Further increase of the magnetic energy showed a transition to the \\epsilon ~ U^2 B / L scaling implying that magnetic shear becomes more efficient at this point at cascading the energy than the velocity fluctuations. Strongly helical configurations form helicity condensates that deviate from these scalings. Weak turbulence scaling was absent from the investigation. Finally, the magnetic energy spectra showed support for the Kolmogorov spectrum k^{-5/3} while kinetic energy spectra are closer to the Iroshnikov-Kraichnan spectrum k^{-3/2}.
MHD turbulence, cloud formation and star formation in the ISM
Vázquez-Semadeni, E; Pouquet, A
1996-01-01
We discuss the role of turbulence in cloud and star formation, as observed in numerical simulations of the interstellar medium. Turbulent compression at the interfaces of colliding gas streams is responsible for the formation of intermediate (\\simlt 100 pc) and small clouds (a few tens of pc), although the smallest clouds can also form from fragmentation of expanding shells around stellar heating centers. The largest cloud complexes (several hundred pc) seem to form by slow, gravitational instability-driven merging of individual clouds, which can actually be described as a large-scale tendency towards homogenization of the flow due to gravity rather than cloud collisions. These mechanisms operate as well in the presence of a magnetic field and rotation, although slight variations on the compressibility and cloud morphology are present which depend on the strength and topology of the field. In summary, the role of turbulence in the life-cycle of clouds appears to be twofold: small-scale modes contribute to clo...
Extended MHD Turbulence and Its Applications to the Solar Wind
Abdelhamid, Hamdi M.; Lingam, Manasvi; Mahajan, Swadesh M.
2016-10-01
Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfvénic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal (k\\lt 1/{λ }i), Hall (1/{λ }i\\lt k\\lt 1/{λ }e), and electron inertia (k\\gt 1/{λ }e) regimes; k is the wavenumber and {λ }s=c/{ω }{ps} is the skin depth of species “s.” In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of -11/3 and -13/3 are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approximately -4 in this regime. It is thus plausible that these spectra may constitute a part of the (extended) inertial range, as opposed to the standard “dissipation” range paradigm.
Extended MHD turbulence and its applications to the solar wind
Abdelhamid, Hamdi M; Mahajan, Swadesh M
2016-01-01
Extended MHD is a one-fluid model that incorporates two-fluid effects such as electron inertia and the Hall drift. This model is used to construct fully nonlinear Alfv\\'enic wave solutions, and thereby derive the kinetic and magnetic spectra by resorting to a Kolmogorov-like hypothesis based on the constant cascading rates of the energy and generalized helicities of this model. The magnetic and kinetic spectra are derived in the ideal $\\left(k 1/\\lambda_e\\right)$ regimes; $k$ is the wavenumber and $\\lambda_s = c/\\omega_{p s}$ is the skin depth of species `$s$'. In the Hall regime, it is shown that the emergent results are fully consistent with previous numerical and analytical studies, especially in the context of the solar wind. The focus is primarily on the electron inertia regime, where magnetic energy spectra with power-law indexes of $-11/3$ and $-13/3$ are always recovered. The latter, in particular, is quite close to recent observational evidence from the solar wind with a potential slope of approxima...
Modeling Statistical Properties of Solar Active Regions through DNS of 3D-MHD Turbulence
Malapaka, Shiva Kumar
2013-01-01
Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($\\zeta_p$) of the order of the structure functions ($\\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper we compare some of the observations from Abramenko et al (2003) with the log-Poisson model (Biskamp 2003) used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustain...
Large-scale Magnetic Structure Formation in 3D-MHD Turbulence
Malapaka, Shiva Kumar
2013-01-01
The inverse cascade of magnetic helicity in 3D-MHD turbulence is believed to be one of the processes responsible for large scale magnetic structure formation in astrophysical systems. In this work we present an exhaustive set of high resolution direct numerical simulations (DNS) of both forced and decaying 3D-MHD turbulence, to understand this structure formation process. It is first shown that an inverse cascade of magnetic helicity in small-scale driven turbulence does not necessarily generate coherent large-scale magnetic structures. The observed large-scale magnetic field, in this case, is severely perturbed by magnetic fluctuations generated by the small-scale forcing. In the decaying case, coherent large-scale structure form similar to those observed astronomically. Based on the numerical results the formation of large-scale magnetic structures in some astrophysical systems, is suggested to be the consequence of an initial forcing which imparts the necessary turbulent energy into the system, which, afte...
Nature of the MHD and Kinetic Scale Turbulence in the Magnetosheath of Saturn: Cassini Observations
Hadid, L. Z.; Sahraoui, F.; Kiyani, K. H.; Retinò, A.; Modolo, R.; Canu, P.; Masters, A.; Dougherty, M. K.
2015-11-01
Low-frequency turbulence in Saturn’s magnetosheath is investigated using in situ measurements of the Cassini spacecraft. Focus is put on the magnetic energy spectra computed in the frequency range of ˜[10-4, 1]Hz. A set of 42 time intervals in the magnetosheath were analyzed, and three main results that contrast with known features of solar wind turbulence are reported. (1) The magnetic energy spectra showed a ˜f-1 scaling at MHD scales followed by an ˜ {f}-2.6 scaling at sub-ion scales without forming the so-called inertial range. (2) The magnetic compressibility and the cross-correlation between the parallel component of the magnetic field and density fluctuations C(δ n,δ {B}| | ) indicate the dominance of the compressible magnetosonic slow-like modes at MHD scales rather than the Alfvén mode. (3) Higher-order statistics revealed a monofractal (multifractal) behavior of the turbulent flow downstream of a quasi-perpendicular (quasi-parallel) shock at sub-ion scales. Implications of these results on theoretical modeling of space plasma turbulence are discussed.
The Efficiency of Second-Order Fermi Acceleration by Weakly Compressible MHD Turbulence
Lynn, Jacob W; Chandran, Benjamin D G; Parrish, Ian J
2013-01-01
We investigate the effects of pitch-angle scattering on the efficiency of particle heating and acceleration by MHD turbulence using phenomenological estimates and simulations of non-relativistic test particles interacting with strong, subsonic MHD turbulence. We include an imposed pitch-angle scattering rate, which is meant to approximate the effects of high frequency plasma waves and/or velocity space instabilities. We focus on plasma parameters similar to those found in the near-Earth solar wind, though most of our results are more broadly applicable. An important control parameter is the size of the particle mean free path lambda_{mfp} relative to the scale of the turbulent fluctuations L. For small scattering rates, particles interact quasi-resonantly with turbulent fluctuations in magnetic field strength. Scattering increases the long-term efficiency of this resonant heating by factors of a few-10, but the distribution function does not develop a significant non-thermal power-law tail. For higher scatter...
Formation of Rotational Discontinuities in Compressive three-dimensional MHD Turbulence
Yang, Liping; He, Jiansen; Tu, Chuanyi; Wang, Linghua; Marsch, Eckart; Wang, Xin; Zhang, Shaohua; Feng, Xueshang
2015-01-01
Measurements of solar wind turbulence reveal the ubiquity of discontinuities. In this study, we investigate how the discontinuities, especially rotational discontinuities (RDs), are formed in magnetohydrodynamic (MHD) turbulence. In a simulation of the decaying compressive three-dimensional (3-D) MHD turbulence with an imposed uniform background magnetic field, we detect RDs with sharp field rotations and little variations of magnetic field intensity as well as mass density. At the same time, in the de Hoffman-Teller (HT) frame, the plasma velocity is nearly in agreement with the Alfv\\'{e}n speed, and is field-aligned on both sides of the discontinuity. We take one of the identified RDs to analyze in details its 3-D structure and temporal evolution. By checking the magnetic field and plasma parameters, we find that the identified RD evolves from the steepening of the Alfv\\'{e}n wave with moderate amplitude, and that steepening is caused by the nonuniformity of the Alfv\\'{e}n speed in the ambient turbulence.
Evidence for Decay of Turbulence by MHD Shocks in Molecular Clouds via CO Emission
Larson, Rebecca L; Green, Joel D; Yang, Yao-Lun
2015-01-01
We utilize observations of sub-millimeter rotational transitions of CO from a Herschel Cycle 2 open time program ("COPS", PI: J. Green) to identify previously predicted turbulent dissipation by magnetohydrodynamic (MHD) shocks in molecular clouds. We find evidence of the shocks expected for dissipation of MHD turbulence in material not associated with any protostar. Two models fit about equally well: model 1 has a density of 10$^{3}$ cm$^{-3}$, a shock velocity of 3 km s$^{-1}$, and a magnetic field strength of 4 ${\\mu}$G; model 2 has a density of 10$^{3.5}$ cm$^{-3}$, a shock velocity of $2$ km s$^{-1}$, and a magnetic field strength of 8 $\\mu$G. Timescales for decay of turbulence in this region are comparable to crossing times. Transitions of CO up to $J$ of 8, observed close to active sites of star formation, but not within outflows, can trace turbulent dissipation of shocks stirred by formation processes. Although the transitions are difficult to detect at individual positions, our Herschel-SPIRE survey o...
On soft stability loss in rotating turbulent MHD flows
Kapusta, Arkady [Center for MHD Studies, Ben-Gurion University of the Negev PO Box 653, Beer-Sheva 84105 (Israel); Mikhailovich, Boris, E-mail: borismic@bgu.ac.il [Department of Mechanical Engineering, Ben-Gurion University of the Negev PO Box 653, Beer-Sheva 84105 (Israel)
2014-08-01
The problem of the stability of turbulent flows of liquid metal in a cylindrical cavity against small velocity disturbances under the action of a rotating magnetic field (RMF) has been studied. The flow is considered in the induction-free approximation using the ‘external’ friction model. A system of dimensionless equations is examined in cylindrical coordinates. The results of computations performed on the basis of this mathematical model using the exchange of stabilities principle have shown a good consistency between the critical values of computed and experimental Reynolds numbers. (paper)
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
Observational Diagnostics of Self-Gravitating MHD Turbulence in Giant Molecular Clouds
Burkhart, Blakesley; Lazarian, Alex
2015-01-01
We study the observable signatures of self-gravitating MHD turbulence by applying the probability density functions (PDFs) and the spatial density power spectrum to synthetic column density maps. We find that there exists three characterizable stages of the evolution of the collapsing cloud which we term "early," "intermediate," and "advanced." At early times, i.e. $t0.35t_{ff}$, the power spectral slope is positive valued, and a dramatic increase is observed in the PDF moments and the Tsallis incremental PDF parameters, which gives rise to deviations between PDF-sonic Mach number relations. Finally, we show that the imprint of gravity on the density power spectrum can be replicated in non-gravitating turbulence by introducing a delta-function with amplitude equivalent to the maximum valued point in a given self-gravitating map. We find that the turbulence power spectrum restored through spatial filtering of the high density material.
Kitiashvili, I N; Goode, P R; Kosovichev, A G; Lele, S K; Mansour, N N; Wray, A A; Yurchyshyn, V B
2012-01-01
Turbulent properties of the quiet Sun represent the basic state of surface conditions, and a background for various processes of solar activity. Therefore understanding of properties and dynamics of this `basic' state is important for investigation of more complex phenomena, formation and development of observed phenomena in the photosphere and atmosphere. For characterization of the turbulent properties we compare kinetic energy spectra on granular and sub-granular scales obtained from infrared TiO observations with the New Solar Telescope (Big Bear Solar Observatory) and from 3D radiative MHD numerical simulations ('SolarBox' code). We find that the numerical simulations require a high spatial resolution with 10 - 25 km grid-step in order to reproduce the inertial (Kolmogorov) turbulence range. The observational data require an averaging procedure to remove noise and potential instrumental artifacts. The resulting kinetic energy spectra show a good agreement between the simulations and observations, opening...
Mikel' son, Yu.Ya.; Yakovich, A.T.; Pavlov, S.I.
1978-01-01
Turbulent stresses are considered in an incompressible fluid due to MHD flow induced within an axisymmetric region by electromagnetic forces on the basis of the linearized equation of motion as well as on the basis of the stress tensor in terms of average velocities and turbulent viscosity. The turbulent viscosity is treated according to the Boussinesq hypothesis (constant turbulent viscosity), according to the generalized Karman hypothesis (turbulent viscosity a function of the derivatives of the velocity components with respect to the respective coordinates), or as the product of its coordinate functions. The results of numerical calculations indicate a close agreement between all these formulas for an average MHD flow and experimental data. Calculations including this additional turbulent force, appropriately related to the flow parameters, are applicable to the design of liquid-metal devices. 7 references, 3 figures.
Nature of the MHD and kinetic scale turbulence in the magnetosheath of Saturn: Cassini observations
Hadid, L Z; Kiyani, K H; Retinò, A; Modolo, R; Canu, P; Masters, A; Dougherty, M K
2016-01-01
Low frequency turbulence in Saturn's magnetosheath is investigated using in-situ measurements of the Cassini spacecraft. Focus is put on the magnetic energy spectra computed in the frequency range $\\sim[10^{-4}, 1]$Hz. A set of 42 time intervals in the magnetosheath were analyzed and three main results that contrast with known features of solar wind turbulence are reported: 1) The magnetic energy spectra showed a $\\sim f^{-1}$ scaling at MHD scales followed by an $\\sim f^{-2.6}$ scaling at the sub-ion scales without forming the so-called inertial range; 2) The magnetic compressibility and the cross-correlation between the parallel component of the magnetic field and density fluctuations $ C(\\delta n,\\delta B_{||}) $ indicates the dominance of the compressible magnetosonic slow-like modes at MHD scales rather than the Alfv\\'en mode; 3) Higher order statistics revealed a monofractal (resp. multifractal) behaviour of the turbulent flow downstream of a quasi-perpendicular (resp. quasi-parallel) shock at the sub-i...
Kinetic cascade beyond MHD of solar wind turbulence in two-dimensional hybrid simulations
Verscharen, Daniel; Motschmann, Uwe; Müller, Joachim
2012-01-01
The nature of solar wind turbulence in the dissipation range at scales much smaller than the large MHD scales remains under debate. Here a two-dimensional model based on the hybrid code abbreviated as A.I.K.E.F. is presented, which treats massive ions as particles obeying the kinetic Vlasov equation and massless electrons as a neutralizing fluid. Up to a certain wavenumber in the MHD regime, the numerical system is initialized by assuming a superposition of isotropic Alfv\\'en waves with amplitudes that follow the empirically confirmed spectral law of Kolmogorov. Then turbulence develops and energy cascades into the dispersive spectral range, where also dissipative effects occur. Under typical solar wind conditions, weak turbulence develops as a superposition of normal modes in the kinetic regime. Spectral analysis in the direction parallel to the background magnetic field reveals a cascade of left-handed Alfv\\'en/ion-cyclotron waves up to wave vectors where their resonant absorption sets in, as well as a cont...
Reproducing the Solar Wind proton temperature profile via DNS of MHD turbulence
Montagud-Camps, Victor; Grappin, Roland; Verdini, Andrea
2017-04-01
Context: The Solar Wind proton temperature Tp shows a radial profile R-0.9 significantly shallower than the adiabatic R-4/3 profile [Totten et al 1996]. This temperature profile has been attributed to turbulent heating, which requires a dissipation rate equal to Q = 3.610-5TpU/R[J/(kg s)] (1) [Vasquez et al 2007]. The possibility of a turbulent heating large enough to modify the radial profile of the temperature has not been verified yet via direct numerical simulations. Aim: We want to test if MHD turbulence developing in the range [0.2,1] AU is able to reproduce the observed R-0.9 temperature profile. Method: We use the expanding box model (EBM) [Grappin & Velli 1996] which incorporates the effects of expansion into the compressible MHD equations, and so allows to follow the evolution of the plasma advected by the solar wind between 0.2 and 1 AU. In the absence of turbulence, the R-4/3 temperature profile is obtained. We start at 0.2 AU with mean field almost aligned with the radial and k⊥-1 spectrum perpendicular to the mean field [Verdini, Grappin 2016]. Simple phenomenology (Kolmogorov) suggests that the ratio between turbulent heating and the required heating (1) is close to M2/ɛ, where M is the Mach number of the large eddies and ɛ is the nonlinear time normalized by the transport time of the plasma by the wind. We thus explore the (M,ɛ) parameter space and examine whether a large enough value of M2/ɛ indeed allows to recover the temperature profile observed by Totten et al (1996). Results: We have obtained significant slowing down of the adiabatic cooling by considering increasing Mach numbers and/or decreasing ɛ and approach in some cases the R-0.9 temperature profile. The role of the compressibility in the cascade is examined.
The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description
Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.
2017-09-01
The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar
Large- and small-scale turbulent spectra in MHD and atmospheric flows
O. G. Chkhetiani
2006-01-01
Full Text Available In the present review we discuss certain studies of large- and small-scale turbulent spectra in MHD and atmospheric flows performed by S. S. Moiseev and his co-authors during the last years of his life and continued by his co-authors after he passed away. It is shown that many ideas developed in these works have not lost their novelty and urgency until now, and can form the basis of future studies in this field.
Global MHD Modelling of the ISM - From large towards small scale turbulence
D'Avillez, M A; Avillez, Miguel A. de; Breitschwerdt, Dieter
2005-01-01
Dealing numerically with the turbulent nature and non-linearity of the physical processes involved in the ISM requires the use of sophisticated numerical schemes coupled to HD and MHD mathematical models. SNe are the main drivers of the interstellar turbulence by transferring kinetic energy into the system. This energy is dissipated by shocks (which is more efficient) and by molecular viscosity. We carried out adaptive mesh refinement simulations (with a finest resolution of 0.625 pc) of the turbulent ISM embedded in a magnetic field with mean field components of 2 and 3 $\\mu$G. The time scale of our run was 400 Myr, sufficiently long to avoid memory effects of the initial setup, and to allow for a global dynamical equilibrium to be reached in case of a constant energy input rate. It is found that the longitudinal and transverse turbulent length scales have a time averaged (over a period of 50 Myr) ratio of 0.52-0.6, almost similar to the one expected for isotropic homogeneous turbulence. The mean characteris...
The flux tube paradigm and its role in MHD turbulence in the solar atmosphere
Matthaeus, W. H.; Greco, A.; Servidio, S.; Wan, M.; Osman, K.; Ruffolo, D. J.
2011-12-01
Descriptions of magnetic field and plasma structures in terms of flux tubes, plasmoids and other bundles of magnetic field lines are familiar in the vocabulary of observational and theoretical space physics. "Spaghetti models" and flux ropes are well known examples. Flux tubes and families of field lines can also be defined in a medium that admits magnetic fluctuations, including strong MHD turbulence, but their behavior can become complicated. In 3D fluctuations the smooth flux tube description itself becomes in some sense unstable, as nearby field lines diverge and flux surfaces shred. This lends complexity to the structure of flux tubes, and can give rise to temporarily trapped field lines and charged test particle trajectories, with immediate implications for transport, e.g., of solar energetic particles. The properties of the turbulent magnetic field can also be strongly influenced by the dynamics of turbulence. Large scale self organizing behavior, or inverse cascade, can enhance very long wavelength structure, favoring Bohm scaling of diffusion coefficients. Meanwhile smaller scale flux tube structures are integral features of the inertial range of turbulence, giving rise to a cellularization of the plasma due to rapid dynamical relaxation processes. These drive the turbulent system locally towards low-acceleration states, including Alfvenic, Beltrami and force-free states. Cell boundaries are natural positions for formation of near discontinuous boundaries, where dynamical activity can be enhanced. A primary example is appearance of numerous discontinuities and active reconnection sites in turbulence, which appear to support a wide distribution of reconnection rates associated with coherent current structures. These discontinuities are also potential sites of enhanced heating, as expected in Kolmogorov's Refined Similarity Hypothesis. All of these features are related to self organization, cascade and intermittency of the turbulence. Examples of these
Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence
Abedian, B.; Hyers, R. W.; Curreri, Peter A. (Technical Monitor)
2002-01-01
When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying
Mathematical and physical theory of turbulence
Cannon, John
2006-01-01
Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...
Coexistence of weak and strong wave turbulence in incompressible Hall MHD
Meyrand, Romain; Kiyani, Khurom; Galtier, Sebastien
2016-04-01
We report a numerical investigation of 3D Hall Magnetohydrodynamic turbulence with a strong mean magnetic field. By using a helicity decomposition and a cross-bicoherence analysis, we observe that the nonlinear 3-wave coupling is substantial among ion cyclotron and whistler waves. By studying in detail the degree of nonlinearity of these two populations we show that ion cyclotron and whistler turbulent fluctuations belong respectively to strong and weak wave turbulence. The non trivial blending of these two regime give rise to anomalous anisotropy and scaling properties. The separation of the weak random wave and strong coherent turbulence component can however be effectively done using simultaneous space and time Fourier transforms. Using this techniques we show that it is possible to recover some statistical prediction of weak turbulent theory.
Fromang, S; Terquem, C; De Villiers, J P; Fromang, Sebastien; Balbus, Steven A.; Terquem, Caroline; Villiers, Jean-Pierre De
2004-01-01
We present 3D magnetohydrodynamic (MHD) numerical simulations of the evolution of self--gravitating and weakly magnetized disks with an adiabatic equation of state. Such disks are subject to the development of both the magnetorotational and gravitational instabilities, which transport angular momentum outward. As in previous studies, our hydrodynamical simulations show the growth of strong m=2 spiral structure. This spiral disturbance drives matter toward the central object and disappears when the Toomre parameter Q has increased well above unity. When a weak magnetic field is present as well, the magnetorotational instability grows and leads to turbulence. In that case, the strength of the gravitational stress tensor is lowered by a factor of about~2 compared to the hydrodynamical run and oscillates periodically, reaching very small values at its minimum. We attribute this behavior to the presence of a second spiral mode with higher pattern speed than the one which dominates in the hydrodynamical simulations...
Malapaka, Shiva Kumar; Mueller, Wolf-Christian [Max-Planck Institute for Plasma Physics, Boltzmannstrasse 2, D-85748 Garching bei Muenchen (Germany)
2013-09-01
Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the active regions (ARs), have been studied using the line-of-sight data from magnetograms taken by the Solar and Heliospheric Observatory and several other instruments. This includes structure functions and their exponents, flatness curves, and correlation functions. In these works, the dependence of structure function exponents ({zeta}{sub p}) of the order of the structure functions (p) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper, we compare some of the observations from Abramenko et al. with the log-Poisson model used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying, and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of {zeta}{sub p} against p of ARs. We also reproduce the trends and changes observed in intermittency in flatness and correlation functions of ARs. It is suggested from this analysis that an AR in the onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase are related to the time taken by the system to reach the initial onset phase.
Why, how and when electrically driven flows and MHD turbulence become three-dimensional
Pothérat, A
2013-01-01
The dimensionality of electrically driven flows and magnetohydrodynamic (MHD) turbulence at low Magnetic Reynolds number is analysed by driving a square array of vortices of alternate spin in a cubic vessel filled with liquid metal, placed in a high homogeneous, static magnetic field $\\mathbf B$. A wide range of steady and unsteady flows is generated by varying the intensity $I$ of the DC current injected to drive them, and their dimensionality is influenced by increasing or decreasing the magnetic field intensity. It is shown theoretically, and then experimentally that three-dimensionality is characterised by scaling laws linking the core velocity $U_b$ near the wall where current is injected to the current intensity $I$, of either forms $U_b\\sim I$ or $U_b\\sim I^{2/3}$, depending on whether three-dimensionality originates from viscous or inertial effects. In turbulent flows. The opposite wall is found to be either active or passive depending whether the ratio of its distance to the bottom wall $h$ to the le...
Turbulent magnetic Prandtl numbers obtained with MHD Taylor-Couette flow experiments
Gellert, M
2008-01-01
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\\_in = B\\_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The...
Zieger, B.; Opher, M.; Toth, G.
2016-12-01
Recently we demonstrated that our three-fluid MHD model of the solar wind plasma (where cold thermal solar wind ions, hot pickup ions, and electrons are treated as separate fluids) is able to reconstruct the microstructure of the termination shock observed by Voyager 2 [Zieger et al., 2015]. We constrained the unknown pickup ion abundance and temperature and confirmed the presence of a hot electron population at the termination shock, which has been predicted by a number of previous theoretical studies [e.g. Chasei and Fahr, 2014; Fahr et al., 2014]. We showed that a significant part of the upstream hydrodynamic energy is transferred to the heating of pickup ions and "massless" electrons. As shown in Zieger et al., [2015], three-fluid MHD theory predicts two fast magnetosonic modes, a low-frequency fast mode or solar wind ion (SW) mode and a high-frequency fast mode or pickup ion (PUI) mode. The coupling of the two ion populations results in a quasi-stationary nonlinear mode or oscilliton, which appears as a trailing wave train downstream of the termination shock. In single-fluid plasma, dispersive effects appear on the scale of the Debye length. However, in a non-equilibrium plasma like the solar wind, where solar wind ions and PUIs have different temperatures, dispersive effects become important on fluid scales [see Zieger et al., 2015]. Here we show that the dispersive effects of fast magnetosonic waves are expected on the scale of astronomical units (AU), and dispersion plays an important role producing compressional turbulence in the heliosheath. The trailing wave train of the termination shock (the SW-mode oscilliton) does not extend to infinity. Downstream propagating PUI-mode waves grow until they steepen into PUI shocklets and overturn starting to propagate backward. The upstream propagating PUI-mode waves result in fast magnetosonic turbulence and limit the downstream extension of the oscilliton. The overturning distance of the PUI-mode, where these waves
Reuter, K.; Jenko, F.; Forest, C. B.; Bayliss, R. A.
2008-08-01
A parallel implementation of a nonlinear pseudo-spectral MHD code for the simulation of turbulent dynamos in spherical geometry is reported. It employs a dual domain decomposition technique in both real and spectral space. It is shown that this method shows nearly ideal scaling going up to 128 CPUs on Beowulf-type clusters with fast interconnect. Furthermore, the potential of exploiting single precision arithmetic on standard x86 processors is examined. It is pointed out that the MHD code thereby achieves a maximum speedup of 1.7, whereas the validity of the computations is still granted. The combination of both measures will allow for the direct numerical simulation of highly turbulent cases ( 1500
Theory of strong turbulence by renormalization
Tchen, C. M.
1981-01-01
The hydrodynamical equations of turbulent motions are inhomogeneous and nonlinear in their inertia and force terms and will generate a hierarchy. A kinetic method was developed to transform the hydrodynamic equations into a master equation governing the velocity distribution, as a function of the time, the position and the velocity as an independent variable. The master equation presents the advantage of being homogeneous and having fewer nonlinear terms and is therefore simpler for the investigation of closure. After the closure by means of a cascade scaling procedure, the kinetic equation is derived and possesses a memory which represents the nonMarkovian character of turbulence. The kinetic equation is transformed back to the hydrodynamical form to yield an energy balance in the cascade form. Normal and anomalous transports are analyzed. The theory is described for incompressible, compressible and plasma turbulence. Applications of the method to problems relating to sound generation and the propagation of light in a nonfrozen turbulence are considered.
LEE; ChunHian
2010-01-01
Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.
Turbulent Boundary Layers - Experiments, Theory and Modelling
1980-01-01
DEVELOPMENT (ORGANISATION DU TRAITE DE L’ATLANTIQUE NORD ) AGARD Conference Proceedings No.271 TURBULENT BOUNDARY LAYERS - EXPERIMENTS, THEORY AND...photographs of Figures 21 and 22. In this case, the photographs are taken with a single flash strobe and thus yield the instantaneous positions of the
On the scaling features of magnetic field fluctuations at non-MHD scales in turbulent space plasmas
Consolini, G.; Giannattasio, F.; Yordanova, E.; Vörös, Z.; Marcucci, M. F.; Echim, M.; Chang, T.
2016-11-01
In several different contexts space plasmas display intermittent turbulence at magneto-hydro-dynamic (MHD) scales, which manifests in anomalous scaling features of the structure functions of the magnetic field increments. Moving to smaller scales, i.e. below the ion-cyclotron and/or ion inertial length, these scaling features are still observed, even though its is not clear if these scaling features are still anomalous or not. Here, we investigate the nature of scaling properties of magnetic field increments at non-MHD scales for a period of fast solar wind to investigate the occurrence or not of multifractal features and collapsing of probability distribution functions (PDFs) using the novel Rank-Ordered Multifractal Analysis (ROMA) method, which is more sensitive than the traditional structure function approach. We find a strong evidence for the occurrence of a near mono-scaling behavior, which suggests that the observed turbulent regime at non-MHD scales mainly displays a mono-fractal nature of magnetic field increments. The results are discussed in terms of a non-compact fractal structure of the dissipation field.
Pratt, J; Müller, W -C; Chapman, S C; Watkins, N W
2016-01-01
We investigate the utility of the convex hull to analyze physical questions related to the dispersion of a group of much more than four Lagrangian tracer particles in a turbulent flow. Validation of standard dispersion behaviors is a necessary preliminary step for use of the convex hull to describe turbulent flows. In simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection we show that the convex hull can be used to reasonably capture the dispersive behavior of a large group of tracer particles. We validate dispersion results produced with convex hull analysis against scalings for Lagrangian particle pair dispersion. In addition to this basic validation study, we show that convex hull analysis provides information that particle pair dispersion does not, in the form of a extreme value statistics, surface area, and volume for a cluster of particles. We use the convex hull surface area and volume to examine the degree of...
Li, Pak Shing; Klein, Richard I. [Astronomy Department, University of California, Berkeley, CA 94720 (United States); Martin, Daniel F. [Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720 (United States); McKee, Christopher F., E-mail: psli@astron.berkeley.edu, E-mail: klein@astron.berkeley.edu, E-mail: DFMartin@lbl.gov, E-mail: cmckee@astro.berkeley.edu [Physics Department and Astronomy Department, University of California, Berkeley, CA 94720 (United States)
2012-02-01
Performing a stable, long-duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and constrained transport electromotive force averaging schemes that can meet this challenge, and using this strategy, we have developed a new adaptive mesh refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma {beta}{sub 0} of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers (M{sub rms}= 17.3) and smaller plasma beta ({beta}{sub 0} = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
Seismic Halos Around Active Regions: An MHD Theory
Hanasoge, Shravan M
2007-01-01
Comprehending the manner in which magnetic fields affect propagating waves is a first step toward the helioseismic construction of accurate models of active region sub-surface structure and dynamics. Here, we present a numerical method to compute the linear interaction of waves with magnetic fields embedded in a solar-like stratified background. The ideal Magneto-Hydrodynamic (MHD) equations are solved in a 3-dimensional box that straddles the solar photosphere, extending from 35 Mm within to 1.2 Mm into the atmosphere. One of the challenges in performing these simulations involves generating a Magneto-Hydro-Static (MHS) state wherein the stratification assumes horizontal inhomogeneity in addition to the strong vertical stratification associated with the near-surface layers. Keeping in mind that the aim of this effort is to understand and characterize linear MHD interactions, we discuss a means of computing statically consistent background states. Results from a simulation of waves interacting with a flux tub...
Statistical theory of turbulent incompressible multimaterial flow
Kashiwa, B.
1987-10-01
Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of kappa-epsilon modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy kappa, and the rate of fluctuational energy dissipation epsilon, for each material. Hence a set of kappa and epsilon equations must be solved, together with mean mass and momentum conservation equations, for each material. Both kappa and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a
Grete, P; Schmidt, W; Schleicher, D R G
2016-01-01
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics (MHD). We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number $\\mathrm{M_s} = 0.2$ to $20$ as reference data for the most extensive \\textit{a priori} tests performed so far in literature. In these tests we explicitly filter the reference data and compare the performance of the new closures against th...
Zhang, Weiqun; Wang, Peng
2008-01-01
Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to $\\epsilon_B \\sim 5 \\times 10^{-3}$. This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization b...
Turbulent Equipartition Theory of Toroidal Momentum Pinch
T.S. Hahm, P.H. Diamond, O.D. Gurcan, and G. Rewaldt
2008-01-31
The mode-independet part of magnetic curvature driven turbulent convective (TuroCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14,072302 (2007)] which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of "magnetically weighted angular momentum density," nmi U|| R/B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustratd that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms which exist in a simpler geometry.
Turbulent equipartition theory of toroidal momentum pincha)
Hahm, T. S.; Diamond, P. H.; Gurcan, O. D.; Rewoldt, G.
2008-05-01
The mode-independent part of the magnetic curvature driven turbulent convective (TurCo) pinch of the angular momentum density [Hahm et al., Phys. Plasmas 14, 072302 (2007)], which was originally derived from the gyrokinetic equation, can be interpreted in terms of the turbulent equipartition (TEP) theory. It is shown that the previous results can be obtained from the local conservation of "magnetically weighted angular momentum density," nmiU∥R/B2, and its homogenization due to turbulent flows. It is also demonstrated that the magnetic curvature modification of the parallel acceleration in the nonlinear gyrokinetic equation in the laboratory frame, which was shown to be responsible for the TEP part of the TurCo pinch of angular momentum density in the previous work, is closely related to the Coriolis drift coupling to the perturbed electric field. In addition, the origin of the diffusive flux in the rotating frame is highlighted. Finally, it is illustrated that there should be a difference in scalings between the momentum pinch originated from inherently toroidal effects and that coming from other mechanisms that exist in a simpler geometry.
Federrath, Christoph; Schleicher, Dominik R G; Banerjee, Robi; Klessen, Ralf S
2011-01-01
Cosmic structure formation is characterized by the complex interplay between gravity, turbulence, and magnetic fields. The processes by which gravitational energy is converted into turbulent and magnetic energies, however, remain poorly understood. Here, we show with high-resolution, adaptive-mesh simulations that MHD turbulence is efficiently driven by extracting energy from the gravitational potential during the collapse of a dense gas cloud. Compressible motions generated during the contraction are converted into solenoidal, turbulent motions, leading to a natural energy ratio of E_sol/E_tot of approximately 2/3. We find that the energy injection scale of gravity-driven turbulence is close to the local Jeans scale. If small seeds of the magnetic field are present, they are amplified exponentially fast via the small-scale dynamo process. The magnetic field grows most efficiently on the smallest scales, for which the stretching, twisting, and folding of field lines, and the turbulent vortices are sufficientl...
3D MHD simulation of post--flare supra--arcade downflows in a turbulent current sheet medium
Cécere, M; Costa, A; Schneiter, M
2014-01-01
Supra--arcade downflows (SADs) are sunward, generally dark, plasma density depletions originated above posteruption flare arcades. In this paper using 3D MHD simulations we investigate if the SAD cavities can be produced by a direct combination of the tearing mode and Kelvin--Helmholtz instabilities leading to a turbulent current sheet (CS) medium or if the current sheet is merely the background where SADs are produced triggered by an impulsive deposition of energy. We find that to give account of the observational dark lane structures an addition of local energy provided by a reconnection event is required. This local reconnection can trigger a nonlinear internal wave dynamic, generated by the bouncing and interfering of shocks and expansion waves that compose relatively stable voids.
An introduction to the theory of plasma turbulence
Tsytovich, V N
1972-01-01
An Introduction to the Theory of Plasma Turbulence is a collection of lectures given by the author at Culham laboratory. The book deals with developments on the theory of plasma turbulence. The author describes plasma properties in the turbulent regions as mostly non-linear in nature, and notes that these properties can be regarded as a universal spectrum independent of any type of instability. The text then discusses the general problems of the theory of plasma turbulence. The author also shows that elementary excitation of """"dressed"""" particles have a finite lifetime associated with non
MHD flow in a cylindrical vessel of finite size with turbulent boundary layers
Gorbachev, L.P.; Nikitin, N.V.
1979-01-01
The hydrodynamic characteristics of flows generated by electromagnetic forces in a cylindrical vessel of finite size, for the case of large values of the hydrodynamic and small values of the magnetic Reynolds numbers have been inadequately analyzed in previous literature, since neither the nonlinear nor the linear theory adequately accounts for secondary flows due to the strong action of boundary layers formed at the end faces of the cylinders at large Reynolds numbers and the results do not agree with experimental data. This paper generalizes the previously more accurate nonlinear scheme of the same authors, the basis for which was the fact that viscosity at large Reynolds numbers is manifest only close to solid surfaces. Two cases are treated: crossed fields and a rotating magnetic field in the cylindrical vessel, where the entire flow region is broken down into an inviscid core and end face boundary layers. It is assumed that the velocity distribution near the end surfaces obeys an empirical one-seventh power law, which is applicable to turbulent liquid flow in a tube in a range of Re = 3 x 10/sup 3/ to 10/sup 5/ simple engineering formulas are derived for the angular velocity, which exhibit good agreement with the experimental data for Hartmann numbers less than 10. The procedure can be generalized to the case of a rotating magnetic field having several pairs of poles. 6 references, 2 figures.
Li, Pak Shing; Klein, Richard I; McKee, Christopher F
2011-01-01
Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $\\beta_0$ of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$) and smaller plasma beta ($\\beta_0 = 0.0067$) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulati...
Yamamoto, Yoshinobu, E-mail: yamamotoy@yamanashi.ac.jp [Division of Mechanical Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu 400-8511 (Japan); Kunugi, Tomoaki, E-mail: kunugi@nucleng.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, C3-d2S06, Kyoto-Daigaku Katsura, Nishikyo-Ku 615-8540, Kyoto (Japan)
2016-11-01
Highlights: • We show the applicability to predict the heat transfer imposed on a uniform wall-normal magnetic field by means of the zero-equation heat transfer model. • Quasi-theoretical turbulent Prandtl numbers with various molecular Prandtl number fluids were obtained. • Improvements of the prediction accuracy in turbulent kinetic energy and turbulent dissipation rate under the magnetic fields were accomplished. - Abstract: Zero-equation heat transfer models based on the constant turbulent Prandtl number are evaluated using direct numerical simulation (DNS) data for fully developed channel flows imposed on a uniform wall-normal magnetic field. Quasi-theoretical turbulent Prandtl numbers are estimated by DNS data of various molecular Prandtl number fluids. From the viewpoint of highly-accurate magneto-hydrodynamic (MHD) heat transfer prediction, the parameters of the turbulent eddy viscosity of the k–É› model are optimized under the magnetic fields. Consequently, we use the zero-equation model based on a constant turbulent Prandtl number to demonstrate MHD heat transfer, and show the applicability of using this model to predict the heat transfer.
MHD-kinetic transition in imbalanced Alfv$\\'{e}$nic turbulence
Voitenko, Yuriy
2016-01-01
Alfvenic turbulence in space is usually imbalanced: amplitudes of waves propagating parallel and anti-parallel to the mean magnetic field $B_0$ are unequal. It is commonly accepted that the turbulence is driven by (counter-) collisions between these counter-propagating wave fractions. Contrary to this, we found a new ion-scale dynamical range of the turbulence established by (co-) collisions among waves co-propagating in the same direction along $B_0$. The turbulent cascade is accelerated there and power spectra are steep and non-universal. The spectral indexes vary around -3 (-4) in the strong (weak) turbulence, such that steeper spectra follow larger imbalances. Intermittency steepens spectra further, up to -3.7 (-4.5). Our theoretical predictions are compatible with steep variable spectra observed in the solar wind at ion kinetic scales.
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
Brachet, M E; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D
2012-01-01
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144^3 points, and three different ones on grids of 4096^3 points. We find that at the highest resolution, two different current and vorticity sheet systems collide, producing two successive accelerations in the development of small scales with, at the latest time, a convergence of magnetic field lines to the location of maximum current, probably leading locally to a strong bending and directional variability of such lines.
del Valle, M V; Kowal, G
2016-01-01
Fast magnetic reconnection may occur in different astrophysical sources, producing flare-like emission and particle acceleration. Currently, this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process. In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical (MHD) domains with large-scale current sheets where reconnection is made fast by the presence of turbulence. We study the dependence of the particle acceleration time with the relevant parameters of the embedded turbulence, i.e., the Alfv\\'en speed $V_{\\rm A}$, the injection power $P_{\\rm inj}$ and scale $k_{\\rm inj}$ ($k_{\\rm inj} = 1/l_{\\rm inj}$). We find that the acceleration time follows a power-law dependence with the particle kinetic energy: $t_{acc} \\propto E^{\\alpha}$, with $0.2 < \\alpha < 0.6$ for a vast range of values of $c / V_{\\rm A} \\sim 20 - 1000$. The acceleration time decreases with the Alfv\\'en...
Turbulence spreading in gyro-kinetic theory
Migliano, P.; Buchholz, R.; Grosshauser, S. R.; Hornsby, W. A.; Peeters, A. G.; Stauffert, O.
2016-01-01
In this letter a new operative definition for the turbulence intensity in connection with magnetized plasmas is given. In contrast to previous definitions the new definition satisfies a Fisher-Kolmogorov-Petrovskii-Piskunov type equation. Furthermore, explicit expressions for the turbulence intensity and the turbulence intensity flux, that allow for the first time direct numerical evaluation, are derived. A carefully designed numerical experiment for the case of a tokamak is performed to study the impact of turbulence spreading. The effective turbulence diffusion coefficient is measured to be smaller than the heat conduction coefficient and the turbulence spreading length is found to be of the order of the turbulence correlation length. The results show that turbulence spreading can play a role in the non-local flux gradient relation, or in the scaling of transport coefficients with the normalized Larmor radius, only over lengths scale of the order of the turbulence correlation length. A new turbulence convection mechanism, due to the drift connected with the magnetic field inhomogeneities, is described. The convective flux integrates to zero under the flux surface average unless there is an up-down asymmetry in the tubulence intensity. The latter asymmetry can be generated through a radial inhomogeneity or plasma rotation. It is shown that the turbulence convection can lead to a spreading of the order of the correlation length.
On the statistical theory of turbulence
Heisenberg, W
1958-01-01
A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.
Kinetic theory and turbulent discontinuities. [shock tube flow
Johnson, J. A., III; I, L.; Li, Y.; Ramaian, R.; Santigo, J. P.
1981-01-01
Shock tube discontinuities were used to test and extend a kinetic theory of turbulence. In shock wave and contact surface fluctuations, coherent phenomena were found which provide new support for the microscopic nonempirical approach to turbulent systems, especially those with boundary layer-like instabilities.
Laminar and Turbulent Dynamos in Chiral Magnetohydrodynamics. I. Theory
Rogachevskii, Igor; Ruchayskiy, Oleg; Boyarsky, Alexey; Fröhlich, Jürg; Kleeorin, Nathan; Brandenburg, Axel; Schober, Jennifer
2017-09-01
The magnetohydrodynamic (MHD) description of plasmas with relativistic particles necessarily includes an additional new field, the chiral chemical potential associated with the axial charge (i.e., the number difference between right- and left-handed relativistic fermions). This chiral chemical potential gives rise to a contribution to the electric current density of the plasma (chiral magnetic effect). We present a self-consistent treatment of the chiral MHD equations, which include the back-reaction of the magnetic field on a chiral chemical potential and its interaction with the plasma velocity field. A number of novel phenomena are exhibited. First, we show that the chiral magnetic effect decreases the frequency of the Alfvén wave for incompressible flows, increases the frequencies of the Alfvén wave and of the fast magnetosonic wave for compressible flows, and decreases the frequency of the slow magnetosonic wave. Second, we show that, in addition to the well-known laminar chiral dynamo effect, which is not related to fluid motions, there is a dynamo caused by the joint action of velocity shear and chiral magnetic effect. In the presence of turbulence with vanishing mean kinetic helicity, the derived mean-field chiral MHD equations describe turbulent large-scale dynamos caused by the chiral alpha effect, which is dominant for large fluid and magnetic Reynolds numbers. The chiral alpha effect is due to an interaction of the chiral magnetic effect and fluctuations of the small-scale current produced by tangling magnetic fluctuations (which are generated by tangling of the large-scale magnetic field by sheared velocity fluctuations). These dynamo effects may have interesting consequences in the dynamics of the early universe, neutron stars, and the quark–gluon plasma.
A 3D MHD simulation of SN 1006: a polarized emission study for the turbulent case
Velázquez, P. F.; Schneiter, E. M.; Reynoso, E. M.; Esquivel, A.; De Colle, F.; Toledo-Roy, J. C.; Gómez, D. O.; Sieyra, M. V.; Moranchel-Basurto, A.
2017-01-01
Three dimensional magnetohydrodynamical simulations were carried out in order to perform a new polarization study of the radio emission of the supernova remnant SN 1006. These simulations consider that the remnant expands into a turbulent interstellar medium (including both magnetic field and figuredensity perturbations). Based on the referenced-polar angle technique, a statistical study was done on observational and numerical magnetic field position-angle distributions. Our results show that a turbulent medium with an adiabatic index of 1.3 can reproduce the polarization properties of the SN 1006 remnant. This statistical study reveals itself as a useful tool for obtaining the orientation of the ambient magnetic field, previous to be swept up by the main supernova remnant shock.
Zhai, X. M.; Yeung, P. K.
2016-11-01
Turbulence in an electrically conducting fluid in the limit of low magnetic Reynolds number is, because of the Lorentz force due to an external magnetic field, very different from classical turbulence at both the large scales and the small scales. The importance of minimizing finite domain-size effects on the large scale development has often tended to limit the Reynolds number reached in the past. In this work we use periodic domains stretched along the magnetic field with aspect ratio up to 8 and beyond. The initial state is obtained from decaying isotropic turbulence with large-eddy length scales of order 1% of the length of the domain. After a transient period the kinetic energy returns to a power law decay while the integral length scales in the direction parallel to the magnetic field show preferential growth. At early times the parallel velocity component becomes stronger than the other two but this anisotropy is subsequently reversed under the combined effects of anisotropic Joule dissipation and viscous dissipation. The small scales show characteristics of quasi two-dimensional behavior in the transverse plane. Results over a range of magnetic interaction parameters and Reynolds numbers are compared with known theoretical predictions. Supported by NSF Grant CBET-1510749 and supercomputer resources at TACC/XSEDE and ALCF.
Turbulence and dynamo interlinks
de Gouveia Dal Pino, E. M.; Santos-Lima, R.; Kowal, G.; Falceta-Gonçalves, D.
2013-07-01
The role of turbulence in astrophysical environments and its interplay with magnetic fields is still highly debated. In this lecture, we will discuss this issue in the framework of dynamo processes. We will first present a very brief summary of turbulent dynamo theories, then will focus on small scale turbulent dynamos and their particular relevance on the origin and maintenance of magnetic fields in the intra-cluster media (ICM) of galaxies. In these environments, the very low density of the flow requires a collisionless-MHD treatment. We will show the implications of this approach in the turbulent amplification of the magnetic fields in these environments. To finalize, we will also briefly address the connection between MHD turbulence and fast magnetic reconnection and its possible implications in the diffusion of magnetic flux in the dynamo process.
Turbulence and Dynamo Interlinks
Pino, E M de Gouveia Dal
2013-01-01
The role of turbulence in astrophysical environments and its interplay with magnetic fields is still highly debated. In this lecture, we will discuss this issue in the framework of dynamo processes. We will first present a very brief summary of turbulent dynamo theories, then will focus on small scale turbulent dynamos and their particular relevance on the origin and maintenance of magnetic fields in the intra-cluster media (ICM) of galaxies. In these environments, the very low density of the flow requires a collisionless-MHD treatment. We will show the implications of this approach in the turbulent amplification of the magnetic fields in these environments. To finalize, we will also briefly address the connection between MHD turbulence and fast magnetic reconnection and its possible implications in the diffusion of magnetic flux in the dynamo process.
Ade, P A R; Alves, M I R; Aniano, G; Armitage-Caplan, C; Arnaud, M; Arzoumanian, D; Ashdown, M; Atrio-Barandela, F; Aumont, J; Baccigalupi, C; Banday, A J; Barreiro, R B; Battaner, E; Benabed, K; Benoit-Lévy, A; Bernard, J -P; Bersanelli, M; Bielewicz, P; Bond, J R; Borrill, J; Bouchet, F R; Boulanger, F; Bracco, A; Burigana, C; Cardoso, J -F; Catalano, A; Chamballu, A; Chiang, H C; Christensen, P R; Colombi, S; Colombo, L P L; Combet, C; Couchot, F; Coulais, A; Crill, B P; Curto, A; Cuttaia, F; Danese, L; Davies, R D; Davis, R J; de Bernardis, P; de Rosa, A; de Zotti, G; Delabrouille, J; Dickinson, C; Diego, J M; Donzelli, S; Doré, O; Douspis, M; Dupac, X; Enßlin, T A; Eriksen, H K; Falgarone, E; Fanciullo, L; Ferrière, K; Finelli, F; Forni, O; Frailis, M; Fraisse, A A; Franceschi, E; Galeotta, S; Ganga, K; Ghosh, T; Giard, M; Giraud-Héraud, Y; González-Nuevo, J; Górski, K M; Gregorio, A; Gruppuso, A; Guillet, V; Hansen, F K; Harrison, D L; Helou, G; Hernández-Monteagudo, C; Hildebrandt, S R; Hivon, E; Hobson, M; Holmes, W A; Hornstrup, A; Huffenberger, K M; Jaffe, A H; Jaffe, T R; Jones, W C; Juvela, M; Keihänen, E; Keskitalo, R; Kisner, T S; Kneissl, R; Knoche, J; Kunz, M; Kurki-Suonio, H; Lagache, G; Lamarre, J -M; Lasenby, A; Lawrence, C R; Leonardi, R; Levrier, F; Liguori, M; Lilje, P B; Linden-Vørnle, M; López-Caniego, M; Lubin, P M; Macías-Pérez, J F; Maino, D; Mandolesi, N; Maris, M; Marshall, D J; Martin, P G; Martínez-González, E; Masi, S; Matarrese, S; Mazzotta, P; Melchiorri, A; Mendes, L; Mennella, A; Migliaccio, M; Miville-Deschênes, M -A; Moneti, A; Montier, L; Morgante, G; Mortlock, D; Munshi, D; Murphy, J A; Naselsky, P; Nati, F; Natoli, P; Netterfield, C B; Noviello, F; Novikov, D; Novikov, I; Oxborrow, C A; Pagano, L; Pajot, F; Paoletti, D; Pasian, F; Pelkonen, V -M; Perdereau, O; Perotto, L; Perrotta, F; Piacentini, F; Piat, M; Pietrobon, D; Plaszczynski, S; Pointecouteau, E; Polenta, G; Popa, L; Pratt, G W; Prunet, S; Puget, J -L; Rachen, J P; Reinecke, M; Remazeilles, M; Renault, C; Ricciardi, S; Riller, T; Ristorcelli, I; Rocha, G; Rosset, C; Roudier, G; Rusholme, B; Sandri, M; Scott, D; Soler, J D; Spencer, L D; Stolyarov, V; Stompor, R; Sudiwala, R; Sutton, D; Suur-Uski, A -S; Sygnet, J -F; Tauber, J A; Terenzi, L; Toffolatti, L; Tomasi, M; Tristram, M; Tucci, M; Umana, G; Valenziano, L; Valiviita, J; Van Tent, B; Vielva, P; Villa, F; Wade, L A; Wandelt, B D; Zonca, A
2014-01-01
Polarized emission observed by Planck HFI at 353 GHz towards a sample of nearby fields is presented, focusing on the statistics of polarization fractions $p$ and angles $\\psi$. The polarization fractions and column densities in these nearby fields are representative of the range of values obtained over the whole sky. We find that: (i) the largest polarization fractions are reached in the most diffuse fields; (ii) the maximum polarization fraction $p_\\mathrm{max}$ decreases with column density $N_\\mathrm{H}$ in the more opaque fields with $N_\\mathrm{H} > 10^{21}\\,\\mathrm{cm}^{-2}$; and (iii) the polarization fraction along a given line of sight is correlated with the local spatial coherence of the polarization angle. These observations are compared to polarized emission maps computed in simulations of anisotropic magnetohydrodynamical (MHD) turbulence in which we assume a uniform intrinsic polarization fraction of the dust grains. We find that an estimate of this parameter may be recovered from the maximum pol...
Three-dimensional fluid and electrodynamic modeling for MHD DCW channels
Liu, B. L.; Lineberry, J. T.; Schmidt, H. J.
1983-01-01
A three dimensional, numerical solution for modeling diagonal conducting wall (DCW) magnetohydrodynamic (MHD) generators is developed and discussed. Cross plane gasdynamic and electrodynamic profiles are computed considering coupled MHD flow and electrical phenomena. A turbulent transport model based on the mixing length theory is used to deal with wall roughness generated turbulence effects. The infinitely fine electrode segmentation formulation is applied to simplify the governing electrical equations. Calculations show the development of distorted temperature and velocity profiles under influence of magnetohydrodynamic interaction. Since both sidewall and electrode wall boundary losses are treated, the results furnish a realistic representation of MHD generator behavior.
Some unsteady turbulent MHD flows in flat channels and circular pipes
Nemirovskiy, Yu.V.; Kheynloo, Ya.L.
1979-04-01
An analysis is made of the kinematic characteristics of turbulent pulsating flow of an electrically conductive fluid in a flat channnel and in a circular pipe in longitudinal and azimuthal magnetic fields. It is assumed that walls are impermeable, and that all averaged flow characteristics depend only on the transverse coordinate in accordance with the equation of continuity (the medium is taken as incompressible) and equations of motion of electrically conductive media. Disregarding the Hall effect, a system of equations is derived for the averaged velocity components and the motion of the medium. The calculations are based on a semiempirical method developed by the authors. The theoretical results agree satisfactorily with experimental data. 4 references, 2 figures.
Resonance broadening modification of weak plasma turbulence theory
Hanssen, A. (Max-Planck-Inst. fuer Aeronomie, Katlenburg-Lindau (West Germany))
1991-02-01
The author examines the effects on energy spectra of weak Langmuir turbulence when he includes a nonlinear damping due to the perturbation of electron orbits. The physical mechanism under consideration is usually known as a resonance broadening effect. The calculations show that the inclusion of this additional damping reduces the number of cascades predicted from weak turbulence theory for waves detectable with the EISCAT UHF (933 MHz) radar in Tromso, Norway, during RF modification of the ionospheric plasma.
Magnetohydrodynamics turbulence: An astronomical perspective
S Sridhar
2011-07-01
Early work on magnetohydrodynamic (MHD) turbulence in the 1960s due, independently, to Iroshnikov and Kraichnan (IK) considered isotropic inertial-range spectra. Whereas laboratory experiments were not in a position to measure the spectral index, they showed that the turbulence was strongly anisotropic. Theoretical horizons correspondingly expanded in the 1980s, to accommodate both the isotropy of the IK theory and the anisotropy suggested by the experiments. Since the discovery of pulsars in 1967, many years of work on interstellar scintillation suggested that small-scale interstellar turbulence must have a hydromagnetic origin; but the IK spectrum was too ﬂat and the ideas on anisotropic spectra too qualitative to explain the observations. In response, new theories of balanced MHD turbulence were proposed in the 1990s, which argued that the IK theory was incorrect, and made quantitative predictions of anisotropic inertial-range spectra; these theories have since found applications in many areas of astrophysics. Spacecraft measurements of solar-wind turbulence show that there is more power in Alfvén waves that travel away from the Sun than towards it. Theories of imbalanced MHD turbulence have now been proposed to address interplanetary turbulence. This very active area of research continues to be driven by astronomy.
Fractal tracer distributions in turbulent field theories
Hansen, J. Lundbek; Bohr, Tomas
1998-01-01
We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and t...
Numerical investigation of the turbulent MHD flow in a circular pipe with transverse magnetic field
Dechamps, Xavier; Rasquin, Michel; Degrez, Gérard
2012-11-01
In modern industrial metallurgical processes, external magnetic fields are often applied to control the motion of liquid metals by a non-intrusive means. The desired results are for example the damping of unwanted motions or the homogenization of a liquid zone in a partially solidified ingot. Because of the commonly appearing parameters in these processes, one can assume the quasi-static assumption for the magnetohydrodynamic equations. Here we are interested in the numerical study of the turbulent flow of a liquid metal inside an electrically insulated pipe with a transverse uniform magnetic field. For this purpose, we will use a hybrid spectral/finite element solver, which allows to study complex flows in Cartesian and axisymmetric geometries. For the case of interest, we consider a bulk Reynolds number of 8200 and a Hartmann number ranging between 5 and 30. Here, the main points of interest are the evolution of the skin friction coefficient as a function of the ratio of the Hartmann number Ha over the Reynolds number Re (with 0 FNRS) is aknowledged.
The theory of gyrokinetic turbulence: A multiple-scales approach
Plunk, Gabriel G
2009-01-01
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of magnetically confined fusion devices. The second project presents gyrokinetic secondary instability theory as a mechanism to bring about saturation of the basic instabilities that drive gyrokinetic turbulence. Emphasis is put on the ability for this analytic theory to predict basic properties of the nonlinear state, which can be applied to a mixing length phenomenology of transport. The final project is an application of the methods from inertial range understanding of fluid turbulence, to describe the stationary state of fully developed two-dimensional ...
New Theories on Boundary Layer Transition and Turbulence Formation
Chaoqun Liu
2012-01-01
Full Text Available This paper is a short review of our recent DNS work on physics of late boundary layer transition and turbulence. Based on our DNS observation, we propose a new theory on boundary layer transition, which has five steps, that is, receptivity, linear instability, large vortex structure formation, small length scale generation, loss of symmetry and randomization to turbulence. For turbulence generation and sustenance, the classical theory, described with Richardson's energy cascade and Kolmogorov length scale, is not observed by our DNS. We proposed a new theory on turbulence generation that all small length scales are generated by “shear layer instability” through multiple level ejections and sweeps and consequent multiple level positive and negative spikes, but not by “vortex breakdown.” We believe “shear layer instability” is the “mother of turbulence.” The energy transferring from large vortices to small vortices is carried out by multiple level sweeps, but does not follow Kolmogorov's theory that large vortices pass energy to small ones through vortex stretch and breakdown. The loss of symmetry starts from the second level ring cycle in the middle of the flow field and spreads to the bottom of the boundary layer and then the whole flow field.
Mikhailovskii, A.B.; Sharapov, S.E.; Timofeev, A.V. [JET Joint Undertaking, Abingdon, Oxfordshire OX14 3EA (United Kingdom)
2000-07-01
The theory of MHD modes driven by strong ExB velocity shear in tokamaks given by Mikhailovskii and Sharapov (2000 Plasma Phys. Control. Fusion 42 57) is revised. It is suggested that, in the approximations taken by these authors, there are no MHD eigenmodes if the cross-field velocity shear is larger then the Alfven frequency shear. (author)
A unified theory for wall turbulence via a symmetry approach
She, Zhen-Su; Chen, Xi; Hussain, Fazle
2014-11-01
First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) remains a great challenge from both physics and engineering standpoints. Physically, a non-equilibrium physical principle governing mean properties in turbulent flows is yet unknown. Here, we outline a recently developed symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. In analogy to the order parameter in Landau's (1937) mean-field theory, we develop a concept of order functions which are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - allowing us to construct a set of new invariant solutions of the (unclosed) mean momentum equation (MME). The theory is validated by recent experimental and numerical data, and identifies a universal bulk flow constant 0.45 for all three canonical wall-bounded flows, which asymptotes to the true Karman constant at large Reynolds numbers. The theory equally applies to the quantification of the effects of roughness (She et al. 2012), pressure gradient, compressibility, and buoyancy, and to the study of Reynolds-averaged Navier-Stokes (RANS) models, such as k- ωmodel, with significant improvement of the prediction accuracy. These results affirm that a simple and unified theory of wall-bounded turbulence is viable with appropriate symmetry considerations.
Wu, C.; Chang, T.
2010-12-01
A new method in describing the multifractal characteristics of intermittent events was introduced by Cheng and Wu [Chang T. and Wu C.C., Physical Rev, E77, 045401(R), 2008]. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has been demonstrated using results obtained from a 2D MHD simulation. It has also been successfully applied to in-situ solar wind observations [Chang T., Wu, C.C. and Podesta, J., AIP Conf Proc. 1039, 75, 2008], and the broadband electric field oscillations from the auroral zone [Tam, S.W.Y. et al., Physical Rev, E81, 036414, 2010]. We take the next step in this procedure. By using the ROMA spectra and the scaled probability distribution functions (PDFs), raw PDFs can be calculated, which can be compared directly with PDFs from observations or simulation results. In addition to 2D MHD simulation results and in-situ solar wind observation, we show clearly using the ROMA analysis the multifractal character of the 3D fluid simulation data obtained from the JHU turbulence database cluster at http://turbulence.pha.jhu.edu. In particular, we show the scaling of the non-symmetrical PDF for the parallel-velocity fluctuations of this 3D fluid data.
Simard, C; Dube, C
2016-01-01
We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos et al. 2014. The turbulent electromotive force operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation's meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. 2011, we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed alpha-tensor shows good agreement with that obtained by Racine et al. 2011, who did not include derivatives of the mean-field in their fit, as well as with the alpha-tensor extracted by Augustson et al. 2015 from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor beta is positive definite and reaches values of 5.0x10^7 m2s-1 in t...
The role of MHD turbulence in magnetic self-excitation: A study of the Madison Dynamo Experiment
Nornberg, Mark D.
2006-07-01
Determining the onset conditions for magnetic field growth in magnetohydrodynamics is fundamental to understanding how astrophysical dynamos such as the Earth, the Sun, and the galaxy self-generate magnetic fields. The Madison Dynamo Experiment was constructed to explore the role of turbulence in changing these onset conditions for an impeller-driven flow of liquid sodium. The flow generates intermittent magnetic bursts with the spatial structure predicted from kinematic dynamo theory. A model of the mean flow was constructed from laser Doppler velocimetry measurements of the flow in an identical-scale water experiment. A kinematic eigenvalue code predicted that the flow would generate a predominantly dipolar magnetic field perpendicular to the symmetry axis for sufficiently high impeller speeds. The flow amplifies the magnetic field by stretching field lines. The field lines are then twisted back onto themselves creating a feedback loop for dynamo growth. The same flow was generated in the sodium experiment and was found to amplify an applied magnetic field oriented perpendicular to the drive shaft axis of the experiment. The amplification increased with motor rotation rate as the induced field became more closely aligned with the applied field, though a reduction in the amplitude is attributed to an enhanced resistivity due to turbulent diffusion. The turbulence was characterized by measurements of the velocity and magnetic power spectra. The velocity spectra have a Kolmogorov scaling. The wavenumber at which resistive dissipation range becomes dominant was observed to increase with flow speed indicating that smaller scale magnetic structures were generated. No amplification due to a small-scale dynamo was observed. The intermittent bursts were analyzed using conditional averaging. The growth rate was found to increase linearly with impeller rotation rate resulting in stronger bursts. The average duration decreased so that the bursts continued to satisfy Poisson
Consistent theory of turbulent transport in two-dimensional magnetohydrodynamics.
Kim, Eun-jin
2006-03-03
A theory of turbulent transport is presented in two-dimensional magnetohydrodynamics with background shear and magnetic fields. We provide theoretical predictions for the transport of magnetic flux, momentum, and particles and turbulent intensities, which show stronger reduction compared with the hydrodynamic case, with different dependences on shearing rate, magnetic field, and values of viscosity, Ohmic diffusion, and particle diffusivity. In particular, particle transport is more severely suppressed than momentum transport, effectively leading to a more efficient momentum transport. The role of magnetic fields in quenching transport without altering the amplitude of flow velocity and in inhibiting the generation of shear flows is elucidated. Implications of the results are discussed.
Large deviation theory for coin tossing and turbulence.
Chakraborty, Sagar; Saha, Arnab; Bhattacharjee, Jayanta K
2009-11-01
Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency in fluid turbulence, where large deviations dominate. Our contention is: in the large deviation theory, the central role is played by the distribution associated with the tossing of a coin and the simple coin toss is the "Gaussian model" of problems where rare events play significant role. We illustrate this by applying it to calculate the multifractal exponents of the order structure factors in fully developed turbulence.
Simard, Corinne; Charbonneau, Paul; Dubé, Caroline
2016-10-01
We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation's meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α -tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α -tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0 ×107 m2 s-1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α - and β -quenching. We find the magnetic quenching of the α -effect to be driven primarily by a reduction of the small-scale flow's kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃ 1.36, than of the α -effect, which in our simulation drops by a factor of three between
The theory of gyrokinetic turbulence: A multiple-scales approach
Plunk, Gabriel G.
2009-01-01
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of magnetically confined fusion devi...
The Application of Statistical Turbulence Theory to Convective Instabilities.
1986-11-01
1985]. Here, we shall discuss the applications of statistical turbulence theory to determine the quasi-steady-state spectral density function (SDF...follow Sudan’s prescription for deriving the form of one- dimensional spectral - density function . The main difference is that we have attempted to relax...the conservation property of the basic equations is ’V preserved in the DIA or WCA equations for the spectral density function itself. This property is
The theory of gyrokinetic turbulence: A multiple-scales approach
Plunk, Gabriel Galad
Gyrokinetics is a rich and rewarding playground to study some of the mysteries of modern physics -- such as turbulence, universality, self-organization and dynamic criticality -- which are found in physical systems that are driven far from thermodynamic equilibrium. One such system is of particular importance, as it is central in the development of fusion energy -- this system is the turbulent plasma found in magnetically confined fusion device. In this thesis I present work, motivated by the quest for fusion energy, which seeks to uncover some of the inner workings of turbulence in magnetized plasmas. I present three projects, based on the work of me and my collaborators, which take a tour of different aspects and approaches to the gyrokinetic turbulence problem. I begin with the fundamental theory of gyrokinetics, and a novel formulation of its extension to the equations for mean-scale transport -- the equations which must be solved to determine the performance of Magnetically confined fusion devices. The results of this work include (1) the equations of evolution for the mean scale (equilibrium) density, temperature and magnetic field of the plasma, (2) a detailed Poynting's theorem for the energy balance and (3) the entropy balance equations. The second project presents gyrokinetic secondary instability theory as a mechanism to bring about saturation of the basic instabilities that drive gyrokinetic turbulence. Emphasis is put on the ability for this analytic theory to predict basic properties of the nonlinear state, which can be applied to a mixing length phenomenology of transport. The results of this work include (1) an integral equation for the calculation of the growth rate of the fully gyrokinetic secondary instability with finite Larmor radius (FLR) affects included exactly, (2) the demonstration of the robustness of the secondary instability at fine scales (krhoi for ion temperature gradient (ITG) turbulence and krhoe ≪ 1 for electron temperature
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go
2016-01-01
It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas. PMID:27160346
On the structure and statistical theory of turbulence of extended magnetohydrodynamics
Miloshevich, George; Morrison, Philip J
2016-01-01
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range - this is s...
Scaling laws in magnetized plasma turbulence
Boldyrev, Stanislav [Univ. of Wisconsin, Madison, WI (United States)
2015-06-28
Interactions of plasma motion with magnetic fields occur in nature and in the laboratory in an impressively broad range of scales, from megaparsecs in astrophysical systems to centimeters in fusion devices. The fact that such an enormous array of phenomena can be effectively studied lies in the existence of fundamental scaling laws in plasma turbulence, which allow one to scale the results of analytic and numerical modeling to the sized of galaxies, velocities of supernovae explosions, or magnetic fields in fusion devices. Magnetohydrodynamics (MHD) provides the simplest framework for describing magnetic plasma turbulence. Recently, a number of new features of MHD turbulence have been discovered and an impressive array of thought-provoking phenomenological theories have been put forward. However, these theories have conflicting predictions, and the currently available numerical simulations are not able to resolve the contradictions. MHD turbulence exhibits a variety of regimes unusual in regular hydrodynamic turbulence. Depending on the strength of the guide magnetic field it can be dominated by weakly interacting Alfv\\'en waves or strongly interacting wave packets. At small scales such turbulence is locally anisotropic and imbalanced (cross-helical). In a stark contrast with hydrodynamic turbulence, which tends to ``forget'' global constrains and become uniform and isotropic at small scales, MHD turbulence becomes progressively more anisotropic and unbalanced at small scales. Magnetic field plays a fundamental role in turbulent dynamics. Even when such a field is not imposed by external sources, it is self-consistently generated by the magnetic dynamo action. This project aims at a comprehensive study of universal regimes of magnetic plasma turbulence, combining the modern analytic approaches with the state of the art numerical simulations. The proposed study focuses on the three topics: weak MHD turbulence, which is relevant for laboratory devices
Relativistic particle transport in extragalactic jets: I. Coupling MHD and kinetic theory
Casse, F
2003-01-01
Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows the investigation of shock acceleration, adiabatic and radiative losses as well as diffusive spatial transport in various diffusion regimes. The applicability of SDEs to astrophysics is first discussed in regards to the different regimes and the MHD code spatial resolution. The procedure is then applied to 2.5D MHD-SDE simulations of kilo-parsec scale extragalactic jets. The ability of SDE to reproduce analytical solutions of the diffusion-convection equation for electrons is tested through the incorporation of an increasing number of effects: shock acceleration, spatially dependent diffusion coefficients and synchrotron losses. The SDEs prove to be efficient in various shock configuration occurring in the inner jet during the development of the Kelvin-Helmholtz instability. ...
Potential landscape and flux field theory of turbulence
Wu, Wei; Wang, Jin
2016-01-01
We have established a potential landscape and flux field theory for stochastic fluid dynamical systems, turbulence systems in particular, governed by stochastically forced Navier-Stokes equations. We have found that detailed balance breaking, which characterizes the nonequilibrium nature of stochastic fluid dynamical systems, leads directly to a pair of interconnected characteristic consequences, namely, the non-Gaussian potential landscape and the nonvanishing irreversible flux. This 'nonequilibrium trinity' is manifested in various aspects and at different levels of nonequilibrium stochastic fluid dynamical systems. The nonequilibrium dynamics of stochastic fluid systems is governed by both the potential landscape and the irreversible flux, due to the potential-flux form of the irreversible driving force arising from detailed balance breaking. We have revealed a deep connection of the energy flux that is essential for turbulence energy cascade to the nonvanishing irreversible flux as well as the non-Gaussia...
A self-consistent theory of collective alpha particle losses induced by Alfvenic turbulence
Biglari, H. (Princeton Univ., NJ (United States). Plasma Physics Lab.); Diamond, P.H. (California Univ., San Diego, La Jolla, CA (United States). Dept. of Physics)
1992-01-01
The nonlinear dynamics of kinetic Alfven waves, resonantly excited by energetic ions/alpha particles, is investigated. It is shown that {alpha}-particles govern both linear instability and nonlinear saturation dynamics, while the background MHD turbulence results only in a nonlinear real frequency shift. The most efficient saturation mechanism is found to be self-induced profile modification. Expressions for the fluctuation amplitudes and the {alpha}-particle radial flux are self-consistently derived. The work represents the first self-consistent, turbulent treatment of collective {alpha}-particle losses by Alfvenic fluctuations.
Incompressible turbulence as non-local field theory
Mahendra K Verma
2005-03-01
It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.
New scenario of turbulence theory and wall-bounded turbulence: Theoretical significance
Kambe, Tsutomu
2016-01-01
New general scenario of turbulence theory is proposed and applied to wall-bounded turbulence. Significance of the theory rests on a mathematical theorem closely related to the fundamental conservation law of current flux of fluid flow, expressed in a form of 4d physical space-time representation, which predicts a system of Maxwell-type equation and supports transverse waves traveling with a phase speed c_t. In streaky wall flows it is remarkable that there exist both dynamical mechanism exciting transverse waves and an energy channel of exchange between flow field and transverse wave field. In developed state of the wave field, energy is supplied from the flow field to the transverse wave field if wavelengths are sufficiently large. The waves are accompanied with a new mechanism of energy dissipation, i.e. an internal friction analogous to the Joule effect. Energy is supplied from the main flow to the wave field, and some part of the energy is dissipated into heat. Thus, there exists a sustaining mechanism, w...
Cardoso, J. F.; Delabrouille, J.; Ganga, K.
2015-01-01
with the local spatial coherence of the polarization angle. These observations are compared to polarized emission maps computed in simulations of anisotropic magnetohydrodynamical turbulence in which we assume a uniform intrinsic polarization fraction of the dust grains. We find that an estimate...
Recent observations of MHD fluctuations in the solar wind
B. Bavassano
Full Text Available A short review of recent observations of solar wind fluctuations in the magnetohydrodynamic (MHD range of scales is presented. In recent years, the use of high time-resolution data on an extended interval of heliocentric distance has allowed significant advances in our knowledge of MHD fluctuations. We first focus on the origin and evolution of the Alfvénic-type fluctuations. The role of interplanetary sources and the influence of interactions with structures convected by the solar wind are examined. Then compressive fluctuations are investigated, with special attention being given to their nature and origin. Observations are discussed in the light of recent theories and models. Finally, predictions for MHD turbulence in polar regions of the heliosphere are highlighted.
On the structure and statistical theory of turbulence of extended magnetohydrodynamics
Miloshevich, George; Lingam, Manasvi; Morrison, Philip J.
2017-01-01
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville’s theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range—this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.
Weak turbulence theory for rotating magnetohydrodynamics and planetary dynamos
Galtier, Sebastien
2014-01-01
A weak turbulence theory is derived for magnetohydrodynamics under rapid rotation and in the presence of a large-scale magnetic field. The angular velocity $\\Omega_0$ is assumed to be uniform and parallel to the constant Alfv\\'en speed ${\\bf b_0}$. Such a system exhibits left and right circularly polarized waves which can be obtained by introducing the magneto-inertial length $d \\equiv b_0/\\Omega_0$. In the large-scale limit ($kd \\to 0$; $k$ being the wave number), the left- and right-handed waves tend respectively to the inertial and magnetostrophic waves whereas in the small-scale limit ($kd \\to + \\infty$) pure Alfv\\'en waves are recovered. By using a complex helicity decomposition, the asymptotic weak turbulence equations are derived which describe the long-time behavior of weakly dispersive interacting waves {\\it via} three-wave interaction processes. It is shown that the nonlinear dynamics is mainly anisotropic with a stronger transfer perpendicular ($\\perp$) than parallel ($\\parallel$) to the rotating a...
Statistical Mechanics of Turbulent Dynamos
Shebalin, John V.
2014-01-01
Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much
Sano, T; Turner, N J; Stone, J M; Sano, Takayoshi; Inutsuka, Shu-ichiro; Turner, Neal J.; Stone, James M.
2004-01-01
The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments it is found that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength, and is unaffected by Ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, an...
Cosmic Ray transport in turbulent magnetic field
Yan, Huirong
2013-01-01
Cosmic ray (CR) transport and acceleration is determined by the properties of magnetic turbulence. Recent advances in MHD turbulence call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall address the issue of the transport of CRs, both parallel and perpendicular to the magnetic field. We shall demonstrate compressible fast modes are dominant cosmic ray scatterer from both quasilinear and nonlinear theories. We shall also show that the self-generated wave growth by CRs are constrained by preexisting turbulence and discuss the process in detail in the context of shock acceleration at supernova remnants and their implications. In addition, we shall dwell on the nonlinear growth of kinetic gyroresonance instability of cosmic rays induced by large scale compressible turbulence. This gyroresonance of cosmic rays on turbulence is d...
Turbulent General Magnetic Reconnection
Eyink, Gregory L
2014-01-01
Plasma flows with an MHD-like turbulent inertial range, such as the solar wind, require a generalization of General Magnetic Reconnection (GMR) theory. We introduce the slip-velocity source vector, which gives the rate of development of slip velocity per unit arc length of field line. The slip source vector is the ratio of the curl of the non ideal electric field in the Generalized Ohm's Law and the magnetic field strength. It diverges at magnetic nulls, unifying GMR with magnetic null-point reconnection. Only under restrictive assumptions is the slip velocity related to the gradient of the quasi potential (integral of parallel electric field along field lines). In a turbulent inertial range the curl becomes extremely large while the parallel component is tiny, so that line slippage occurs even while ideal MHD becomes accurate. The resolution of this paradox is that ideal MHD is valid for a turbulent inertial-range only in a weak sense which does not imply magnetic line freezing. The notion of weak solution i...
Resonant interactions of perturbations in MHD flows
Sagalakov, A.M.; Shtern, V.N.
1977-01-17
The nonlinear theory of hydrodynamic stability differentiates three types of interactions: deformation of the initial velocity profile by Reynolds stress pulsations, multiplication of harmonics, and the resonant interaction of harmonics with dissimilar wave numbers and frequencies. This article analyzes an approach considering the first and third of these non-linear mechanisms, producing an acceptable approximation of the averaged characteristics of a developing pulsation movement, particularly the averaged turbulent velocity profile. The approach consists in analysis of triharmonic oscillations, the parameters of which satisfy the resonant relationships. A model of a triharmonic pulsation mode is studied which is applicable to MHD flows. It is shown in particular how a magnetic field transverse to the flow plane suppresses the resonant interaction of three-dimensional perturbations. This agrees with experimental studies on two-dimensional turbulence conducted earlier. 11 references, 3 figures.
Turbulence theories and modelling of fluids and plasmas
Yoshizawa, Akira; Yokoi, Nobumitsu [Institute of Industrial Science, Univ. of Tokyo, Tokyo (Japan); Itoh, Sanae-I. [Research Institute for Applied Mechanics, Kyushu Univ., Kasuga, Fukuoka (Japan); Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-04-01
Theoretical and heuristic modelling methods are reviewed for studying turbulence phenomena of fluids and plasmas. Emphasis is put on understanding of effects on turbulent characteristics due to inhomogeneities of field and plasma parameters. The similarity and dissimilarity between the methods for fluids and plasmas are sought in order to shed light on the properties that are shared or not by fluid and plasma turbulence. (author)
Turbulence theories and modelling of fluids and plasmas
Yoshizawa, Akira; Yokio, Nobumitsu [Institute of Industrial Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, 87, Kasuga 816-8580 (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan)
2001-03-01
Theoretical and heuristic modelling methods are reviewed for studying turbulence phenomena of fluids and plasmas. Emphasis is placed on understanding of effects on turbulence characteristics due to inhomogeneities of field and plasma parameters. The similarity and dissimilarity between the methods for fluids and plasmas are sought in order to shed light on the properties that are shared or not by fluid and plasma turbulence. (author)
Bailly, Christophe
2015-01-01
This book covers the major problems of turbulence and turbulent processes, including physical phenomena, their modeling and their simulation. After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also introduced. Wall-bounded flows are presented in Chapter 3, and aspects specific to boundary layers and channel or pipe flows are also pointed out. Free shear flows, namely free jets and wakes, are considered in Chapter 4. Chapter 5 deals with vortex dynamics. Homogeneous turbulence, isotropy, and dynamics of isotropic turbulence are presented in Chapters 6 and 7. Turbulence is then described both in the physical space and in the wave number space. Time dependent numerical simulations are presented in Chapter 8, where an introduction to large eddy simulation is offered. The last three chapters of the book summarize remarka...
Radiative heat transfer in turbulent combustion systems theory and applications
Modest, Michael F
2016-01-01
This introduction reviews why combustion and radiation are important, as well as the technical challenges posed by radiation. Emphasis is on interactions among turbulence, chemistry and radiation (turbulence-chemistry-radiation interactions – TCRI) in Reynolds-averaged and large-eddy simulations. Subsequent chapters cover: chemically reacting turbulent flows; radiation properties, Reynolds transport equation (RTE) solution methods, and TCRI; radiation effects in laminar flames; TCRI in turbulent flames; and high-pressure combustion systems. This Brief presents integrated approach that includes radiation at the outset, rather than as an afterthought. It stands as the most recent developments in physical modeling, numerical algorithms, and applications collected in one monograph.
Dynamic multiscaling in magnetohydrodynamic turbulence
Ray, Samriddhi Sankar; Pandit, Rahul
2016-01-01
We present the first study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Dynamic multiscaling in magnetohydrodynamic turbulence.
Ray, Samriddhi Sankar; Sahoo, Ganapati; Pandit, Rahul
2016-11-01
We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.
Krommes, J.A.
2000-01-18
Recent results and future challenges in the systematic analytical description of plasma turbulence are described. First, the importance of statistical realizability is stressed, and the development and successes of the Realizable Markovian Closure are briefly reviewed. Next, submarginal turbulence (linearly stable but nonlinearly self-sustained fluctuations) is considered and the relevance of nonlinear instability in neutral-fluid shear flows to submarginal turbulence in magnetized plasmas is discussed. For the Hasegawa-Wakatani equations, a self-consistency loop that leads to steady-state vortex regeneration in the presence of dissipation is demonstrated and a partial unification of recent work of Drake (for plasmas) and of Waleffe (for neutral fluids) is given. Brief remarks are made on the difficulties facing a quantitatively accurate statistical description of submarginal turbulence. Finally, possible connections between intermittency, submarginal turbulence, and self-organized criticality (SOC) are considered and outstanding questions are identified.
3D MHD Coronal Oscillations About a Magnetic Null Point: Application of WKB Theory
McLaughlin, J A; Hood, A W
2007-01-01
This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit's Method and a Runge-Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, ${\\bf{B}}=(x,\\epsilon y -(\\epsilon +1)z)$. Under our cold plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfv\\'en waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point, and that the effect of this refraction depends upon the Alfv\\'en speed profile. The wave, and thus the wave energy, accumulates at the null point. We have found that current build up is exponential and the exponent is dependent upon $\\epsilon$. Thus, for the fast wave there is preferential heating at the null point. For the Alfv\\'en wave, we find that the wave propagates along the fieldlines. For an Alfv\\'en wave generated along the fan-plane, the wave accumulates along the spine. For an Alfv\\'en wa...
Numerical simulation of MHD duct flow about laminar and turbulence model%磁流体管流的层流与湍流模型数值模拟
侯俊; 毛洁; 潘华辰
2013-01-01
采用FLUENT软件分别对外加均匀横向磁场的等截面三维充分发展液态金属管流的层流模型和低雷诺数湍流Lam/Bremhost(LB)模型进行了数值模拟,分析了外加磁场对普通方管LB模型速度分布和压降的影响.比较在相同哈特曼数下,层流和湍流模型方管截面上速度分布和管道中MHD压降.其中,对电流的计算采用磁感应方程来求得.数值模拟结果证明了用低雷诺数LB湍流模型解决方管磁流体流动的可行性.通过层流模型和湍流模型的对比可知,层流模型有较短的入口长度,但管内流体的压降却很大；而湍流模型管内速度更加平均化,管内压降较小,但管内入口长度较长.%The numerical analysis of full-developed flow of a liquid metal in a rectangular duct of constant cross-section with a uniform transverse magnetic field was proceeded in laminar and low-Reynolds number Lam/Bremhost turbulence model (for short LB model) using FLUENT software. The paper analyzed the influence of external magnetic field for velocity distribution and MHD pressure drop in turbulence model. Under the same Hartmann number conductions, the paper compared the velocity distribution and MHD pressure drop of laminar model and turbulent model. The solution of current density was obtained by means of induced magnetic field formulation. The result of numerical simulation proved that this was a feasible scheme to use the low-Reynolds LB turbulence model to calculate MHD duct flow. Comparison between laminar model and turbulent model show that laminar model made shorter entrance length, but the pressure drop in the duct increased. Turbulent model had more average speed and smaller pressure drop, but entrance length was longer.
Stretching vortices as a basis for the theory of turbulence
Sirota, V A
2014-01-01
Turbulent flows play an important role in many aspects of nature and technics from sea storms to transport of particles or chemicals. Transport of energy from large scales to small fluctuations is the essential feature of three-dimensional turbulence. What mechanism is responsible for this transport and how do the small fluctuations appear? The conventional conception implies a cascade of breaking vortices. But it faces crucial problems in explaining the mechanism of the breaking, and fails to explain the observed long-living structures in turbulent flows. We suggest a new concept based on recent analysis of stochastic Navier-Stokes equation: stretching of vortices instead of their breaking may be the main mechanism of turbulence. This conception is free of the disadvantages of the cascade paradigm; it also does not need finite-time singularities to explain the observed statistical properties of turbulent flows. Moreover, the introduction of the new conception allows immediately to get velocity scaling parame...
Sun, Jielun; Lenschow, Donald; LeMone, Margaret; Mahrt, Larry
2015-04-01
Turbulent fluxes from the Cooperative Atmosphere-Surface Exchange Study in 1999 (CASES-99) field experiment are further analyzed for both day- and nighttime as a follow-on to the investigation of the nighttime turbulence in Sun et al. (2012). The behavior of momentum and heat fluxes is investigated as functions of wind speed and the bulk temperature difference between observation heights and the surface. Vertical variations of momentum and heat flux at a given height z are correlated and are explained in terms of the energy and heat balance in a layer above the ground surface in which the surface heating/cooling and momentum sink need to be included. In addition, the surface also plays an important role in constraining the size of the dominant turbulent eddies, which is directly related to turbulence strength and the length scale of turbulence generation. The turbulence generation is not related to local vertical gradients especially under neutral condition as assumed in Monin-Obukhov similarity theory. Based on the observed relationships between momentum and heat fluxes, a new bulk formula for turbulence parameterization is developed to mainly examine the above-mentioned surface effects on vertical variation of turbulent momentum and heat fluxes. The new understanding of the observed relationships between these turbulent variables and mean variables explains the observed nighttime turbulence regime change observed in Sun et al. (2012) as well as the daytime momentum and heat flux variations with height up to the maximum observation height of 55 m.
Diamond, P.H.; Biglari, H.; Gang, F.Y.; Kim, Y.B.; Rosenbluth, M.N.; Wang, X.H.; Xu, X.Q. (California Univ., San Diego, La Jolla, CA (USA). Dept. of Physics); Dominguez, N.; Carreras, B.A.; Leboeuf, J.N.; Lynch, V.E.; Charlton, L.A.; Garcia, L. (Oak Ridge National Lab., TN (USA)); Terry, P.W.; Newman, D.E. (Wisconsin Univ., Madison, WI (USA). Dept. of Physics); Koniges, A.E.; Crotinger, J.; Dannevik, W. (Lawre
1990-12-01
Recent advances in the theory of trapped particle pressure gradient driven turbulence are summarized. A novel theory of trapped ion convective cell turbulence is presented. It is shown that nonlinear transfer to small scales occurs, and that saturation levels are not unphysically large, as previously thought. As the virulent saturation mechanism of ion Compton scattering is shown to result in weak turbulence at higher frequencies, it is thus likely that trapped ion convective cells are the major agent of tokamak transport. Fluid-like trapped electron modes at short wavelengths (k{sub {theta}} {rho}{sub i} > 1) are shown to drive an inward particle pinch. The characteristics of convective cell turbulence in flat density discharges are described, as is the stability of dissipative trapped electron modes in stellarators, with flexible magnetic field structure. The role of cross-correlations in the dynamics of multi-field models of drift wave turbulence is discussed. 32 refs., 7 figs., 1 tab.
Weak turbulence theory and simulation of the gyro-water-bag model.
Besse, Nicolas; Bertrand, Pierre; Morel, Pierre; Gravier, Etienne
2008-05-01
The thermal confinement time of a magnetized fusion plasma is essentially determined by turbulent heat conduction across the equilibrium magnetic field. To achieve the study of turbulent thermal diffusivities, Vlasov gyrokinetic description of the magnetically confined plasmas is now commonly adopted, and offers the advantage over fluid models (MHD, gyrofluid) to take into account nonlinear resonant wave-particle interactions which may impact significantly the predicted turbulent transport. Nevertheless kinetic codes require a huge amount of computer resources and this constitutes the main drawback of this approach. A unifying approach is to consider the water-bag representation of the statistical distribution function because it allows us to keep the underlying kinetic features of the problem, while reducing the Vlasov kinetic model into a set of hydrodynamic equations, resulting in a numerical cost comparable to that needed for solving multifluid models. The present paper addresses the gyro-water-bag model derived as a water-bag-like weak solution of the Vlasov gyrokinetic models. We propose a quasilinear analysis of this model to retrieve transport coefficients allowing us to estimate turbulent thermal diffusivities without computing the full fluctuations. We next derive another self-consistent quasilinear model, suitable for numerical simulation, that we approximate by means of discontinuous Galerkin methods.
Plasma instabilities and turbulence in non-Abelian gauge theories
Scheffler, Sebastian Herwig Juergen
2010-02-17
quasi-stationary phase following the saturation of instabilities is studied. Numerical as well as analytical calculations show that the classical time evolution drives the system towards a nonthermal fixed point which exhibits properties of turbulence. The fixed point is characterised by power-law correlation functions of the gauge field. The determined exponents 4/3 and 5/3 are identical to those found in scalar field theories, which provides indication for universality out of thermal equilibrium. Taking into account the quantum contributions in the analytical approach it is demonstrated that the full quantum theory does not possess a nonthermal fixed point at large momenta. (orig.)
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
D. Schertzer
1996-01-01
. It had an appropriate editorial structure, in particular a large number of editors covering a wide range of methodologies, expertises and schools. At least two of its sections (Scaling and Multifractals, Turbulence and Diffusion were directly related to the topics of the workshop, in any case contributors were invited to choose their editor freely. 2 Goals of the Workshop The objective of this meeting was to enhance the confrontation between turbulence theories and empirical data from geophysics and astrophysics fluids with very high Reynolds numbers. The importance of these data seems to have often been underestimated for the evaluation of theories of fully developed turbulence, presumably due to the fact that turbulence does not appear as pure as in laboratory experiments. However, they have the great advantage of giving access not only to very high Reynolds numbers (e.g. 1012 for atmospheric data, but also to very large data sets. It was intended to: (i provide an overview of the diversity of potentially available data, as well as the necessary theoretical and statistical developments for a better use of these data (e.g. treatment of anisotropy, role of processes which induce other nonlinearities such as thermal instability, effect of magnetic field and compressibility ... , (ii evaluate the means of discriminating between different theories (e.g. multifractal intermittency models or to better appreciate the relevance of different notions (e.g. Self-Organized Criticality or phenomenology (e.g. filaments, structures, (iii emphasise the different obstacles, such as the ubiquity of catastrophic events, which could be overcome in the various concerned disciplines, thanks to theoretical advances achieved. 3 Outlines of the Workshop During the two days of the workshop, the series of presentations covered many manifestations of turbulence in geophysics, including: oceans, troposphere, stratosphere, very high atmosphere, solar wind, giant planets, interstellar clouds
Z. Lin; R.E. Waltz
2007-01-01
@@ Turbulent transport driven by plasma pressure gradients [Tangl978] is one of the most important scientific challenges in burning plasma experiments since the balance between turbulent transport and the self-heating by the fusion products (a-particles) determines the performance of a fusion reactor like ITER.
Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
Gioia, G; Chakraborty, Pinaki
2005-01-01
The classical experiments on turbulent friction in rough pipes were performed by J. Nikuradse in the 1930's. Seventy years later, they continue to defy theory. Here we model Nikuradse's experiments using the phenomenological theory of Kolmogorov, a theory that is widely thought to be applicable only to highly idealized flows. Our results include both the empirical scalings of Blasius and Strickler, and are otherwise in minute qualitative agreement with the experiments; they suggest that the phenomenological theory may be relevant to other flows of practical interest; and they unveil the existence of close ties between two milestones of experimental and theoretical turbulence.
Methods of separation of variables in turbulence theory
Tsuge, S.
1978-01-01
Two schemes of closing turbulent moment equations are proposed both of which make double correlation equations separated into single-point equations. The first is based on neglected triple correlation, leading to an equation differing from small perturbed gasdynamic equations where the separation constant appears as the frequency. Grid-produced turbulence is described in this light as time-independent, cylindrically-isotropic turbulence. Application to wall turbulence guided by a new asymptotic method for the Orr-Sommerfeld equation reveals a neutrally stable mode of essentially three dimensional nature. The second closure scheme is based on an assumption of identity of the separated variables through which triple and quadruple correlations are formed. The resulting equation adds, to its equivalent of the first scheme, an integral of nonlinear convolution in the frequency describing a role due to triple correlation of direct energy-cascading.
Using Synthetic Spacecraft Data to Interpret Compressible Fluctuations in Solar Wind Turbulence
Klein, K G; TenBarge, J M; Bale, S D; Chen, C H K; Salem, C S
2012-01-01
Kinetic plasma theory is used to generate synthetic spacecraft data to analyze and interpret the compressible fluctuations in the inertial range of solar wind turbulence. The kinetic counterparts of the three familiar linear MHD wave modes---the fast, Alfven, and slow waves---are identified and the properties of the density-parallel magnetic field correlation for these kinetic wave modes is presented. The construction of synthetic spacecraft data, based on the quasi-linear premise---that some characteristics of magnetized plasma turbulence can be usefully modeled as a collection of randomly phased, linear wave modes---is described in detail. Theoretical predictions of the density-parallel magnetic field correlation based on MHD and Vlasov-Maxwell linear eigenfunctions are presented and compared to the observational determination of this correlation based on 10 years of Wind spacecraft data. It is demonstrated that MHD theory is inadequate to describe the compressible turbulent fluctuations and that the observ...
A new probability distribution model of turbulent irradiance based on Born perturbation theory
无
2010-01-01
The subject of the PDF (Probability Density Function) of the irradiance fluctuations in a turbulent atmosphere is still unsettled.Theory reliably describes the behavior in the weak turbulence regime,but theoretical description in the strong and whole turbulence regimes are still controversial.Based on Born perturbation theory,the physical manifestations and correlations of three typical PDF models (Rice-Nakagami,exponential-Bessel and negative-exponential distribution) were theoretically analyzed.It is shown that these models can be derived by separately making circular-Gaussian,strong-turbulence and strong-turbulence-circular-Gaussian approximations in Born perturbation theory,which denies the viewpoint that the Rice-Nakagami model is only applicable in the extremely weak turbulence regime and provides theoretical arguments for choosing rational models in practical applications.In addition,a common shortcoming of the three models is that they are all approximations.A new model,called the Maclaurin-spread distribution,is proposed without any approximation except for assuming the correlation coefficient to be zero.So,it is considered that the new model can exactly reflect the Born perturbation theory.Simulated results prove the accuracy of this new model.
Phenomenology treatment of magnetohydrodynamic turbulence with non-equipartition and anisotropy
Zhou, Y; Matthaeus, W H
2005-02-07
Magnetohydrodynamics (MHD) turbulence theory, often employed satisfactorily in astrophysical applications, has often focused on parameter ranges that imply nearly equal values of kinetic and magnetic energies and length scales. However, MHD flow may have disparity magnetic Prandtl number, dissimilar kinetic and magnetic Reynolds number, different kinetic and magnetic outer length scales, and strong anisotropy. Here a phenomenology for such ''non-equipartitioned'' MHD flow is discussed. Two conditions are proposed for a MHD flow to transition to strong turbulent flow, extensions of (1) Taylor's constant flux in an inertial range, and (2) Kolmogorov's scale separation between the large and small scale boundaries of an inertial range. For this analysis, the detailed information on turbulence structure is not needed. These two conditions for MHD transition are expected to provide consistent predictions and should be applicable to anisotropic MHD flows, after the length scales are replaced by their corresponding perpendicular components. Second, it is stressed that the dynamics and anisotropy of MHD fluctuations is controlled by the relative strength between the straining effects between eddies of similar size and the sweeping action by the large-eddies, or propagation effect of the large-scale magnetic fields, on the small scales, and analysis of this balance in principle also requires consideration of non-equipartition effects.
Theory of self-sustained turbulence in confined plasmas
Itoh, Kimitaka; Itoh, Sanae; Fukuyama, Atsushi; Yagi, Masatoshi
1996-02-01
This article overviews some aspect of the recent theoretical activities in Japan on the problem of turbulent transport in confined plasmas. The method of self-sustained turbulence is discussed. The process of the renormalization is shown and the turbulent Prandtl number is introduced. Nonlinear destabilization by the electron momentum diffusion is explained. The nonlinear eigenmode equation is derived for the dressed-test-mode for the inhomogeneous plasma in the shear magnetic field. The eigenvalue equation is solved, and the least stable mode determines the anomalous transport coefficient. Formula of thermal conductivity is presented for the system of bad average magnetic curvature (current diffusive interchange mode (CDIM) turbulence) and that for the average good magnetic curvature (current diffusive ballooning mode (CDBM) turbulence). The transport coefficient, scale length of fluctuations and fluctuation level are shown to be the increasing function of the pressure gradient. Verification by use of the nonlinear simulation is shown. The bifurcation of the electric field and improved confinement is addressed, in order to explain the H-mode physics. Improved confinement and the dynamics such as ELMs are explained. Application to the transport analysis of tokamaks is also presented, including the explanations of the L-mode confinement, internal transport barrier as well as the role of current profile control. (author). 102 refs.
Magnetic reconnection as an element of turbulence
S. Servidio
2011-10-01
Full Text Available In this work, recent advances on the study of reconnection in turbulence are reviewed. Using direct numerical simulations of decaying incompressible two-dimensional magnetohydrodynamics (MHD, it was found that in fully developed turbulence complex processes of reconnection locally occur (Servidio et al., 2009, 2010a. In this complex scenario, reconnection is spontaneous but locally driven by the fields, with the boundary conditions provided by the turbulence. Matching classical turbulence analysis with a generalized Sweet-Parker theory, the statistical features of these multiple-reconnection events have been identified. A discussion on the accuracy of our algorithms is provided, highlighting the necessity of adequate spatial resolution. Applications to the study of solar wind discontinuities are reviewed, comparing simulations to spacecraft observations. New results are shown, studying the time evolution of these local reconnection events. A preliminary study on the comparison between MHD and Hall MHD is reported. Our new approach to the study of reconnection as an element of turbulence has broad applications to space plasmas, shedding a new light on the study of magnetic reconnection in nature.
A Theory of Grain Clustering in Turbulence: The Origin and Nature of Large Density Fluctuations
Hopkins, Philip F
2016-01-01
We propose a theory for the density fluctuations of aerodynamic grains embedded in a turbulent, gravitating gas disk. The theory combines calculations for the average behavior of grains encountering a single turbulent eddy, with a hierarchical description of the eddy velocity statistics. We show that this makes analytic predictions for a wide range of quantities, including: the distribution of volume-average grain densities, the power spectrum and correlation functions of grain density fluctuations, and the maximum volume density of grains reached. For each, we predict how these scale as a function of grain stopping/friction time (t_stop), spatial scale, grain-to-gas mass ratio, strength of the turbulence (alpha), and detailed disk properties (orbital frequency, sound speed). We test these against numerical simulations and find good agreement over a huge parameter space. Results from 'turbulent concentration' simulations and laboratory experiments are also predicted as a special case. We predict that vortices...
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. IV
Itoh, Sanae-I.; Itoh, Kimitaka [Max-Planck-Institut fuer Plasmaphysik, Garching bei Muenchen (Germany)
2000-02-01
A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A Fokker-Planck equation for the probability distribution function of the magnitude of turbulence is deduced. In the statistical description, both the contributions of thermal excitation and turbulence are kept. From the Fokker-Planck equation, the transition probability between the thermal fluctuation and turbulent fluctuation is derived. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. The equilibrium distribution function describes the thermal fluctuation, self-sustained turbulence and the hysteresis between them as a function of the plasma gradient. The plasma inhomogeneity is the controlling parameter that governs time turbulence. The formula of transition probability recovers the Arrhenius law in the thermodynamical equilibrium limit. In the presence of self-noise, the transition probability deviates form the exponential law and provides a power law. Application is made to the submarginal interchange mode turbulence, being induced by the turbulent current-diffusivity, in inhomogeneous plasmas. The power law dependence of the transition probability is obtained on the distance between the pressure gradient and the critical gradient for linear instability. Thus a new type of critical exponent is explicitly deduced in the phenomena of subcritical excitation of turbulence. The method provides an extension of the nonequilibrium statistical physics to the far-nonequilibrium states. (author)
Krommes, John A.
2015-12-01
> In honour of the 50th anniversary of the influential review/monograph on plasma turbulence by B. B. Kadomtsev as well as the seminal works of T. H. Dupree and J. Weinstock on resonance-broadening theory, an introductory tutorial is given about some highlights of the statistical-dynamical description of turbulent plasmas and fluids, including the ideas of nonlinear incoherent noise, coherent damping, and self-consistent dielectric response. The statistical closure problem is introduced. Incoherent noise and coherent damping are illustrated with a solvable model of passive advection. Self-consistency introduces turbulent polarization effects that are described by the dielectric function . Dupree's method of using to estimate the saturation level of turbulence is described; then it is explained why a more complete theory that includes nonlinear noise is required. The general theory is best formulated in terms of Dyson equations for the covariance and an infinitesimal response function , which subsumes . An important example is the direct-interaction approximation (DIA). It is shown how to use Novikov's theorem to develop an -space approach to the DIA that is complementary to the original -space approach of Kraichnan. A dielectric function is defined for arbitrary quadratically nonlinear systems, including the Navier-Stokes equation, and an algorithm for determining the form of in the DIA is sketched. The independent insights of Kadomtsev and Kraichnan about the problem of the DIA with random Galilean invariance are described. The mixing-length formula for drift-wave saturation is discussed in the context of closures that include nonlinear noise (shielded by ). The role of in the calculation of the symmetry-breaking (zonostrophic) instability of homogeneous turbulence to the generation of inhomogeneous mean flows is addressed. The second-order cumulant expansion and the stochastic structural stability theory are also discussed in that context. Various historical
Non Axi-symmetric Anisotropy of Solar Wind Turbulence
Turner, A J; Chapman, S C; Hnat, B; Mueller, W -C
2011-01-01
A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent solar wind are observed to be ordered with respect to the bulk macroscopic flow as well as the background magnetic field. Here, non- axisymmetry across the inertial and dissipation ranges is quantified using in-situ observations from Cluster. The observed inertial range non- axisymmetry is reproduced by a 'fly through' sampling of a Direct Numerical Simulation of MHD turbulence. Furthermore, 'fly through' sampling of a linear superposition of transverse waves with axisymmetric fluctuations generates the trend in non- axisymmetry with power spectral exponent. The observed non-axisymmetric anisotropy may thus simply arise as a sampling effect related to Taylor's hypothesis and is not related to the plasma dynamics itself.
Plasmoid Instabilities Mediated Three-Dimensional Magnetohydrodynamic Turbulent Reconnection
Huang, Yi-min [Princeton University; Guo, Fan [Los Alamos National Laboratory
2015-07-21
After some introductory remarks on fast reconnection in resistive MHD due to plasmoid instability, oblique tearing modes in 3D, and previous studies on 3D turbulent reconnection, the subject is presented under the following topics: 3D simulation setup, time evolution of the 3D simulation, comparison with Sweet-Parker and 2D plasmoid reconnection, and diagnostics of the turbulent state (decomposition of mean fields and fluctuations, power spectra of energy fluctuations, structure function and eddy anisotropy with respect to local magnetic field). Three primary conclusions were reached: (1) The results suggest that 3D plasmoid instabilities can lead to self-generated turbulent reconnection (evidence of energy cascade and development of inertial range, energy fluctuations preferentially align with the local magnetic field, which is one of the characteristics of MHD turbulence); (2) The turbulence is highly inhomogeneous, due to the presence of magnetic shear and outflow jets (conventional MHD turbulence theories or phenomenologies may not be applicable – e.g. scale-dependent anisotropy as predicted by Goldreich & Sridhar is not found); (3) 3D turbulent reconnection is different from 2D plasmoid-dominated reconnection in many aspects. However, in fully developed state, reconnection rates in 2D and 3D are comparable — this result needs to be further checked in higher S.
On Conditional Statistics in Scalar Turbulence Theory vs. Experiment
Ching, E S C; Podivilov, E V; Procaccia, I; Ching, Emily S.C.; L'vov, Victor S.; Podivilov, Evgeni; Procaccia, Itamar
1996-01-01
We consider turbulent advection of a scalar field $T(\\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $\\Delta T(R)$ across a scale $R$. In particular we focus on two conditional averages $\\langle\
The J–S model versus a non-ideal MHD theory
Franchi, Franca, E-mail: franca.franchi@unibo.it; Lazzari, Barbara, E-mail: barbara.lazzari@unibo.it; Nibbi, Roberta, E-mail: roberta.nibbi@unibo.it
2015-07-17
A new non-ideal electromagnetic interpretation of the J–S type viscoelastic model for polymeric fluids is given and a generalized resisto-elastic magnetohydrodynamic scenario for collisionless plasmas is proposed. The influence of the new theory on the incompressible transverse Alfvén waves is thoroughly investigated. - Highlights: • A non-ideal electromagnetic interpretation of the J–S type viscoelasticity is shown. • A generalized resisto-elastic magneto-hydrodynamic scenario for collision-less plasmas is proposed. • The shear-type magnetic waves are investigated.
B. A. Kashiwa; W. B. VanderHeyden
2000-12-01
A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. III
Itoh, Sanae-I.; Itoh, Kimitaka [Max-Planck-Institut fuer Plasmaphysik, Garching bei Muenchen (Germany)
2000-02-01
A statistical theory of nonlinear-nonequilibrium plasma state with strongly developed turbulence and with strong inhomogeneity of the system has been developed. A unified theory for both the thermally excited fluctuations and the strongly turbulent fluctuations is presented. With respect to the turbulent fluctuations, the coherent part to a certain test mode is renormalized as the drag to the test mode, and the rest, the incoherent part, is considered to be a random noise. The renormalized operator includes the effect of nonlinear destabilization as well as the decorrelation by turbulent fluctuations. Formulation is presented by deriving an Fokker-Planck equation for the probability distribution function. Equilibrium distribution function of fluctuations is obtained. Transition from the thermal fluctuations, that is governed by the Boltzmann distribution, to the turbulent fluctuation is clarified. The distribution function for the turbulent fluctuation has tail component and the width of which is in the same order as the mean fluctuation level itself. The Lyapunov function is constructed for the strongly turbulent plasma, and it is shown that an approach to a certain equilibrium distribution is assured. The result for the most probable state is expressed in terms of 'minimum renormalized dissipation rate', which is given by the ratio of the nonlinear decorrelation rate of fluctuation energy and the random excitation rate which includes both the thermal noise and turbulent self-noise effects. Application is made for example to the current-diffusive interchange mode turbulence in inhomogeneous plasmas. The applicability of this method covers plasma turbulences in much wider circumstance as well as neutral fluid turbulence. This method of analyzing strong turbulence has successfully extended the principles of statistical physics, i.e., Kubo-formula, Prigogine's principle of minimum entropy production rate. The condition for the turbulence transition is
Chougule, Abhijit S.; Mann, Jakob; Kelly, Mark C.
2017-01-01
A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using...... the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate epsilon, length scale of energy-containing eddies L, a turbulence anisotropy parameter Gamma, gradient Richardson number (Ri) representing...... separation. Finally, it is shown that the RDT output can deviate from Monin-Obukhov similarity theory....
Magnetohydrodynamic Turbulence and the Geodynamo
Shebalin, John V.
2016-01-01
Recent research results concerning forced, dissipative, rotating magnetohydrodynamic (MHD) turbulence will be discussed. In particular, we present new results from long-time Fourier method (periodic box) simulations in which forcing contains varying amounts of magnetic and kinetic helicity. Numerical results indicate that if MHD turbulence is forced so as to produce a state of relatively constant energy, then the largest-scale components are dominant and quasistationary, and in fact, have an effective dipole moment vector that aligns closely with the rotation axis. The relationship of this work to established results in ideal MHD turbulence, as well as to models of MHD turbulence in a spherical shell will also be presented. These results appear to be very pertinent to understanding the Geodynamo and the origin of its dominant dipole component. Our conclusion is that MHD turbulence, per se, may well contain the origin of the Earth's dipole magnetic field.
Resistive MHD jet simulations with large resistivity
Cemeljic, Miljenko; Vlahakis, Nektarios; Tsinganos, Kanaris
2009-01-01
Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for nu...
Organised structures in wall turbulence as deduced from stability theory-based methods
P K Sen; S V Veeravalli; P W Carpenter; G Joshi; P S Josan
2007-02-01
In earlier work, we have explored the relevance of hydrodynamic stability theory to fully developed turbulent wall ﬂows. Using an extended Orr-Summerfeld Equation, based on an anisotropic eddy-viscosity model, it was shown that there exists a wide range of unstable wave numbers (wall modes), which mimic some of the key features of turbulent wall ﬂows. Here we present experimental conﬁrmation for the same. There is good qualitative and quantitative agreement between theory and experiment. Once the dominant coherent structure is obtained from stability theory, control of turbulence would be the next logical step. As shown, the use of a compliant wall shows considerable promise. We also present some theoretical work for bypass transition (Klebanoff/K-modes), wherein the receptivity of a laminar boundary layer to a vortex sheet in the freestream has been studied. Further, it is shown that triadic interaction between K-modes, 2D TS waves and 3D TS waves can lead to rapid algebraic growth. A similar mechanism seems to carry over to inner wall structures in wall turbulence and perhaps this is the “root cause” for sustenance of turbulence.
Williams, Pd; Knox, Ja; McCann, Dw
2009-09-01
A new method of clear-air turbulence (CAT) forecasting based on the Lighthill-Ford theory of spontaneous imbalance and emission of inertia-gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill-Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill-Ford theory to CAT forecasting for the 3 November 2005-26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational. Reference Knox, J.A., D.W. McCann, and P.D. Williams, 2008: Application of the Lighthill-Ford Theory of Spontaneous Imbalance to Clear-Air Turbulence Forecasting. J. Atmos. Sci., 65, 3292-3304.
Wave turbulence in magnetized plasmas
S. Galtier
2009-02-01
Full Text Available The paper reviews the recent progress on wave turbulence for magnetized plasmas (MHD, Hall MHD and electron MHD in the incompressible and compressible cases. The emphasis is made on homogeneous and anisotropic turbulence which usually provides the best theoretical framework to investigate space and laboratory plasmas. The solar wind and the coronal heating problems are presented as two examples of application of anisotropic wave turbulence. The most important results of wave turbulence are reported and discussed in the context of natural and simulated magnetized plasmas. Important issues and possible spurious interpretations are also discussed.
A general Reynolds analogy theory for the compressible wall-bounded turbulence
Zhang, You-sheng; Husain, Fazle; Li, Xin-liang; She, Zhen-su
2012-01-01
A general Reynolds analogy (GRA) theory is proposed for the mean and fluctuating velocity and temperature in compressible wall-bounded turbulent flows. In particular, an exact analogy solution is derived for compressible turbulent pipe and channel flows and an approximate analogy solution is derived for compressible turbulent boundary layers (CTBL), both of which are independent of fluid Prandtl number and wall temperature condition. The analogy solutions are in excellent agreement with direct numerical simulation data, able to reproduce empirical relations, and can be viewed as extensions of existing theories. In contrast to Walz's equation for adiabatic CTBL, the mean temperature-velocity relation derived by GRA can be applied to different wall-bounded flows in non-adiabatic wall condition, which is achieved by extending Walz's adiabatic recovery factor to a heat flux dependent one. The fluctuation temperature-velocity relations derived by GRA are slightly different from the modified strong Reynolds analogy...
A theory of turbulence based on scale relativity
de Montera, Louis
2013-01-01
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale dependence and the use of a higher algebra. The law of mechanics transfers directly these properties to the velocity of fluid particles whose trajectories in velocity space become fractal and non-deterministic. The principle of relativity is used to find the form of the equation governing velocity in scale space. The solution of this equation contains a fractal and a non-fractal term. The fractal part is shown to be equivalent to the Lagrangian version of the Kolmogorov law of fully-developed and isotropic turbulence. It is therefore associated with turbulence, whereas the non-fractal deterministic term is associated with a laminar behavior. These terms are found to be balanced when the typical velocity reaches a level at which the Reynolds number is equal to one, in agree...
Efimov, Anatoly
2015-03-01
A partially coherent beam generated by coupling the output of a superluminescent diode to a multimode optical fiber is propagated through a stationary laboratory turbulence. Statistical quantities are measured as a function of propagation distance and coherence radius of the beam and are compared to existing theories in the regime of weak fluctuations.
Xiao, Xifeng; Voelz, David G; Toselli, Italo; Korotkova, Olga
2016-05-20
Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.
Ristorcelli, J. R.
1995-01-01
The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.
Helicity and its role in the varieties of magnetohydrodynamic turbulence
Montgomery, David C.; Bates, Jason W.
Magnetic helicity has appeared as an important but slippery quantity in the theory of magnetohydrodynamic (MHD) turbulence in two contexts: (1) as a slowly-decaying ideal invariant that can control to some extent the formation of a "relaxed" MHD state—one far from thermal equilibrium—in laboratory confinement devices such as the toroidal pinch; and (2) as a potentially inversely-cascadable global quantity in driven, homogeneous MHD turbulence. In the former case, the origin of helicity is straightforwardly clear: electric current is forced to flow along a dc magnetic field, generating poloidal magnetic flux and causing the magnetic field lines to kink up, helically. In the latter, helicity's origins and physical interpretation are more obscure, sometimes having to do with mechanically driven helical motions which supposedly generate magnetic helicity that, however, no longer has any obvious "linked flux" interpretation. In both cases, its usefulness and even its definition sometimes depend sensitively on boundary conditions in a way that, say, those for energy do not. We will examine what the utility of the concept of magnetic helicity has so far been shown to be in discussing turbulent MHD, and comment on some of the ways it differs from other global ideal invariants that have been discussed, such as kinetic energy in 2D Navier-Stokes flows, and mean-square magnetic vector potential in 2D MHD. Attention will be devoted to the evidence for variational principles such as "maximal helicity," or "minimum energy," conjectured to predict various relaxation processes and late-time laminar states in evolving MHD situations. What is believed to be an important distinction between applications of the principles to decaying and driven situations will be stressed. Our discussion will be confined to the cases of small but non-zero transport coefficients, and will not deal with any possible role of helicity in ideal MHD.
Limits on the ions temperature anisotropy in turbulent intracluster medium
Santo-Lima, R; Pino, E M de Gouveia Dal; Lazarian, A
2016-01-01
Turbulence in the weakly collisional intracluster medium of galaxies (ICM) is able to generate strong thermal velocity anisotropies in the ions (with respect to the local magnetic field direction), if the magnetic moment of the particles is conserved in the absence of Coulomb collisions. In this scenario, the anisotropic MHD turbulence shows a very different statistical behaviour from the isotropic (standard) one and is unable to amplify seed magnetic fields, in disagreement with previous cosmological MHD simulations which are able to explain the observed magnetic fields in the ICM. On the other hand, temperature anisotropy can also drive kinetic instabilities which grow faster near the ions kinetic scales. Observations from the solar wind suggest that these micro- instabilities scatter the ions, thus relaxing the anisotropy. This work aims to compare this relaxation rate with the growth rate of the anisotropies driven by the turbulence. We employ quasilinear theory to estimate the scattering rate provided by...
On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory
Speziale, Charles G.; Abid, Ridha; Blaisdell, Gregory A.
1995-01-01
The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.
The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem
Eckert, M.
2010-07-01
More than a hundred years ago William McFadden Orr and Arnold Sommerfeld conceived an approach to account for the transition from laminar to turbulent flow in terms of hydrodynamic stability theory. But the “turbulence problem”, as this challenge became notoriously famous, could not be solved by this method. By 1920, it was widely recognized as an outstanding riddle. Although famous theoretical physicists like Werner Heisenberg dedicated a considerable effort to this problem, the “Orr-Sommerfeld method” has never found the attention of historians of science. This article describes its early perception and development in Germany, and how the “turbulence problem” reached center stage after the First World war as a major challenge for theorists with different perspectives.
A Similarity Theory of the Tropospheric Turbulence Energy Spectrum.
Gifford, F. A.
1988-04-01
A three-range model is proposed for the energy spectrum of tropospheric turbulence in which the range-I spectrum is governed by the cascade of eddy enstrophy, that of range-II by the cascade of eddy kinetic energy, and that of range-III by viscous dissipation. Values of the spectral densities in ranges-I and -II, as well as wavenumbers of transition from range-I to -II to -III, are determined in terms of the integrated values of the energy spectrum, V2¯, and the dissipation spectrum, , of range-II. The resulting spectra for ranges-I and -II are shown to agree well with the recent GASP data on atmospheric spectra covering wave-lengths of from less than 3 km to 10000 km. A property of this model is that /V2¯ = f, the Coriolis parameter. This is shown to give very close agreement with the observed latitude variation of the GASP-Spectrum in range-II, to correctly indicate that this variation is much greater in range-I, and to explain why the atmosphere's eddy viscosity, K, is more variable over the globe than the energy-dissipation rate, . The observed seasonal variation of spectra is explained by the hemispheric variation of due to the seasonal change in the pole-equator temperature gradient.
Langmuir turbulence in the auroral ionosphere 1: Linear theory
Newman, D. L.; Goldman, M. V.; Ergun, R. E.; Boehm, M. H.
1994-01-01
Intense bursts of Langmuir waves with electric fields of 50 to 500 mV / m have been frequently observed at altitudes greater than 500 km in the auroral ionosphere. These bursts are driven by 20 eV to 4 keV field-aligned electrons, which are embedded in an approximately isotropic nonthermal tail of scattered electrons. The Langmuir bursts are often observed at altitudes where the ionosphere is moderately magnetized (OMEGA (sub e) approximately equals omega (sub pe)). Both the moderate magnetization and the scattered electrons have a major influence on the linear dispersion and damping of Langmuir waves. In particular, the linear dispersion is topologically different depending on whether the magnetic field is subcritical (OMEGA (sub e) less than omega (sub pe)) or supercritical (OMEGA (sub e) greater than omega (sub pe)). The correct dispersion and damping can account for the observed polarization of the Langmuir waves, which is very nearly parallel to the geomagnetic field. Inferred properties of the linear instability driven by the field-aligned electrons are discussed. The linear dispersion and damping derived here provide the basis for a nonlinear turbulence study described in a companion paper (Newman et al., this issue).
Asymptotic theory for Brownian semi-stationary processes with application to turbulence
Corcuera, José Manuel; Hedevang, Emil; Pakkanen, Mikko S.;
2013-01-01
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed......-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps......, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data....
Piest, Jürgen
1989-06-01
This is the first of a series of three papers which report on an theoretical turbulence investigation. In the present part, the Reynolds equation for the mean velocity field in turbulent shear flow is derived in a systematic way starting from established physical knowledge. A basic problem of contemporary turbulence theory is that, at the hydrodynamic level, there seems to be no way presently to derive systematically the initial probability distribution of the fluctuating momentum density. For this reason, N-particle statistical mechanics is employed in this investigation. The closure problem of continuum turbulence theory is avoided by this method. The technique of deriving transport equations from the Liouville equation by projection operator methods is used for the derivation. Stationary constant density/temperature processes are considered only. The dissipative term of the momemtum transport equation is analyzed in order to obtain the formulas for the laminar and turbulent friction forces. The latter is obtained as a second-order convolution in the mean velocity field. The kernel function is a time integral of an equilibrium triple correlation function; it constitutes a physical “constant” of the fluid which is needed in addition to the viscosity constant. Its calculation has been the object of a separate investigation which will be reported in the second paper. The third paper describes the numerical evaluation and comparison with experiment for the spherical case of the circular jet. In the present state, the theoretical formula does not reproduce the experimental data. This is considered a preliminary result which, in view of the systematic nature of the derivation, offers the possibility to trace it back to the spots where the theoretical structure is still not adequate.
On the theory of weak turbulence for the nonlinear Schrödinger equation
Escobedo, M
2015-01-01
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Yoon, Peter H.
2015-09-01
A previous paper [P. H. Yoon, "Kinetic theory of turbulence for parallel propagation revisited: Formal results," Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. In the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.
Yoon, Peter H., E-mail: yoonp@umd.edu [University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)
2015-09-15
A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. In the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.
Competition between shock and turbulent heating in coronal loop system
Matsumoto, Takuma
2016-11-01
2.5-dimensional magnetohydrodynamic (MHD) simulations are performed with high spatial resolution in order to distinguish between competing models of the coronal heating problem. A single coronal loop powered by Alfvén waves excited in the photosphere is the target of this study. The coronal structure is reproduced in our simulations as a natural consequence of the transportation and dissipation of Alfvén waves. Further, the coronal structure is maintained as the spatial resolution is changed from 25 to 3 km, although the temperature at the loop top increases with the spatial resolution. The heating mechanisms change gradually across the magnetic canopy at a height of 4 Mm. Below the magnetic canopy, both the shock and the MHD turbulence are dominant heating processes. Above the magnetic canopy, the shock heating rate reduces to less than 10 per cent of the total heating rate while the MHD turbulence provides significant energy to balance the radiative cooling and thermal conduction loss or gain. The importance of compressibility shown in this study would significantly impact on the prospects of successful MHD turbulence theory in the solar chromosphere.
The Contributions of A. N. Kolmogorov to the theory of turbulence
Jiménez, Javier
2004-08-01
Full Text Available Two of the papers published by Kolmogorov in 1941 are generally considered to be the origin of modern turbulence theory, including the concepts of scale similarity and of a universal inertial cascade. His third important paper, in 1962, although later superseded, was in the same way the origin of the modern investigations on intermittency. This note summarizes the history of turbulence theory before Kolmogorov, his contributions in these three papers, and his influence on the present understanding of turbulence in fluids.
Dos de los artículos publicados por Kolmogorov en 1941 son considerados generalmente como el origen de la teoría moderna de la turbulencia. Estos artículos incluyen los conceptos de semejanza de escala y de una cascada universal inercial. Su tercer artículo importante sobre el tema, publicado en 1962, es igualmente el origen de las investigaciones modernas sobre intermitencia. En esta nota se resume la historia de las teorías sobre la turbulencia antes de Kolmogorov, sus aportaciones en estos tres artículos, y su influencia sobre la comprensión actual del movimiento turbulento de los fluidos.
Magnetohydrodynamic flow and turbulence: a report on the fifth Beer-Sheva seminar
Branover, H.; Moffatt, H.K.; Mond, M.; Pierson, E.S.; Sulem, P.S.; Yakhot, A.
1988-03-01
This paper is a summary of the Fifth Beer-Sheva Seminar on Magnetohydrodynamic (MHD) Flows and Turbulence, held in Jerusalem during 2-6 March 1987, with 99 participants from 12 countries. Reviews and research papers were presented on general problems of turbulence. MHD turbulence, fundamental MHD, two-phase flows with and without magnetic fields, and on different applications of liquid-metal MHD, especially in power generation nuclear fission and fusion, and in metallurgy.
Statistical theory and transition in multiple-scale-lengths turbulence in plasmas
Itoh, Sanae-I. [Research Institute for Applied Mechanics, Kyushu Univ., Kasuga, Fukuoka (Japan); Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2001-06-01
The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale-lengths coexist. Nonlinear interactions in the same kind of fluctuations as well as nonlinear interplay between different classes of fluctuations are kept in the analysis. Nonlinear interactions are modelled as turbulent drag, nonlinear noise and nonlinear drive, and a set of Langevin equations is formulated. With the help of an Ansatz of a large number of degrees of freedom with positive Lyapunov number, Langevin equations are solved and the fluctuation dissipation theorem in the presence of strong plasma turbulence has been derived. A case where two driving mechanisms (one for micro mode and the other for semi-micro mode) coexist is investigated. It is found that there are several states of fluctuations: in one state, the micro mode is excited and the semi-micro mode is quenched; in the other state, the semi-micro mode is excited, and the micro mode remains at finite but suppressed level. New type of turbulence transition is obtained, and a cusp type catastrophe is revealed. A phase diagram is drawn for turbulence which is composed of multiple classes of fluctuations. Influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of internal transport barrier. Finally, the nonlocal heat transport due to the long-wave-length fluctuations, which are noise-pumped by shorter-wave-length ones, is analyzed and the impact on transient transport problems is discussed. (author)
Statistical theory and transition in multiple-scale-length turbulence in plasmas
Itoh, Sanae-I [Research Institute for Applied Mechanics, Kyushu University, Kasuga (Japan); Itoh, Kimitaka [National Institute for Fusion Science, Toki (Japan)
2001-08-01
The statistical theory of strong turbulence in inhomogeneous plasmas is developed for the cases where fluctuations with different scale lengths coexist. Nonlinear interactions in the same kind of fluctuations as well as nonlinear interplay between different classes of fluctuations are kept in the analysis. Nonlinear interactions are modelled as turbulent drag, nonlinear noise and nonlinear drive, and a set of Langevin equations is formulated. With the help of an Ansatz of a large number of degrees of freedom with positive Lyapunov number, Langevin equations are solved and the fluctuation dissipation theorem in the presence of strong plasma turbulence has been derived. A case where two driving mechanisms (one for the micro mode and the other for semi-micro mode) coexist is investigated. It is found that there are several states of fluctuations: in one state, the micro mode is excited and the semi-micro mode is quenched; in the other state, the semi-micro mode is excited, and the micro mode remains at finite but at a suppressed level. A new type of turbulence transition is obtained, and a cusp-type catastrophe is revealed. A phase diagram is drawn for turbulence which is composed of multiple classes of fluctuations. The influence of the inhomogeneous global radial electric field is discussed. A new insight is given for the physics of the internal transport barrier. Finally, the non-local heat transport due to the long-wavelength fluctuations, which are noise-pumped by shorter-wavelength fluctuations, is analysed and its impact on transient transport problems is discussed. (author)
Rosenblum, Erica; Traxler, Adrienne; Stellmach, Stephan
2010-01-01
Double-diffusive convection, often referred to as semi-convection in astrophysics, occurs in thermally and compositionally stratified systems which are stable according to the Ledoux-criterion but unstable according to the Schwarzchild criterion. This process has been given relatively little attention so far, and its properties remain poorly constrained. In this paper, we present and analyze a set of three-dimensional simulations of this phenomenon in a Cartesian domain under the Boussinesq approximation. We find that in some cases the double-diffusive convection saturates into a state of homogeneous turbulence, but with turbulent fluxes several orders of magnitude smaller than those expected from direct overturning convection. In other cases the system rapidly and spontaneously develops closely-packed thermo-compositional layers, which later successively merge until a single layer is left. We compare the output of our simulations with an existing theory of layer formation in the oceanographic context, and fi...
Roger Bruce Mason
2013-05-01
Full Text Available This article proposes that the external environment influences the choice of distribution tactics. Since businesses and markets are complex adaptive systems, using complexity theory to understand such environments is necessary, but it has not been widely researched. A qualitative case method using in-depth interviews investigated four successful, versus less successful, companies in turbulent versus stable environments. The results tentatively confirmed that the more successful company, in a turbulent market, sees distribution activities as less important than other aspects of the marketing mix, but uses them to stabilise customer relationships and to maintain distribution processes. These findings can benefit marketers by emphasising a new way to consider place activities. How marketers can be assisted, and suggestions for further research, are provided.
Depolarization canals and interstellar turbulence
Fletcher, A.; Shukurov, A.
Recent radio polarization observations have revealed a plethora of unexpected features in the polarized Galactic radio background that arise from propagation effects in the random (turbulent) interstellar medium. The canals are especially striking among them, a random network of very dark, narrow regions clearly visible in many directions against a bright polarized Galactic synchrotron background. There are no obvious physical structures in the ISM that may have caused the canals, and so they have been called Faraday ghosts. They evidently carry information about interstellar turbulence but only now is it becoming clear how this information can be extracted. Two theories for the origin of the canals have been proposed; both attribute the canals to Faraday rotation, but one invokes strong gradients in Faraday rotation in the sky plane (specifically, in a foreground Faraday screen) and the other only relies on line-of-sight effects (differential Faraday rotation). In this review we discuss the physical nature of the canals and how they can be used to explore statistical properties of interstellar turbulence. This opens studies of magnetized interstellar turbulence to new methods of analysis, such as contour statistics and related techniques of computational geometry and topology. In particular, we can hope to measure such elusive quantities as the Taylor microscale and the effective magnetic Reynolds number of interstellar MHD turbulence.
Ozawa, Hisashi; Shimokawa, Shinya; Sakuma, Hirofumi
Turbulence is ubiquitous in nature, yet remains an enigma in many respects. Here we investigate dissipative properties of turbulence so as to find out a statistical "law" of turbulence. Two general expressions are derived for a rate of entropy increase due to thermal and viscous dissipation (turbulent dissipation) in a fluid system. It is found with these equations that phenomenological properties of turbulence such as Malkus's suggestion on maximum heat transport in thermal convection as well as Busse's sug- gestion on maximum momentum transport in shear turbulence can rigorously be ex- plained by a unique state in which the rate of entropy increase due to the turbulent dissipation is at a maximum (dS/dt = Max.). It is also shown that the same state cor- responds to the maximum entropy climate suggested by Paltridge. The tendency to increase the rate of entropy increase has also been confirmed by our recent GCM ex- periments. These results suggest the existence of a universal law that manifests itself in the long-term statistics of turbulent fluid systems from laboratory-scale turbulence to planetary-scale circulations. Ref.) Ozawa, H., Shimokawa, S., and Sakuma, H., Phys. Rev. E 64, 026303, 2001.
Lee, Dorothy B; Faget, Maxime A
1956-01-01
A modified method of Van Driest's flat-plate theory for turbulent boundary layer has been found to simplify the calculation of local skin-friction coefficients which, in turn, have made it possible to obtain through Reynolds analogy theoretical turbulent heat-transfer coefficients in the form of Stanton number. A general formula is given and charts are presented from which the modified method can be solved for Mach numbers 1.0 to 12.0, temperature ratios 0.2 to 6.0, and Reynolds numbers 0.2 times 10 to the 6th power to 200 times 10 to the 6th power.
A theory for narrow-banded radio bursts at Uranus - MHD surface waves as an energy driver
Farrell, W. M.; Curtis, S. A.; Desch, M. D.; Lepping, R. P.
1992-01-01
A possible scenario for the generation of the narrow-banded radio bursts detected at Uranus by the Voyager 2 planetary radio astronomy experiment is described. In order to account for the emission burstiness which occurs on time scales of hundreds of milliseconds, it is proposed that ULF magnetic surface turbulence generated at the frontside magnetopause propagates down the open/closed field line boundary and mode-converts to kinetic Alfven waves (KAW) deep within the polar cusp. The oscillating KAW potentials then drive a transient electron stream that creates the bursty radio emission. To substantiate these ideas, Voyager 2 magnetometer measurements of enhanced ULF magnetic activity at the frontside magnetopause are shown. It is demonstrated analytically that such magnetic turbulence should mode-convert deep in the cusp at a radial distance of 3 RU.
Usmanov, Arcadi V.; Matthaeus, William H. [Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 (United States); Goldstein, Melvyn L., E-mail: arcadi.usmanov@nasa.gov [Code 672, NASA Goddard Space Flight Center, Greenbelt, MD 20771 (United States)
2016-03-20
We have developed a four-fluid, three-dimensional magnetohydrodynamic model of the solar wind interaction with the local interstellar medium. The unique features of the model are: (a) a three-fluid description for the charged components of the solar wind and interstellar plasmas (thermal protons, electrons, and pickup protons), (b) the built-in turbulence transport equations based on Reynolds decomposition and coupled with the mean-flow Reynolds-averaged equations, and (c) a solar corona/solar wind model that supplies inner boundary conditions at 40 au by computing solar wind and magnetic field parameters outward from the coronal base. The three charged species are described by separate energy equations and are assumed to move with the same velocity. The fourth fluid in the model is the interstellar hydrogen which is treated by separate continuity, momentum, and energy equations and is coupled with the charged components through photoionization and charge exchange. We evaluate the effects of turbulence transport and pickup protons on the global heliospheric structure and compute the distribution of plasma, magnetic field, and turbulence parameters throughout the heliosphere for representative solar minimum and maximum conditions. We compare our results with Voyager 1 observations in the outer heliosheath and show that the relative amplitude of magnetic fluctuations just outside the heliopause is in close agreement with the value inferred from Voyager 1 measurements by Burlaga et al. The simulated profiles of magnetic field parameters in the outer heliosheath are in qualitative agreement with the Voyager 1 observations and with the analytical model of magnetic field draping around the heliopause of Isenberg et al.
Energy Cascade Rate in Compressible Fast and Slow Solar Wind Turbulence
Hadid, L. Z.; Sahraoui, F.; Galtier, S.
2017-03-01
Estimation of the energy cascade rate in the inertial range of solar wind turbulence has been done so far mostly within incompressible magnetohydrodynamics (MHD) theory. Here, we go beyond that approximation to include plasma compressibility using a reduced form of a recently derived exact law for compressible, isothermal MHD turbulence. Using in situ data from the THEMIS/ARTEMIS spacecraft in the fast and slow solar wind, we investigate in detail the role of the compressible fluctuations in modifying the energy cascade rate with respect to the prediction of the incompressible MHD model. In particular, we found that the energy cascade rate (1) is amplified particularly in the slow solar wind; (2) exhibits weaker fluctuations in spatial scales, which leads to a broader inertial range than the previous reported ones; (3) has a power-law scaling with the turbulent Mach number; (4) has a lower level of spatial anisotropy. Other features of solar wind turbulence are discussed along with their comparison with previous studies that used incompressible or heuristic (nonexact) compressible MHD models.
Limits on the ions temperature anisotropy in turbulent intracluster medium
Santos-Lima, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Potsdam Univ. (Germany). Inst. fuer Physik und Astronomie; Univ. de Sao Paulo (Brazil). Inst. de Astronomia, Geofisica e Ciencias Atmosfericas; Yan, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Potsdam Univ. (Germany). Inst. fuer Physik und Astronomie; Gouveia Dal Pino, E.M. de [Univ. de Sao Paulo (Brazil). Inst. de Astronomia, Geofisica e Ciencias Atmosfericas; Lazarian, A. [Wisconsin Univ., Madison, WI (United States). Dept. of Astronomy
2016-05-15
Turbulence in the weakly collisional intracluster medium of galaxies (ICM) is able to generate strong thermal velocity anisotropies in the ions (with respect to the local magnetic field direction), if the magnetic moment of the particles is conserved in the absence of Coulomb collisions. In this scenario, the anisotropic pressure magnetohydrodynamic (AMHD) turbulence shows a very different statistical behaviour from the standard MHD one and is unable to amplify seed magnetic fields, in disagreement with previous cosmological MHD simulations which are successful to explain the observed magnetic fields in the ICM. On the other hand, temperature anisotropies can also drive plasma instabilities which can relax the anisotropy. This work aims to compare the relaxation rate with the growth rate of the anisotropies driven by the turbulence. We employ quasilinear theory to estimate the ions scattering rate due to the parallel firehose, mirror, and ion-cyclotron instabilities, for a set of plasma parameters resulting from AMHD simulations of the turbulent ICM. We show that the ICM turbulence can sustain only anisotropy levels very close to the instabilities thresholds. We argue that the AMHD model which bounds the anisotropies at the marginal stability levels can describe the Alfvenic turbulence cascade in the ICM.
The Implications of Discontinuities for Testing Theories of Turbulence in the Solar Wind
Turner, A J; Gogoberidze, G
2012-01-01
In-situ observations of magnetic field fluctuations in the solar wind show a broad continuum in the power spectral density (PSD) with a power-law range of scaling often identified as an inertial range of magnetohydrodynamic turbulence. However, both turbulence and discontinuities are present in the solar wind on these inertial range of scales. We identify and remove these discontinuities using a method which for the first time does not impose a characteristic scale on the resultant time-series. The PSD of vector field fluctuations obtained from at-a point observations is a tensor that can in principle be anisotropic with scaling exponents that depend on background field and flow direction. This provides a key test of theories of turbulence. We find that the removal of discontinuities from the observed time-series can significantly alter the PSD trace anisotropy. It becomes quasi-isotropic, in that the observed exponent does not vary with the background field angle once the discontinuities are removed. This is...
Turbulent cross-field transport of non-thermal electrons in coronal loops: theory and observations
Bian, N; McKinnon, A
2011-01-01
A fundamental problem in astrophysics is the interaction between magnetic turbulence and charged particles. It is now possible to use \\emph{Ramaty High Energy Solar Spectroscopic Imager (RHESSI)} observations of hard X-rays (HXR) emitted by electrons to identify the presence of turbulence and to estimate the magnitude of the magnetic field line diffusion coefficient at least in dense coronal flaring loops.} {We discuss the various possible regimes of cross-field transport of non-thermal electrons resulting from broadband magnetic turbulence in coronal loops. The importance of the Kubo number $K$ as a governing parameter is emphasized and results applicable in both the large and small Kubo number limits are collected.} {Generic models, based on concepts and insights developed in the statistical theory of transport, are applied to the coronal loops and to the interpretation of hard X-ray imaging data in solar flares. The role of trapping effects, which become important in the non-linear regime of transport, is ...
Coupled mode theory approach to depolarization associated with propagation in turbulent media
Crosignani, B.; di Porto, P.; Clifford, Steven F.
1988-06-01
Marcuse's (1974) coupled-mode theory is invoked in the present consideration of the problem of light depolarization in a turbulent atmosphere, in order to allow the evaluation of the depolarization ratio for a plane wave and comparison of its expression with that obtained in the frame of two distinct approaches predicting different behaviors. It is found that both approaches yield the same result when calculated to the same order in both of the relevant smallness parameters, thereby resolving a long-standing controversy.
Majda, Andrew J.; Qi, Di
2016-02-01
Turbulent dynamical systems with a large phase space and a high degree of instabilities are ubiquitous in climate science and engineering applications. Statistical uncertainty quantification (UQ) to the response to the change in forcing or uncertain initial data in such complex turbulent systems requires the use of imperfect models due to the lack of both physical understanding and the overwhelming computational demands of Monte Carlo simulation with a large-dimensional phase space. Thus, the systematic development of reduced low-order imperfect statistical models for UQ in turbulent dynamical systems is a grand challenge. This paper applies a recent mathematical strategy for calibrating imperfect models in a training phase and accurately predicting the response by combining information theory and linear statistical response theory in a systematic fashion. A systematic hierarchy of simple statistical imperfect closure schemes for UQ for these problems is designed and tested which are built through new local and global statistical energy conservation principles combined with statistical equilibrium fidelity. The forty mode Lorenz 96 (L-96) model which mimics forced baroclinic turbulence is utilized as a test bed for the calibration and predicting phases for the hierarchy of computationally cheap imperfect closure models both in the full phase space and in a reduced three-dimensional subspace containing the most energetic modes. In all of phase spaces, the nonlinear response of the true model is captured accurately for the mean and variance by the systematic closure model, while alternative methods based on the fluctuation-dissipation theorem alone are much less accurate. For reduced-order model for UQ in the three-dimensional subspace for L-96, the systematic low-order imperfect closure models coupled with the training strategy provide the highest predictive skill over other existing methods for general forced response yet have simple design principles based on a
M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence.
Alexakis, Alexandros; Mininni, Pablo D; Pouquet, Annick
2005-10-01
We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional magnetohydrodynamics (MHD) turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from large scales to kinetic energy at smaller scales and the transfer of magnetic energy from large scales to magnetic energy at smaller scales are local, as is also found in the case of neutral fluids and in a way that is compatible with the Kolmogorov theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly nonlocal process in Fourier space. Energy from the velocity field at large scales can be transferred directly into small-scale magnetic fields without the participation of intermediate scales. Some implications of our results to MHD turbulence modeling are also discussed.
Shell Models of Magnetohydrodynamic Turbulence
Plunian, Franck; Frick, Peter
2012-01-01
Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accu...
Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence
Wu Feng
2007-01-01
Main mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence are presented and discussed. The underlying fact is that there does not exist the absolute zero fluid-volume. Therefore, the physical object corresponding to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, while the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one is based on the absolute point, and the other based on the monad. The former is adopted in the Navier-Stokes equations, and the latter in the fundamental equations presented in this paper for the nonstandard analysis theory of turbulence. The continuity of fluid is elucidated by virtue of the concepts of the fluid-particle and fluid-particle at a lower level. Furthermore, the characters of the continuity in two cases, i.e. in the standard and nonstandard analyses, are presented in this paper. And the difference in discretization between the Navier-Stokes equations and the fundamental equations given herein is also pointed out.
Pessah, Martin Elias
2010-01-01
The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its nonlinear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions i...
Pessah, Martin Elias
2010-01-01
The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its nonlinear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions i...
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Planetary migration in weakly magnetized turbulent discs
Baruteau, C.; Fromang, S.; Nelson, R. P.; Masset, F.
2011-12-01
In laminar viscous disc models, the migration of protoplanets embedded in their nascent protoplanetary discs may be directed inwards or outwards, depending on the relative magnitude of the Lindblad and corotation torques. The long-term evolution of the corotation torque is intimately related to diffusion processes inside the planet's horseshoe region. This communication examines the properties of the corotation torque in discs where magnetohydrodynamic (MHD) turbulence develops as a result of the magnetorotational instability (MRI), considering a weak initial toroidal magnetic field. We show that the differential Lindblad torque takes very similar values in MHD turbulent and laminar viscous discs, and there exists an unsaturated corotation torque in MHD turbulent discs.
Information Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence
Massimo Materassi
2014-02-01
Full Text Available The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k, so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive.
Statistical theory of subcritically-excited strong turbulence in inhomogeneous plasmas. V
Itoh, Sanae-I. [Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka (Japan); Itoh, Kimitaka [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-10-01
A statistical theory of strong plasma turbulence in nonlinear-nonequilibrium state is extended. By use of the spectral decomposition method, the renormalized propagator is decomposed into the projection operators. The decomposition of fluctuation fields into the least stable branch and other branches is explicitly made. The extended fluctuation dissipation theorem is derived for each decomposed renormalized mode. The decorrelation rate, eddy damping rate, fluctuation level and correlation functions are obtained even in the case that the cross-correlation functions and auto-correlation functions are of the same order of magnitude. The Fokker-Planck equation is reformulated for fluctuation components of each branch. These results are generalization of the previous result. It is confirmed that the solutions, probability distribution function and related transition probability which have been obtained in previous analyses are found valid apart from a numerical coefficient of the order of unity. In order to show the wider applicability, a case of plasma turbulence which is described by the four-field reduced set of equations is also discussed. (author)
2006-09-01
Aerospace Applications, AIAA-Paper 96-2355, New Orleans, 1996 2. V.A.Bityurin, A.N.Bocharov, J.Lineberry, MHD Aerospace Applications, Invited Lecture ...Paper 2003- 4303, Orlando, FL 8. V.A.Bityurin, Prospective of MHD Interaction in Hypersonic and Propulsion Technologies, In: von Karman Series : Lectures ...Efforts in MHD AeoSpace Applications, In: von Karman Series : Lectures , Introduction of Magneto-Fluid Dynamics for AeroSpace Applications, von Karman
Rica, Sergio
2016-01-01
The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general relativity. This nonlinear wave interaction allows the spectral energy transfer from mode to mode. According to the wave turbulence theory, the weakly nonlinear interaction of gravitational waves leads to the existence of an irreversible kinetic regime that dominates the longtime evolution. The resulting kinetic equation suggests the existence of an equilibrium wave spectrum and the existence of a non-equilibrium Kolmogorov-Zakharov spectrum for spatio-temporal fluctuations. Evidence of these solutions extracted in the fluctuating signal of the recent observations will be discussed in the paper. Probably, the present results would be pertinent in the new age of development of gravitational astronomy, as well as, in new tests of General Relativity.
Dispersion of swimming algae in laminar and turbulent channel flows: theory and simulations
Croze, O A; Ahmed, M; Bees, M A; Brandt, L
2012-01-01
Algal swimming is often biased by environmental cues, e.g. gravitational and viscous torques drive cells towards downwelling fluid (gyrotaxis). In view of biotechnological applications, it is important to understand how such biased swimming affects cell dispersion in a flow. Here, we study the dispersion of gyrotactic swimming algae in laminar and turbulent channel flows. By direct numerical simulation (DNS) of cell motion within upwelling and downwelling channel flows, we evaluate time-dependent measures of dispersion for increasing values of the flow Peclet (Reynolds) numbers, Pe (Re). Furthermore, we derive an analytical `swimming Taylor-Aris dispersion' theory, using flow-dependent transport parameters given by existing microscopic models. In the laminar regime, DNS results and analytical predictions compare very well, providing the first confirmation that cells' response to flow is best described by the generalized-Taylor-dispersion microscopic model. We predict that cells drift along a channel faster th...
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
A formal derivation of the local energy transfer (LET) theory of homogeneous turbulence
McComb, W. D.; Yoffe, S. R.
2017-09-01
A statistical closure of the Navier-Stokes hierarchy which leads to equations for the two-point, two-time covariance of the velocity field for stationary, homogeneous isotropic turbulence is presented. It is a generalisation of the self-consistent field method due to Edwards (1964) for the stationary, single-time velocity covariance. The probability distribution functional P≤ft[\\mathbf{u},t\\right] is obtained, in the form of a series, from the Liouville equation by means of a perturbation expansion about a Gaussian distribution, which is chosen to give the exact two-point, two-time covariance. The triple moment is calculated in terms of an ensemble-averaged infinitesimal velocity-field propagator, and shown to yield the Edwards result as a special case. The use of a Gaussian zero-order distribution has been found to justify the introduction of a fluctuation-response relation, which is in accord with modern dynamical theories. In a sense this work completes the analogy drawn by Edwards between turbulence and Brownian motion. Originally Edwards had shown that the noise input was determined by the correlation of the velocity field with the externally applied stirring forces but was unable to determine the system response. Now we find that the system response is determined by the correlation of the velocity field with internal quasi-entropic forces. This analysis is valid to all orders of perturbation theory, and allows the recovery of the local energy transfer (LET) theory, which had previously been derived by more heuristical methods. The LET theory is known to be in good agreement with experimental results. It is also unique among two-point statistical closures in displaying an acceptable (i.e. non-Markovian) relationship between the transfer spectrum and the system response, in accordance with experimental results. As a result of the latter property, it is compatible with the Kolmogorov (K41) spectral phenomenology. In memory of Professor Sir Sam Edwards F
Drake, D J; Howes, G G; Kletzing, C A; Skiff, F; Carter, T A; Auerbach, D W
2013-01-01
Turbulence is a phenomenon found throughout space and astrophysical plasmas. It plays an important role in solar coronal heating, acceleration of the solar wind, and heating of the interstellar medium. Turbulence in these regimes is dominated by Alfven waves. Most turbulence theories have been established using ideal plasma models, such as incompressible MHD. However, there has been no experimental evidence to support the use of such models for weakly to moderately collisional plasmas which are relevant to various space and astrophysical plasma environments. We present the first experiment to measure the nonlinear interaction between two counterpropagating Alfven waves, which is the building block for astrophysical turbulence theories. We present here four distinct tests that demonstrate conclusively that we have indeed measured the daughter Alfven wave generated nonlinearly by a collision between counterpropagating Alfven waves.
CUDA Simulation of Homogeneous, Incompressible Turbulence
Morin, Lee; Shebalin, John V.; Shum, Victor; Fu, Terry
2011-01-01
We discuss very fast Compute Unified Device Architecture (CUDA) simulations of ideal homogeneous incompressible turbulence based on Fourier models. These models have associated statistical theories that predict that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. Prior numerical simulations have shown that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We review the theoretical basis of this "broken ergodicity" as applied to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence. Our new simulations examine the phenomenon of broken ergodicity through very long time and large grid size runs performed on a state-of-the-art CUDA platform. Results comparing various CUDA hardware configurations and grid sizes are discussed. NS and MHD results are compared.
Theory to predict shear stress on cells in turbulent blood flow.
Morshed, Khandakar Niaz; Bark, David; Forleo, Marcio; Dasi, Lakshmi Prasad
2014-01-01
Shear stress on blood cells and platelets transported in a turbulent flow dictates the fate and biological activity of these cells. We present a theoretical link between energy dissipation in turbulent flows to the shear stress that cells experience and show that for the case of physiological turbulent blood flow: (a) the Newtonian assumption is valid, (b) turbulent eddies are universal for the most complex of blood flow problems, and (c) shear stress distribution on turbulent blood flows is possibly universal. Further we resolve a long standing inconsistency in hemolysis between laminar and turbulent flow using the theoretical framework. This work demonstrates that energy dissipation as opposed to bulk shear stress in laminar or turbulent blood flow dictates local mechanical environment of blood cells and platelets universally.
Procaccia, I
1995-01-01
The lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in the literature and there is no real need to reproduce them here. Quite on the contrary, some of the basic tools of the field and theoretical techniques are not available in a pedagogical format, and it seems worthwhile to present them here for the benefit of the interested student. We begin with a detailed exposition of the naive perturbation theory for the ensemble averages of hydrodynamic observables (the mean velocity, the response functions and the correlation functions). The effective expansion parameter in such a theory is the Reynolds number (Re); one needs therefore to perform infinite resummations to change the effective expansion parameter. We present in detail the Dyson-Wyld line resummation which allows one to dress the propagators, and to change the effective expansion parameter from Re to O(1). Next w...
The Aharonov-Bohm effect in a spatially confining theory based on a turbulent fluid
Antonov, Dmitri
2012-01-01
Wilson loops in a turbulent fluid are shown to respect a specific area law corresponding to the Kolmogorov scaling. This law leads to the condensation of a complex-valued scalar field minimally coupled to the velocity field. We use this finding to estimate a v.e.v. of the dual Higgs field, which appears in the hydrodynamic description of a spatially confining dual Landau-Ginzburg theory. The temperature dependence of all other parameters of this theory is found upon a comparison with the spatial string tension and the chromo-magnetic vacuum correlation length of the Yang-Mills gluon plasma. In particular, a nonperturbative contribution to the shear viscosity of the dual fluid comes out exponentially suppressed with temperature. Interactions of the dual Abrikosov vortices with excitations of the fluid yield a long-range Aharonov-Bohm effect. This effect is shown to take place for all but calculated discrete values of the product of the kinematic viscosity of the fluid to the coupling constant of the dual Higgs...
Kinetics of a network of vortex loops in He II and a theory of superfluid turbulence
Nemirovskii, Sergey K.
2008-06-01
A theory is developed to describe the superfluid turbulence on the base of kinetics of the merging and splitting vortex loops. Because of very frequent reconnections the vortex loops (as a whole) do not live long enough to perform any essential evolution due to the deterministic motion. On the contrary, they rapidly merge and split, and these random recombination processes prevail over other slower dynamic processes. To develop quantitative description we take the vortex loops to have a Brownian structure with the only degree of freedom, which is the length l of the loop. We perform investigation on the base of the Boltzmann type “kinetic equation” for the distribution function n(l) of number of loops with length l . This equation describes a slow change of the density of loops (in space of their lengths l ) due to the deterministic equation of motion and due to fast random change because of the frequent reconnections. By use of the special ansatz in the “collision” integral, we have found the exact power-like solution n(l)∝l-5/2 of “kinetic equation” in the stationary case. This solution is not (thermodynamically) equilibrium, but on the contrary, it describes the state with two mutual fluxes of the length (or energy) in space of sizes of the vortex loops. The term “flux” means just redistribution of length (or energy) among the loops of different sizes due to reconnections. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the turbulent superfluid helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space. We also evaluated the full rate of the reconnection events. Assuming, further, that the processes of random collisions are the fastest ones, we studied the evolution of full length of vortex loops per unit volume—the so-called vortex line density L(t) . It is shown this evolution to obey the famous Vinen equation. The properties of the Vinen
Magnetohydrodynamic flows and turbulence: a report on the Fourth Beer-Sheva seminar
Branover, H.; Mond, M. (Ben-Gurion Univ. of the Negev, Beersheba (Israel). Dept. of Mechanical Engineering); Pierson, E.S. (Purdue Univ. Calumet, Hammond, IN (USA)); Walker, J.S. (Illinois Univ., Urbana (USA))
1984-11-01
This paper is a summary of the Fourth Beer-Sheva Seminar on Magnetohydrodynamic (MHD) Flows and Turbulence held in Israel during 27 February-2 March 1984 with 67 participants from 13 countries. Reviews and contributed papers were presented on laminar and turbulent single-phase and two-phase MHD flows, turbulent and two-phase flows without magnetic fields, and applications of MHD in power generation, in nuclear fission and fusion and in metallurgy.
Rincon, F; Schekochihin, A A; Rieutord, M
2016-01-01
The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov scaling theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly a...
Muñoz-Jaramillo, Andrés; Martens, Petrus C H
2010-01-01
The turbulent magnetic diffusivity in the solar convection zone is one of the most poorly constrained ingredients of mean-field dynamo models. This lack of constraint has previously led to controversy regarding the most appropriate set of parameters, as different assumptions on the value of turbulent diffusivity lead to radically different solar cycle predictions. Typically, the dynamo community uses double step diffusivity profiles characterized by low values of diffusivity in the bulk of the convection zone. However, these low diffusivity values are not consistent with theoretical estimates based on mixing-length theory -- which suggest much higher values for turbulent diffusivity. To make matters worse, kinematic dynamo simulations cannot yield sustainable magnetic cycles using these theoretical estimates. In this work we show that magnetic cycles become viable if we combine the theoretically estimated diffusivity profile with magnetic quenching of the diffusivity. Furthermore, we find that the main featur...
Gibson, C H
1999-01-01
A theory of fossil turbulence presented in the 11th Liege Colloquium on Marine turbulence is "revisited" in the 29th Liege Colloquium "Marine Turbulence Revisited". The Gibson (1980) theory applied universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as it is constrained and fossilized by buoyancy forces. Towed oceanic microstructure measurements of Schedvin (1979) confirmed the predicted universal constants. Universal constants, spectra, hydrodynamic phase diagrams (HPDs) and other predictions of the theory have been reconfirmed by a wide variety of field and laboratory observations. Fossil turbulence theory has many applications; for example, in marine biology, laboratory and field measurements suggest phytoplankton species with different swimming abilities adjust their growth strategies differently by pattern recognition of several days of turbulence-fossil-turbulence dissipation and persistence times above thres...
Rincon, F.; Roudier, T.; Schekochihin, A. A.; Rieutord, M.
2017-03-01
The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future high-resolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.
Limits on the ion temperature anisotropy in the turbulent intracluster medium
Santos-Lima, R.; Yan, H.; de Gouveia Dal Pino, E. M.; Lazarian, A.
2016-08-01
Turbulence in the weakly collisional intracluster medium (ICM) of galaxies is able to generate strong thermal velocity anisotropies in the ions (with respect to the local magnetic field direction), if the magnetic moment of the particles is conserved in the absence of Coulomb collisions. In this scenario, the anisotropic pressure magnetohydrodynamic (AMHD) turbulence shows a very different statistical behaviour from the standard MHD one and is unable to amplify seed magnetic fields. This is in contrast to previous cosmological MHD simulations that are successful in explaining the observed magnetic fields in the ICM. On the other hand, temperature anisotropies can also drive plasma instabilities that can relax the anisotropy. This work aims to compare the relaxation rate with the growth rate of the anisotropies driven by the turbulence. We employ quasi-linear theory to estimate the ion scattering rate resulting from the parallel firehose, mirror and ion-cyclotron instabilities, for a set of plasma parameters resulting from AMHD simulations of the turbulent ICM. We show that the ICM turbulence can sustain only anisotropy levels very close to the instability thresholds. We argue that the AMHD model that bounds the anisotropies at the marginal stability levels can describe the Alfvénic turbulence cascade in the ICM.
Lattice Boltzmann Large Eddy Simulation Model of MHD
Flint, Christopher
2016-01-01
The work of Ansumali \\textit{et al.}\\cite{Ansumali} is extended to Two Dimensional Magnetohydrodynamic (MHD) turbulence in which energy is cascaded to small spatial scales and thus requires subgrid modeling. Applying large eddy simulation (LES) modeling of the macroscopic fluid equations results in the need to apply ad-hoc closure schemes. LES is applied to a suitable mesoscopic lattice Boltzmann representation from which one can recover the MHD equations in the long wavelength, long time scale Chapman-Enskog limit (i.e., the Knudsen limit). Thus on first performing filter width expansions on the lattice Boltzmann equations followed by the standard small Knudsen expansion on the filtered lattice Boltzmann system results in a closed set of MHD turbulence equations provided we enforce the physical constraint that the subgrid effects first enter the dynamics at the transport time scales. In particular, a multi-time relaxation collision operator is considered for the density distribution function and a single rel...
Magnetohydrodynamic turbulence: Observation and experiment
Brown, M. R.; Schaffner, D. A.; Weck, P. J. [Department of Physics and Astronomy, Swarthmore College, 500 College Avenue, Swarthmore, Pennsylvania 19081 (United States)
2015-05-15
We provide a tutorial on the paradigms and tools of magnetohydrodynamic (MHD) turbulence. The principal paradigm is that of a turbulent cascade from large scales to small, resulting in power law behavior for the frequency power spectrum for magnetic fluctuations E{sub B}(f). We will describe five useful statistical tools for MHD turbulence in the time domain: the temporal autocorrelation function, the frequency power spectrum, the probability distribution function of temporal increments, the temporal structure function, and the permutation entropy. Each of these tools will be illustrated with an example taken from MHD fluctuations in the solar wind. A single dataset from the Wind satellite will be used to illustrate all five temporal statistical tools.
Turbulence theory and infrared images falsify the 2011 Nobel Prize in Physics
Gibson, Carl
2012-11-01
Turbulence defined by the inertial vortex force explains Planck scale big bang processes as temporary, rendering a permanent Einstein cosmological constant Λ and a positive expansion rate of the universe driven by anti-gravitational dark energy forces unnecessary. Large kinematic viscosity stresses during the plasma epoch from 1011 s to 1013 s cause fragmentation by proto-super-cluster-voids at 1012 s and proto-galaxies at the 1013 s transition to gas. Fragmentation of gas proto-galaxies is at Earth-mass planet viscous scales in Jeans mass clumps of a trillion planets. These Proto-Globular-star-Clusters (PGCs) freeze to form the dark matter of galaxies according to the Gibson (1996) Hydro-Gravitational-Dynamics (HGD) theory, and as observed by Schild (1996) by quasar microlensing. White dwarf carbon stars explode as Supernovae Ia events (SNeIa) when their mass increases to 1.44 solar, providing the standard candles used to justify the Nobel Prize claim of a positive expansion rate. However, if all stars form from primordial planet mergers in PGC clumps as claimed by HGD cosmology, the SNeIa become subject to a systematic dimming error depending on the line of sight to the event. New space telescope infrared images strongly support HGD cosmology.
Nonlocal bottleneck effect in two-dimensional turbulence
Biskamp, D; Schwarz, E
1998-01-01
The bottleneck pileup in the energy spectrum is investigated for several two-dimensional (2D) turbulence systems by numerical simulation using high-order diffusion terms to amplify the effect, which is weak for normal diffusion. For 2D magnetohydrodynamic (MHD) turbulence, 2D electron MHD (EMHD) turbulence and 2D thermal convection, which all exhibit direct energy cascades, a nonlocal behavior is found resulting in a logarithmic enhancement of the spectrum.
Han, Jongil; Arya, S. Pal; Shaohua, Shen; Lin, Yuh-Lang; Proctor, Fred H. (Technical Monitor)
2000-01-01
Algorithms are developed to extract atmospheric boundary layer profiles for turbulence kinetic energy (TKE) and energy dissipation rate (EDR), with data from a meteorological tower as input. The profiles are based on similarity theory and scalings for the atmospheric boundary layer. The calculated profiles of EDR and TKE are required to match the observed values at 5 and 40 m. The algorithms are coded for operational use and yield plausible profiles over the diurnal variation of the atmospheric boundary layer.
Schnack, Dalton D.
In this lecture we will examine some simple examples of MHD equilibrium configurations. These will all be in cylindrical geometry. They form the basis for more complicated equilibrium states in toroidal geometry.
Hodograph method in MHD orthogonal fluid flows
P. V. Nguyen
1992-01-01
Full Text Available Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.
Polarimetric studies of magnetic turbulence with interferometer
Lee, Hyeseung; Cho, Jungyeon
2016-01-01
We study statistical properties of synchrotron polarization emitted from media with magnetohydrodynamic (MHD) turbulence. We use both synthetic and MHD turbulence simulation data for our studies. We obtain the spatial spectrum and its derivative with respect to wavelength of synchrotron polarization arising from both synchrotron radiation and Faraday rotation fluctuations. In particular, we investigate how the spectrum changes with frequency. We find that our simulations agree with the theoretical predication in Lazarian \\& Pogosyan (2016). We conclude that the spectrum of synchrotron polarization and it derivative can be very informative tools to get detailed information about the statistical properties of MHD turbulence from radio observations of diffuse synchrotron polarization. Especially, they are useful to recover the statistics of turbulent magnetic field as well as turbulent density of electrons. We also simulate interferometric observations that incorporate the effects of noise and finite telesco...
Turbulent Plasmoid Reconnection
Widmer, Fabien; Yokoi, Nobumitsu
2016-01-01
The plasmoid instability may lead to fast magnetic reconnection through long current sheets(CS). It is well known that large-Reynolds-number plasmas easily become turbulent. We address the question whether turbulence enhances the energy conversion rate of plasmoid-unstable current sheets. We carry out appropriate numerical MHD simulations, but resolving simultaneously the relevant large-scale (mean-) fields and the corresponding small-scale, turbulent, quantities by means of direct numerical simulations (DNS) is not possible. Hence we investigate the influence of small scale turbulence on large scale MHD processes by utilizing a subgrid-scale (SGS) turbulence model. We verify the applicability of our SGS model and then use it to investigate the influence of turbulence on the plasmoid instability. We start the simulations with Harris-type and force-free CS equilibria in the presence of a finite guide field in the direction perpendicular to the reconnection plane. We use the DNS results to investigate the growt...
The Solar Wind as a Turbulence Laboratory
Vincenzo Carbone
2013-05-01
Full Text Available In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses' high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.
Statistical properties of transport in plasma turbulence
Naulin, V.; Garcia, O.E.; Nielsen, A.H.;
2004-01-01
The statistical properties of the particle flux in different types of plasma turbulence models are numerically investigated using probability distribution functions (PDFs). The physics included in the models range from two-dimensional drift wave turbulence to three-dimensional MHD dynamics...
胡隐樵; 陈晋北; 吕世华
2012-01-01
The turbulence is one of the ubiquitous natural phenomena in everyday experience,and a puzzle that is not yet fully resolved in classical physics.All the more so,it is a basic characteristic of the atmospheric motion.This paper reviews by the numbers the develop history of classic theory of atmospheric turbulence,further more introduces detailedly the nonequilibrium thermodynamic theory of atmospheric turbulence.In the nonequilibrium thermodynamic theory of atmospheric turbulence,the entropy equilibrium equation of atmospheric system with dynamic processes is introduced,and then Fourier′s and Flick′s laws,Newton′s Law deducted by,and both the Dufour and the Soret effects,the cross coupling effect between the dynamic and turbulent transport processes in the atmosphere,and the turbulent intensity theorem are uniformly proved by atmospheric nonequilibrium thermodynamics.These laws and theorem are partially validated by using observed data,further to determine their phenomenological coefficients.The turbulent intensity theorem reveals that the macroscopic cause of the development of fluid turbulence is a result of the shearing effects of velocity together with temperature and proves that both Reynolds turbulence and Rayleigh-Bé nard turbulence coexist in the atmosphere.The discovery of the coupling effect phenomenon between the thermodynamic and dynamic processes breaks through the viewpoint of the theories of traditional turbulent transport,Fourier′s and Flick′s laws,and Newton′s Law,i.e.,the transport flux of one kind of macroscopic quantity is equivalent to the gradient turbulent transport flux of this macroscopic quantity.Moreover,the coupling principle between the thermodynamic and dynamic processes deems that the transport flux of one kind of macroscopic quantity should include the velocity coupling transport in addition to the gradient turbulent transport flux of this macroscopic quantity.Consequently,the vertical transport flux of energy and matter
Kolesnikov, R.A.; Krommes, J.A.
2005-09-22
The collisionless limit of the transition to ion-temperature-gradient-driven plasma turbulence is considered with a dynamical-systems approach. The importance of systematic analysis for understanding the differences in the bifurcations and dynamics of linearly damped and undamped systems is emphasized. A model with ten degrees of freedom is studied as a concrete example. A four-dimensional center manifold (CM) is analyzed, and fixed points of its dynamics are identified and used to predict a ''Dimits shift'' of the threshold for turbulence due to the excitation of zonal flows. The exact value of that shift in terms of physical parameters is established for the model; the effects of higher-order truncations on the dynamics are noted. Multiple-scale analysis of the CM equations is used to discuss possible effects of modulational instability on scenarios for the transition to turbulence in both collisional and collisionless cases.
Nonlinear MHD dynamo operating at equipartition
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims.We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider...... the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods.We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results.We find that this dynamo has a high growth rate in the linear regime...
Statistical theory of reversals in two-dimensional confined turbulent flows
Shukla, Vishwanath; Brachet, Marc
2016-01-01
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined 2D Navier-Stokes flow with bottom friction and a spatially periodic forcing. In particular, the random reversals of the large scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation velocity that are described by the related microcanonical distribution which displays transitions from gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.
Jurčišinová, E; Jurčišin, M; Remecký, R
2011-10-01
The turbulent magnetic Prandtl number in the framework of the kinematic magnetohydrodynamic (MHD) turbulence, where the magnetic field behaves as a passive vector field advected by the stochastic Navier-Stokes equation, is calculated by the field theoretic renormalization group technique in the two-loop approximation. It is shown that the two-loop corrections to the turbulent magnetic Prandtl number in the kinematic MHD turbulence are less than 2% of its leading order value (the one-loop value) and, at the same time, the two-loop turbulent magnetic Prandtl number is the same as the two-loop turbulent Prandtl number obtained in the corresponding model of a passively advected scalar field. The dependence of the turbulent magnetic Prandtl number on the spatial dimension d is investigated and the source of the smallness of the two-loop corrections for spatial dimension d=3 is identified and analyzed.
Multifluid magnetohydrodynamic turbulent decay
Downes, Turlough P
2011-01-01
It is generally believed that turbulence has a significant impact on the dynamics and evolution of molecular clouds and the star formation which occurs within them. Non-ideal magnetohydrodynamic effects are known to influence the nature of this turbulence. We present the results of a suite of 512-cubed resolution simulations of the decay of initially super-Alfvenic and supersonic fully multifluid MHD turbulence. We find that ambipolar diffusion increases the rate of decay of the turbulence while the Hall effect has virtually no impact. The decay of the kinetic energy can be fitted as a power-law in time and the exponent is found to be -1.34 for fully multifluid MHD turbulence. The power spectra of density, velocity and magnetic field are all steepened significantly by the inclusion of non-ideal terms. The dominant reason for this steepening is ambipolar diffusion with the Hall effect again playing a minimal role except at short length scales where it creates extra structure in the magnetic field. Interestingl...
Dynamics of Turbulence-generated E × B Flows: Simulation and Theory
Hahm, T. S.
1998-11-01
Many magnetic confinement experiments have indicated that E × B shear can suppress turbulence and consequently lead to significant reduction of plasma transport.^1 It has been observed in flux-tube gyrofluid^2,3 and gyrokinetic^4 simulations that small radial scale fluctuating E × B flows driven by turbulence (often called radial modes,^3 or zonal flows) play a dominant role in regulating toroidal ITG (ion temperature gradient) turbulence. Furthermore, the radial modes with similar characteristics and significant impact on transport have been also observed in the recent global gyrokinetic simulations with improved numerical capabilities^5 as well as in edge turbulence simulations with a collisional poloidal flow damping.^6 In this work, we analyze turbulence and flow statistics from gyrofluid and gyrokinetic simulations and compare to various theoretical predictions. The observed radial modes contain significant components with radial scales and frequencies comparable to those of turbulence. While the fast time varying components (including Geodesic Acoustic Modes) contribute the most to the instantaneous E × B shearing rate, they are less influential in suppressing turbulence. The effective E × B shearing rate capturing this important physics is analytically derived and evaluated from the recent nonlinear simulation results. Its magnitude is much smaller than the instantaneous E × B shearing rate, but typically of the order of the decorrelation rate of the ambient turbulence. This is consistent with the reduced, not completely stabilized level of turbulence with broadened kr spectrum observed in simulations. Zonal flows are linearly stable, but can be generated either by incoherent emission of turbulence or by inverse cascade of spectrum yielding negative turbulent viscosity which is related to the Reynolds' stress.^7 Various analytical calculations and proposed mechanisms for zonal flow generation and saturation^7,8 will be tested numerically. Finally, the
Using Coronal Hole Maps to Constrain MHD Models
Caplan, Ronald M.; Downs, Cooper; Linker, Jon A.; Mikic, Zoran
2017-08-01
In this presentation, we explore the use of coronal hole maps (CHMs) as a constraint for thermodynamic MHD models of the solar corona. Using our EUV2CHM software suite (predsci.com/chd), we construct CHMs from SDO/AIA 193Å and STEREO-A/EUVI 195Å images for multiple Carrington rotations leading up to the August 21st, 2017 total solar eclipse. We then contruct synoptic CHMs from synthetic EUV images generated from global thermodynamic MHD simulations of the corona for each rotation. Comparisons of apparent coronal hole boundaries and estimates of the net open flux are used to benchmark and constrain our MHD model leading up to the eclipse. Specifically, the comparisons are used to find optimal parameterizations of our wave turbulence dissipation (WTD) coronal heating model.
Using Faraday Rotation to Probe MHD Instabilities in Intracluster Media
Bogdanovic, Tamara; Massey, Richard
2010-01-01
It has recently been suggested that conduction-driven magnetohydrodynamic (MHD) instabilities may operate at all radii within an intracluster medium (ICM), and profoundly affect the structure of a cluster's magnetic field. Where MHD instabilities dominate the dynamics of an ICM, they will re-orient magnetic field lines perpendicular to the temperature gradient inside a cooling core, or parallel to the temperature gradient outside it. This characteristic structure of magnetic field could be probed by measurements of polarized radio emission from background sources. Motivated by this possibility we have constructed 3-d models of a magnetized cooling core cluster and calculated Faraday rotation measure (RM) maps in the plane of the sky under realistic observing conditions. We compare a scenario in which magnetic field geometry is characterized by conduction driven MHD instabilities to that where it is determined by the turbulent motions. We find that future high-sensitivity spectro-polarimetric measurements of R...
Lectures in magnetohydrodynamics. With an appendix on extended MHD
Schnack, Dalton D. [Wisconsin Univ., Madison, WI (United States). Dept. Physics
2009-07-01
This concise and self-contained primer is based on class-tested notes for an advanced graduate course in MHD. The broad areas chosen for presentation are the derivation and properties of the fundamental equations, equilibrium, waves and instabilities, self-organization, turbulence, and dynamos. The latter topics require the inclusion of the effects of resistivity and nonlinearity. Together, these span the range of MHD issues that have proven to be important for understanding magnetically confined plasmas as well as in some space and astrophysical applications. The combined length and style of the thirty-eight lectures are appropriate for complete presentation in a single semester. An extensive appendix on extended MHD is included as further reading. (orig.)
Validation of a Pseudo-Sound Theory for the Pressure-Dilatation in DNS of Compressible Turbulence
Ristorcelli, J. R.; Blaisdell, G. A.
1997-01-01
The results of an asymptotic theory for statistical closures for compressible turbulence are explored and validated with the direct numerical simulation of the isotropic decay and the homogeneous shear. An excellent collapse of the data is seen. The slow portion is found to scale, as predicted by the theory, with the quantity M(sub t)(sup 2) and epsilon(sub s). The rapid portion has an unambiguous scaling with alpha(sup 2)M(sub t)(sup s)epsilon(sub s)[P(sub k)/epsilon - l](Sk/epsilon)(sup 2). Implicit in the scaling is a dependence, as has been noted by others, on the gradient Mach number. A new feature of the effects of compressibility, that of the Kolmogorov scaling coefficient, alpha, is discussed. It is suggested that alpha may contain flow specific physics associated with large scales that might provide further insight into the structural effects of compressibility.
Bruno, Roberto
2016-01-01
This book provides an overview of solar wind turbulence from both the theoretical and observational perspective. It argues that the interplanetary medium offers the best opportunity to directly study turbulent fluctuations in collisionless plasmas. In fact, during expansion, the solar wind evolves towards a state characterized by large-amplitude fluctuations in all observed parameters, which resembles, at least at large scales, the well-known hydrodynamic turbulence. This text starts with historical references to past observations and experiments on turbulent flows. It then introduces the Navier-Stokes equations for a magnetized plasma whose low-frequency turbulence evolution is described within the framework of the MHD approximation. It also considers the scaling of plasma and magnetic field fluctuations and the study of nonlinear energy cascades within the same framework. It reports observations of turbulence in the ecliptic and at high latitude, treating Alfvénic and compressive fluctuations separately in...
Schertzer, D.; Falgarone, E.
appropriate editorial structure, in particular a large number of editors covering a wide range of methodologies, expertises and schools. At least two of its sections (Scaling and Multifractals, Turbulence and Diffusion) were directly related to the topics of the workshop, in any case contributors were invited to choose their editor freely. 2 Goals of the Workshop The objective of this meeting was to enhance the confrontation between turbulence theories and empirical data from geophysics and astrophysics fluids with very high Reynolds numbers. The importance of these data seems to have often been underestimated for the evaluation of theories of fully developed turbulence, presumably due to the fact that turbulence does not appear as pure as in laboratory experiments. However, they have the great advantage of giving access not only to very high Reynolds numbers (e.g. 1012 for atmospheric data), but also to very large data sets. It was intended to: (i) provide an overview of the diversity of potentially available data, as well as the necessary theoretical and statistical developments for a better use of these data (e.g. treatment of anisotropy, role of processes which induce other nonlinearities such as thermal instability, effect of magnetic field and compressibility ... ), (ii) evaluate the means of discriminating between different theories (e.g. multifractal intermittency models) or to better appreciate the relevance of different notions (e.g. Self-Organized Criticality) or phenomenology (e.g. filaments, structures), (iii) emphasise the different obstacles, such as the ubiquity of catastrophic events, which could be overcome in the various concerned disciplines, thanks to theoretical advances achieved. 3 Outlines of the Workshop During the two days of the workshop, the series of presentations covered many manifestations of turbulence in geophysics, including: oceans, troposphere, stratosphere, very high atmosphere, solar wind, giant planets, interstellar clouds... up to the
Turner, A J; Gogoberidze, G; Chapman, S C
2012-02-24
Single point spacecraft observations of the turbulent solar wind flow exhibit a characteristic nonaxisymmetric anisotropy that depends sensitively on the perpendicular power spectral exponent. We use this nonaxisymmetric anisotropy as a function of wave vector direction to test models of MHD turbulence. Using Ulysses magnetic field observations in the fast, quiet polar solar wind we find that the Goldreich-Sridhar model of MHD turbulence is not consistent with the observed anisotropy, whereas the observations are well reproduced by the "slab+2D" model. The Goldreich-Sridhar model alone cannot account for the observations unless an additional component is also present.
Spectral properties of electromagnetic turbulence in plasmas
D. Shaikh
2009-03-01
Full Text Available We report on the nonlinear turbulent processes associated with electromagnetic waves in plasmas. We focus on low-frequency (in comparison with the electron gyrofrequency nonlinearly interacting electron whistlers and nonlinearly interacting Hall-magnetohydrodynamic (H-MHD fluctuations in a magnetized plasma. Nonlinear whistler mode turbulence study in a magnetized plasma involves incompressible electrons and immobile ions. Two-dimensional turbulent interactions and subsequent energy cascades are critically influenced by the electron whisters that behave distinctly for scales smaller and larger than the electron skin depth. It is found that in whistler mode turbulence there results a dual cascade primarily due to the forward spectral migration of energy that coexists with a backward spectral transfer of mean squared magnetic potential. Finally, inclusion of the ion dynamics, resulting from a two fluid description of the H-MHD plasma, leads to several interesting results that are typically observed in the solar wind plasma. Particularly in the solar wind, the high-time-resolution databases identify a spectral break at the end of the MHD inertial range spectrum that corresponds to a high-frequency regime. In the latter, turbulent cascades cannot be explained by the usual MHD model and a finite frequency effect (in comparison with the ion gyrofrequency arising from the ion inertia is essentially included to discern the dynamics of the smaller length scales (in comparison with the ion skin depth. This leads to a nonlinear H-MHD model, which is presented in this paper. With the help of our 3-D H-MHD code, we find that the characteristic turbulent interactions in the high-frequency regime evolve typically on kinetic-Alfvén time-scales. The turbulent fluctuation associated with kinetic-Alfvén interactions are compressive and anisotropic and possess equipartition of the kinetic and magnetic energies.
Proceedings of the workshop on nonlinear MHD and extended MHD
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
Non-white noise and a multiple-rate Markovian closure theory for turbulence
Hammett, G W; Hammett, Gregory W.; Bowman, John C.
2002-01-01
Markovian models of turbulence can be derived from the renormalized statistical closure equations of the direct-interaction approximation (DIA). Various simplifications are often introduced, including an assumption that the two-time correlation function is proportional to the renormalized infinitesimal propagator (Green's function), i.e. the decorrelation rate for fluctuations is equal to the decay rate for perturbations. While this is a rigorous result of the fluctuation--dissipation theorem for thermal equilibrium, it does not necessarily apply to all types of turbulence. Building on previous work on realizable Markovian closures, we explore a way to allow the decorrelation and decay rates to differ (which in some cases affords a more accurate treatment of effects such as non-white noise), while retaining the computational advantages of a Markovian approximation. Some Markovian approximations differ only in the initial transient phase, but the multiple-rate Markovian closure (MRMC) presented here could modi...
Parkin, E R
2012-01-01
Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions - perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with...
The Heating of Test Particles in Numerical Simulations of Alfvenic Turbulence
Lehe, Remi; Quataert, Eliot
2009-01-01
We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (``Alfvenic turbulence''); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle is comparable to the frequency of a turbulent fluctuation that is resolved on the computational domain. Particles with these frequencies nearly equal undergo strong perpendicular heating (relative to the local magnetic field) and pitch angle scattering. By contrast, particles with large gyrofrequency undergo strong parallel heating. Simulations with a finite resistivity produce additional parallel heating due to parallel electric fields in small-scale current sheets. Many of our results are consistent with linear theory predictions for the particle heating produced by the ...
Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence
Galtier, S
2014-01-01
The role of magnetic helicity is investigated in kinetic Alfv\\'en wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0 {\\bf e_\\parallel}$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \\& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\\tilde n = -6$, where $n$ and $\\tilde n$ are the power law indices of the perpendicular (to ${\\bf b_0}$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\\tilde n = - 3.5$,...
Extension of Golay's plate height equation from laminar to turbulent flow I - Theory.
Gritti, Fabrice
2017-04-07
The reduced plate height (RPH) equation of Golay derived in 1958 for open tubular columns (OTC) is extended from laminar to turbulent-like flow. The mass balance equation is solved under near-equilibrium conditions in the mobile phase for changing shapes of the velocity profile across the OTC diameter. The final expression of the general RPH equation is: [Formula: see text] where ν is the reduced linear velocity, k is the retention factor, Dm is the bulk diffusion coefficient in the mobile phase, Da¯ is the average axial dispersion coefficient, Dr¯ is the average radial dispersion coefficient, Ds is the diffusion coefficient of the analyte in the stationary film of thickness df, D is the OTC inner diameter, and n≥2 is a positive number controlling the shape of the flow profile (polynomial of degree n). The correctness of the derived RPH equation is verified for Poiseuille (n=2), turburlent-like (n=10), and uniformly flat (n→∞) flow profiles. The derived RPH equation is applied to predict the gain in speed-resolution of a 180μm i.d.×20m OTC (df=2μm) from laminar to turbulent flow in supercritical fluid chromatography. Using pure carbon dioxide as the mobile phase at 297K, k=1, and increasing the Reynolds number from 2000 (laminar) to 4000 (turbulent), the OTC efficiency is expected to increase from 125 to 670 (×5.4) while the hold-up time decreases from 19 to 9s (×0.5). Despite the stronger resistance to mass transfer in the stationary phase, the projected improvement of the column performance in turbulent flow is explained by the quasi-elimination of the resistance to mass transfer in the mobile phase while axial dispersion remains negligible. Copyright © 2017 Elsevier B.V. All rights reserved.
Scaling theory of relative diffusion of charged particles in a weakly magneto-turbulent plasma
Haida Wang (University of Science and Technology of China, Hefei, Anhui. Dept. of Modern Physics); Xiaoming Qui (Southwest Inst. of Physics, Leshan, SC (China))
1989-02-01
Stochastic motion of charged particles in a magneto-turbulent plasma is studied for the whole time region. A set of nonlinear differential equations for describing relative spatial diffusion of charged particles is derived and some explicit results are obtained in the case of a weak magnetic field. It is found that, for the diffusion in the present system there are some new and interesting properties which do not exist in an unmagnetized plasma. The clump effect is also discussed. (author).
Heinemann, T
2008-01-01
We study and elucidate the mechanism of inertial-acoustic wave excitation in a turbulent, differentially rotating flow. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these using a WKBJ method. It is found that, for a particular azimuthal wave length, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Pairs of trailing waves of equal amplitude propagating in opposite directions are produced and give rise to an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wave length. By solving the wave amplitude equations numerically we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation approach completely the important wave source term...
A Fractional PDE Approach to Turbulent Mixing; Part I: an Anomalous Transport Theory
Zayernouri, Mohsen; Samiee, Mehdi
2016-11-01
It has been experimentally and theoretically shown that even in the most ideal cases of homogeneous and isotropic turbulence, the statistical distributions are asymmetric and heavy-tailed. Similar observations, in addition to high peaks, have been made in grid turbulence and atmospheric boundary layer. In the aforementioned problems, the skewness, as a measure of asymmetry, is non-zero and negative, also the flatness (kurtosis), as a notion of the tail heaviness in the distribution, significantly exceeds the Gaussian value 3, reflecting a strong non-Gaussianity. In this talk, we demonstrate that the existence of such anomalous characteristics e.g., heavy tails, asymmetric distributions, and high peaks can naturally put the phenomenology of Taylor, Richardson, and Kolmogorov in broader framework, where the generalizing fractional Brownian motions and stochastic Lévy jump processes (or Lévy flights), investigated in the context of fractional PDEs in the fluid limit, can physically and mathematically explain, hence, predict the notion of anomalously enhanced (sub-to-super) diffusion and self-similar features in passive scalar turbulence. Assistant Professor, Department Computational Mathematics, Science, and Engineering, & Department of Mechanical Engineering.
A Numerical Study of Resistivity and Hall Effects for a Compressible MHD Model
Yee, H. C.; Sjogreen, B.
2005-01-01
The effect of resistive, Hall, and viscous terms on the flow structure compared with compressible ideal MHD is studied numerically for a one-fluid non-ideal MHD model. The goal of the present study is to shed some light on the emerging area of non-ideal MHD modeling and simulation. Numerical experiments are performed on a hypersonic blunt body flow with future application to plasma aerodynamics flow control in reentry vehicles. Numerical experiments are also performed on a magnetized time-developing mixing layer with possible application to magnetic/turbulence mixing.
Frutos-Alfaro, Francisco
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a code that can be used as a seed for a MHD code for numerical applications. As an example, we present part of output of our programs for Cartesian coordinates and how to do the discretization.
SHOCKFIND - An algorithm to identify magnetohydrodynamic shock waves in turbulent clouds
Lehmann, Andrew; Wardle, Mark
2016-01-01
The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetised turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks --- fast, intermediate and slow --- distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here we introduce the publicly available algorithm, SHOCKFIND, to extract and characterise the mixture of shock families in MHD turbulence. The algorithm is applied to a 3-dimensional simulation of a magnetised turbulent molecular cloud, and we find that both fast and slow MHD shocks are present in the simulation. We give the first prediction of the mixture of turbulence-driven MHD shock families in this molecular cloud, and present their distinct distributions of s...
Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence
Shebalin, John V.
2010-01-01
Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures
Nonlinear helical MHD instability
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Study of Nonlinear Interaction and Turbulence of Alfven Waves in LAPD Experiments
Boldyrev, Stanislav; Perez, Jean Carlos
2013-11-29
The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracy the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectral properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the
Effective Medium Theory for Drag Reducing Micro-patterned Surfaces in Turbulent Flows
Battiato, Ilenia
2013-01-01
Inspired by the lotus effect, many studies in the last decade have focused on micro- and nano-patterned surfaces. They revealed that patterns at the micro-scale combined with high contact angles can significantly reduce skin drag. However, the mechanisms and parameters that control drag reduction, e.g. Reynolds number and pattern geometry, are still unclear. We propose an effective medium representation of the micro-features, that treats the latter as a porous medium, and provides a framework to model flow over patterned surfaces in both Cassie and Wenzel states. Our key result is a closed-form expression for the skin friction coefficient in terms of frictional Reynolds (or K\\'arm\\'an) number in turbulent regime, the viscosity ratio between the fluid in and above the features, and their geometrical properties. We apply the proposed model to turbulent flows over superhydrophobic ridged surfaces. The model predictions agree with laboratory experiments for Reynolds numbers ranging from 3000 to 10000.
Theory and hybrid simulations of the radial evolution of the solar wind turbulence
Comisel, Horia; Narita, Yasuhito; Motschmann, Uwe
2016-04-01
Solar wind turbulence in the inner heliosphere is believed to evolve in the radial direction away from the Sun driven by various nonlinear processes. When a perturbative treatment is applicable, plasma fluctuations evolve along the dispersion relations while the frequencies deviate from the normal-mode frequency by exciting non-normal modes or sideband waves. Direct numerical simulations of magnetized plasma at the scale of ion gyro-radius or smaller using the hybrid code AIKEF show smooth transitions and evolutions into nonlinear stage with sideband wave excitations. The evolution profile of linear and nonlinear modes as well as the intrinsic nature of wave vector anisotropy can be unambiguously classified according to the values of ion plasma beta. By using a mapping based on a one-dimensional solar wind expansion model, the resulting ion kinetic scale turbulence is related to the solar distance from the Sun. We find that the relevant normal modes such as ion cyclotron and Bernstein mode will occur first at radial distance of about 0.2-0.3 AU, i.e., near the Mercury orbit. Furthermore, a radial dependence of the wave-vector anisotropy is obtained. The predominance of the filament structures highlights the strong impact of Alfvénic waves.
Langmuir turbulence in the auroral ionosphere 2: Nonlinear theory and simulations
Newman, D. L.; Goldman, M. V.; Ergun, R. E.
1994-01-01
A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (less than or equal to 500 mV/m) driven by a stream of 20 eV to 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 microseconds sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam-driven Langmuir turbulence in the presence of a moderate magnetic field (OMEGA (sub e) approximately equals Omega (sub pe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream-driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.
Frutos-Alfaro, Francisco; Carboni-Mendez, Rodrigo
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a c...
G. García Segura
2000-01-01
Full Text Available Se presenta un escenario auto consistente para explicar la morfolog a de las nebulosas planetarias. El escenario es consistente con la distribuci on Gal actica de los diferentes tipos morfol ogicos. Este trabajo resuelve, por medio de efectos MHD, algunas de las caracter sticas controversiales que aparecen en las nebulosas planetarias. Estas caracter sticas incluyen la presencia de ujos axisim etricos y colimados, con una cinem atica que aumenta linealmente con la distancia y la existencia de morfolog as asim etricas tales como las de las nebulosas con simetr a de punto.
Retallick, F.D.
1978-04-01
This document establishes criteria to be utilized for the design of a pilot-scale (150 to 300 MW thermal) open cycle, coal-fired MHD/steam plant. Criteria for this Engineering Test Facility (ETF) are presented relative to plant siting, plant engineering and operations, MHD-ETF testing, costing and scheduling.
Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence
Li, Yang; Gao, Zhe; Chen, Jiale
2016-08-01
A second order kinetic model for turbulent ion parallel momentum transport is presented. A new nonresonant second order parallel momentum flux term is calculated. The resonant component of the ion parallel electrostatic force is the momentum source, while the nonresonant component of the ion parallel electrostatic force compensates for that of the nonresonant second order parallel momentum flux. The resonant component of the kinetic momentum flux can be divided into three parts, including the pinch term, the diffusive term, and the residual stress. By reassembling the pinch term and the residual stress, the residual stress can be considered as a pinch term of parallel wave-particle resonant velocity, and, therefore, may be called as "resonant velocity pinch" term. Considering the resonant component of the ion parallel electrostatic force is the transfer rate between resonant ions and waves (or, equivalently, nonresonant ions), a conservation equation of the parallel momentum of resonant ions and waves is obtained.
Direct Numerical Simulation and Theories of Wall Turbulence with a Range of Pressure Gradients
Coleman, G. N.; Garbaruk, A.; Spalart, P. R.
2014-01-01
A new Direct Numerical Simulation (DNS) of Couette-Poiseuille flow at a higher Reynolds number is presented and compared with DNS of other wall-bounded flows. It is analyzed in terms of testing semi-theoretical proposals for universal behavior of the velocity, mixing length, or eddy viscosity in pressure gradients, and in terms of assessing the accuracy of two turbulence models. These models are used in two modes, the traditional one with only a dependence on the wall-normal coordinate y, and a newer one in which a lateral dependence on z is added. For pure Couette flow and the Couette-Poiseuille case considered here, this z-dependence allows some models to generate steady streamwise vortices, which generally improves the agreement with DNS and experiment. On the other hand, it complicates the comparison between DNS and models.
Mathematical modeling of turbulent reacting plumes - I. General theory and model formulation
Georgopoulos, P.G.; Seinfeld, J.H.
1986-01-01
A new, comprehensive model for a chemically reacting plume is presented that accounts for the effects of incomplete turbulent macro- and micromixing on chemical reactions between plume and atmospheric constituents. The model is modular in nature, allowing for the use of different levels of approximation of the phenomena involved. The core of the model consists of the evolution equations for reaction progress variables appropriate for evolving spatially varying systems. These equations estimate the interaction of mixing and chemical reaction and require input parameters characterizing internal plume behavior, such as relative dispersion and fine scale plume segregation. The model addresses deficiencies in previous reactive plume models. Part II is devoted to atmospheric application of the model. (authors).
EVIDENCE OF ACTIVE MHD INSTABILITY IN EULAG-MHD SIMULATIONS OF SOLAR CONVECTION
Lawson, Nicolas; Strugarek, Antoine; Charbonneau, Paul, E-mail: nicolas.laws@gmail.ca, E-mail: strugarek@astro.umontreal.ca, E-mail: paulchar@astro.umontreal.ca [Département de Physique, Université de Montréal, C.P. 6128 Succ. Centre-ville, Montréal, Qc H3C 3J7 (Canada)
2015-11-10
We investigate the possible development of magnetohydrodynamical instabilities in the EULAG-MHD “millennium simulation” of Passos and Charbonneau. This simulation sustains a large-scale magnetic cycle characterized by solar-like polarity reversals taking place on a regular multidecadal cadence, and in which zonally oriented bands of strong magnetic fields accumulate below the convective layers, in response to turbulent pumping from above in successive magnetic half-cycles. Key aspects of this simulation include low numerical dissipation and a strongly sub-adiabatic fluid layer underlying the convectively unstable layers corresponding to the modeled solar convection zone. These properties are conducive to the growth and development of two-dimensional instabilities that are otherwise suppressed by stronger dissipation. We find evidence for the action of a non-axisymmetric magnetoshear instability operating in the upper portions of the stably stratified fluid layers. We also investigate the possibility that the Tayler instability may be contributing to the destabilization of the large-scale axisymmetric magnetic component at high latitudes. On the basis of our analyses, we propose a global dynamo scenario whereby the magnetic cycle is driven primarily by turbulent dynamo action in the convecting layers, but MHD instabilities accelerate the dissipation of the magnetic field pumped down into the overshoot and stable layers, thus perhaps significantly influencing the magnetic cycle period. Support for this scenario is found in the distinct global dynamo behaviors observed in an otherwise identical EULAG-MHD simulations, using a different degree of sub-adiabaticity in the stable fluid layers underlying the convection zone.
湍流理论的一种新方法%A New Approach to the Theory of Turbulence
吴峰
2005-01-01
On the basis of the fact that physical world possesses hierarchical structure and the concepts of nonstandard mathematics, a new description of turbulence was presented. Fundamental equations of turbulent flows were also given. It is natural in this nonstandard picture of turbulence that the closure methods are obtained and seem to be precise.
Magnetohydrodynamic simulation of reconnection in turbulent astrophysical plasmas
Widmer, Fabien
2016-07-19
Turbulence is ubiquitous at large-Reynolds-number astrophysical plasmas like in the Solar corona. In such environments, the turbulence is thought to enhance the energy conversion rate by magnetic reconnection above the classical model predictions. Since turbulence cannot be simulated together with the large scale behaviour of the plasma, magnetic reconnection is studied through the average properties of turbulence. A Reynolds-averaged turbulence model is explored in which turbulence is self-sustained and -generated by the large scales (mean-) field inhomogeneities. Employing that model, the influence of turbulence is investigated by large-scale MHD numerical simulations solving evolution equations of the energy and cross-helicity of the turbulence together with the MHD equations. Magnetic reconnection is found to be either rapidly enhanced or suppressed by turbulence depending on the turbulence timescale. If the turbulence timescale is self-consistently calculated, reconnection is always strongly enhanced. Since the solar corona bears strong guide magnetic fields perpendicular to the reconnecting magnetic fields, the influences of a strong guide field on turbulent reconnection is separately investigated. A slow down of reconnection, obtained in the presence of a finite guide field, can be understood by a finite residual helicity working against the enhancement of reconnection by the turbulence. The influence of turbulence on magnetic reconnection is further studied by means of high resolution simulations of plasmoid-unstable current sheets. These simulations revealed the importance of turbulence for reaching fast reconnection.
Bec, Jeremie [Laboratoire Cassiopee UMR6202, CNRS, OCA, BP4229, 06304 Nice Cedex 4 (France)]. E-mail: jeremie.bec@obs-nice.fr; Khanin, Konstantin [Department of Mathematics, University of Toronto, Toronto, Ont., M5S 3G3 (Canada)]. E-mail: khanin@math.toronto.edu
2007-08-15
The last decades witnessed a renewal of interest in the Burgers equation. Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J.M. Burgers, and more precisely on the problem of Burgers turbulence, that is the study of the solutions to the one- or multi-dimensional Burgers equation with random initial conditions or random forcing. Such work was frequently motivated by new emerging applications of Burgers model to statistical physics, cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the simplest instances of a nonlinear system out of equilibrium. The study of random Lagrangian systems, of stochastic partial differential equations and their invariant measures, the theory of dynamical systems, the applications of field theory to the understanding of dissipative anomalies and of multiscaling in hydrodynamic turbulence have benefited significantly from progress in Burgers turbulence. The aim of this review is to give a unified view of selected work stemming from these rather diverse disciplines.
Observations of turbulence and fluctuations in the solar wind
Klein, L.W.
1987-01-01
Observational and theoretical studies of turbulent fluctuations in space plasma have been ongoing for many years. There are still many unanswered questions about the origin and evolution of the fluctuations in the heliosphere. This work pursues the subject and uses Voyage 1 and 2, and ISEE-3 measurements to study the evolution of solar-wind plasma and the magnetic field between heliocentric distances of 1 and 20 AU and to more than 25/sup 0/ in latitude above the ecliptic plane. Parker's 1958 solar-wind model is found to be accurate to within 5% in predicting the behavior of long-term (solar rotation) averages in the interplanetary magnetic field when time dependencies in the bulk plasma speed are included. No evidence was found of flux loss in the outer heliosphere as recently reported in the literature. Methods of turbulence analysis and are used to organize the observations and several predictions and expectations of ideal MHD turbulence theory are tested. Spectral indices expected for inertial-range turbulence are present in much of the data analyzed, and this inertial range is found in increasingly larger spatial scales with increasing radial distance from the sun. Evidence for inverse cascade of magnetic helicity is observed in selected intervals, although this was not found to be true in general in the solar wind.
Theory of fully developed hydrodynamic turbulent flow: Applications of renormalization-group methods
Yuan, Jian-Yang; Ronis, David
1992-04-01
A model for randomly stirred or homogeneous turbulent fluids is analyzed using renormalization-group methods on a path-integral representation of the Navier-Stokes equations containing a spatially and temporally colored noise source. For moderate Reynolds numbers and certain values of the dynamic exponent governing the noise correlation, an additional scaling regime is found at wave vectors k beyond those where the Kolmogorov 5/3 law holds. In this case, the energy spectrum decays as k-1-z, where 1zz, and the velocity-distribution function (as characterized by its skewness) deviates from a Gaussian. The additional scaling region disappears, and the Kolmogorov constant and Prandtl number become universal in the limit of infinite Reynolds number. In three spatial dimensions, the latter two equal 3/2( 5) / 3 )1/3 and √0.8 , respectively. The recent homodyne scattering experiments of Tong and co-workers [Phys. Rev. Lett. 65, 2780 (1990)] are analyzed, and the connection of the new scaling region with intermittency is discussed.
Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry
Furukawa, M
2016-01-01
Simulated annealing (SA) is applied for three-dimensional (3D) equilibrium calculation of ideal, low-beta reduced MHD in cylindrical geometry. The SA is based on the theory of Hamiltonian mechanics. The dynamical equation of the original system, low-beta reduced MHD in this study, is modified so that the energy changes monotonically while preserving the Casimir invariants in the artificial dynamics. An equilibrium of the system is given by an extremum of the energy, therefore SA can be used as a method for calculating ideal MHD equilibrium. Previous studies demonstrated that the SA succeeds to lead to various MHD equilibria in two dimensional rectangular domain. In this paper, the theory is applied to 3D equilibrium of ideal, low-beta reduced MHD. An example of equilibrium with magnetic islands, obtained as a lower energy state, is shown. Several versions of the artificial dynamics are developed that can effect smoothing.
MHD Energy Bypass Scramjet Performance with Real Gas Effects
Park, Chul; Mehta, Unmeel B.; Bogdanoff, David W.
2000-01-01
The theoretical performance of a scramjet propulsion system incorporating an magneto-hydro-dynamic (MHD) energy bypass scheme is calculated. The one-dimensional analysis developed earlier, in which the theoretical performance is calculated neglecting skin friction and using a sudden-freezing approximation for the nozzle flow, is modified to incorporate the method of Van Driest for turbulent skin friction and a finite-rate chemistry calculation in the nozzle. Unlike in the earlier design, in which four ramp compressions occurred in the pitch plane, in the present design the first two ramp compressions occur in the pitch plane and the next two compressions occur in the yaw plane. The results for the simplified design of a spaceliner show that (1) the present design produces higher specific impulses than the earlier design, (2) skin friction substantially reduces thrust and specific impulse, and (3) the specific impulse of the MHD-bypass system is still better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Results suggest that the energy management with MHD principles offers the possibility of improving the performance of the scramjet. The technical issues needing further studies are identified.
MHD Energy Bypass Scramjet Engine
Mehta, Unmeel B.; Bogdanoff, David W.; Park, Chul; Arnold, Jim (Technical Monitor)
2001-01-01
Revolutionary rather than evolutionary changes in propulsion systems are most likely to decrease cost of space transportation and to provide a global range capability. Hypersonic air-breathing propulsion is a revolutionary propulsion system. The performance of scramjet engines can be improved by the AJAX energy management concept. A magneto-hydro-dynamics (MHD) generator controls the flow and extracts flow energy in the engine inlet and a MHD accelerator downstream of the combustor accelerates the nozzle flow. A progress report toward developing the MHD technology is presented herein. Recent theoretical efforts are reviewed and ongoing experimental efforts are discussed. The latter efforts also include an ongoing collaboration between NASA, the US Air Force Research Laboratory, US industry, and Russian scientific organizations. Two of the critical technologies, the ionization of the air and the MHD accelerator, are briefly discussed. Examples of limiting the combustor entrance Mach number to a low supersonic value with a MHD energy bypass scheme are presented, demonstrating an improvement in scramjet performance. The results for a simplified design of an aerospace plane show that the specific impulse of the MHD-bypass system is better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Equilibrium ionization and non-equilibrium ionization are discussed. The thermodynamic condition of air at the entrance of the engine inlet determines the method of ionization. The required external power for non-equilibrium ionization is computed. There have been many experiments in which electrical power generation has successfully been achieved by magneto-hydrodynamic (MHD) means. However, relatively few experiments have been made to date for the reverse case of achieving gas acceleration by the MHD means. An experiment in a shock tunnel is described in which MHD acceleration is investigated experimentally. MHD has several
Scale locality of magnetohydrodynamic turbulence.
Aluie, Hussein; Eyink, Gregory L
2010-02-26
We investigate the scale locality of cascades of conserved invariants at high kinetic and magnetic Reynold's numbers in the "inertial-inductive range" of magnetohydrodynamic (MHD) turbulence, where velocity and magnetic field increments exhibit suitable power-law scaling. We prove that fluxes of total energy and cross helicity-or, equivalently, fluxes of Elsässer energies-are dominated by the contributions of local triads. Flux of magnetic helicity may be dominated by nonlocal triads. The magnetic stretching term may also be dominated by nonlocal triads, but we prove that it can convert energy only between velocity and magnetic modes at comparable scales. We explain the disagreement with numerical studies that have claimed conversion nonlocally between disparate scales. We present supporting data from a 1024{3} simulation of forced MHD turbulence.
Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks
Hahm, T.S.; Tang, W.M.
1990-10-01
The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady state solution of the wave-kinetic equation. Distant nonlinear interactions between low-k{sub {theta}} and high-k{sub {theta}} modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-k{sub {theta}} (k{sub {theta}}{rho}{sub s} {much lt} (L{sub n}/R){sup 1/2}) modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from k{sub {theta}}{rho}{sub s} {congruent} (L{sub n}/R){sup 1/2} to k{sub {theta}}{rho}{sub s} {congruent} 1 according to an approximate power law k{sub {theta}}{sup {minus}3}. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher T{sub i}/T{sub e}, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.
Scaling properties of small-scale fluctuations in magnetohydrodynamic turbulence
Perez, J C; Boldyrev, S; Cattaneo, F
2014-01-01
Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments. Much attention is therefore drawn to the universal scaling properties of small-scale fluctuations, which can be reliably measured in the simulations and then extrapolated to astrophysical scales. However, in contrast with hydrodynamic turbulence, where the universal structure of the inertial and dissipation intervals is described by the Kolmogorov self-similarity, the scaling for MHD turbulence cannot be established based solely on dimensional arguments due to the presence of an intrinsic velocity scale -- the Alfven velocity. In this Letter, we demonstrate that the Kolmogorov first self-similarity hypothesis cannot be formulated for MHD turbulence in the same way it is formulated for the hydrodynamic case. Besides profound consequences for the analytical consideration, this...
Talbot, L.; Cheng, R.K. [Lawrence Berkeley Laboratory, CA (United States)
1993-12-01
Turbulent combustion is the dominant process in heat and power generating systems. Its most significant aspect is to enhance the burning rate and volumetric power density. Turbulent mixing, however, also influences the chemical rates and has a direct effect on the formation of pollutants, flame ignition and extinction. Therefore, research and development of modern combustion systems for power generation, waste incineration and material synthesis must rely on a fundamental understanding of the physical effect of turbulence on combustion to develop theoretical models that can be used as design tools. The overall objective of this program is to investigate, primarily experimentally, the interaction and coupling between turbulence and combustion. These processes are complex and are characterized by scalar and velocity fluctuations with time and length scales spanning several orders of magnitude. They are also influenced by the so-called {open_quotes}field{close_quotes} effects associated with the characteristics of the flow and burner geometries. The authors` approach is to gain a fundamental understanding by investigating idealized laboratory flames. Laboratory flames are amenable to detailed interrogation by laser diagnostics and their flow geometries are chosen to simplify numerical modeling and simulations and to facilitate comparison between experiments and theory.
Multi-Spacecraft Turbulence Analysis Methods
Horbury, Tim S.; Osman, Kareem T.
analyse; and, most important of all, the solar wind speed, V SW , is much higher than the local MHD wave speeds. This means that a spacecraft time series is essentially a "snapshot" spatial sample of the plasma along the flow direction, so we can consider measurements at a set of times ti to be at a set of locations in the plasma given by xi = VSW. This approximation,known as Taylor's hypothesis, greatly simplifies the analysis of the data. In contrast, in the magnetosheath the flow speed is lower than the wave speed and therefore temporal changes at the spacecraft are due to a complex combination of the plasma moving over the spacecraft and the turbulent fluctuations propagating in the plasma frame. This is also the case for ion and electron kinetic scale turbulence in the solar wind and dramatically complicates the analysis of the data. As a result, the application of multi-spacecraft techniques such as k filtering to Cluster data (see Chapter 5, which make it possible to disentangle the effects of flow and wave propagation, have probably resulted in the greatest increase in our understanding of magnetosheath turbulence rather than in the solar wind. We can therefore summarise the key advantages for plasma turbulence analysis of multi-spacecraft data sets such as those from Cluster, compared to single spacecraft data. Multiple sampling points allow us to measure how the turbulence varies in many directions, and on a range of scales, simultaneously, enabling the study of anisotropy in ways that have not previously been possible. They also allow us to distinguish between the motion of fluctuations in the plasma and motion of the plasma itself, enabling the study of turbulence in highly disturbed environments such as the magnetosheath. A number of authors have studied turbulence with Cluster data, using different techniques, the choice of which is motivated by the characteristics of the plasma environment in which they are interested. The complexity of both the Cluster
Cantorian Fractal Space-Time Fluctuations in Turbulent Fluid Flows and the Kinetic Theory of Gases
Selvam, A M
1999-01-01
Fluid flows such as gases or liquids exhibit space-time fluctuations on all scales extending down to molecular scales. Such broadband continuum fluctuations characterise all dynamical systems in nature and are identified as selfsimilar fractals in the newly emerging multidisciplinary science of nonlinear dynamics and chaos. A cell dynamical system model has been developed by the author to quantify the fractal space-time fluctuations of atmospheric flows. The earth's atmosphere consists of a mixture of gases and obeys the gas laws as formulated in the kinetic theory of gases developed on probabilistic assumptions in 1859 by the physicist James Clerk Maxwell. An alternative theory using the concept of fractals and chaos is applied in this paper to derive these fundamental gas laws.
Magnetic stresses in ideal MHD plasmas
Jensen, V.O.
1995-01-01
and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem......The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma...
Solar Wind Turbulence and the Role of Ion Instabilities
Alexandrova, Olga; Sorriso-Valvo, Luca; Horbury, Timothy S; Bale, Stuart D
2013-01-01
Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: weakness of collisional dissipation and presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field. Solar wind turbulence is compressible in nature. The spectrum of velocity fluctuations do not follow magnetic field one. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuat...
Approach to the origin of turbulence on the basis of two-point kinetic theory
Tsuge, S.
1974-01-01
Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.
Course 1: Accretion and Ejection-Related MHD
Heyvaerts, Jean
This lecture is an introduction to MHD. Relevant equations, both in the classical and special-relativistic regimes are derived. The magnetic field evolution is considered both in the perfect-MHD limit and when weak resistivity is present, giving rise to reconnection flows. A short section gives a flavour of dynamo theory. Examples of simple stationnary flows and equilibria are then presented. Stationnary, axisymmetric, rotating perfect-MHD winds and jets are discussed in some more detail. Their asymptotic structure is described. The last sections deal with small motions about an equilibrium and stability. These issues are illustrated by a few classical examples. The last section discusses linear aspects of the magneto-rotationnal instability.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Stochastic differential equations and turbulent dispersion
Durbin, P. A.
1983-01-01
Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.
Turbulence and Fossil Turbulence in Oceans and Lakes
Pak-Tao Leung; Carl H. Gibson
2004-01-01
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any of the other forces that tend to damp the eddies out. Energy cascades of irrotational flows from large scales to small are non-turbulent, even if they supply energy to turbulence. Turbulent flows are rotational and cascade from small scales to large, with feedback. Viscous forces limit the smallest turbulent eddy size to the Kolmogorov scale. In stratified fluids, buoyancy forces limit large vertical overturns to the Ozmidov scale and convert the largest turbulent eddies into a unique class of saturated, non-propagating, internal waves, termed fossil-vorticity-turbulence. These waves have the same energy but different properties and spectral forms than the original turbulence patch. The Gibson (1980, 1986) theory of fossil turbulence applies universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as its growth is constrained and fossilized by buoyancy forces. Quantitative hydrodynamic-phase-diagrams (HPDs) from the theory are used to classify microstructure patches according to their hydrodynamic states. When analyzed in HPD space, previously published oceanic datasets showed their dominant microstructure patches are fossilized at large scales in all layers. Laboratory and field measurements suggested phytoplankton species with different swimming abilities adjust their growth strategies by pattern recognition of turbulence-fossil-turbulence dissipation and persistence times that predict survival-relevant surface layer sea changes. New data collected near a Honolulu waste-water outfall showed the small-to-large evolution of oceanic turbulence microstructure from active to fossil states, and revealed the ability of fossil-density-turbulence patches to absorb, and vertically radiate, internal wave energy, information, and enhanced turbulent
Anisotropic turbulence in weakly stratified rotating magnetoconvection
Giesecke, A
2010-01-01
Numerical simulations of the 3D MHD-equations that describe rotating magnetoconvection in a Cartesian box have been performed using the code NIRVANA. The characteristics of averaged quantities like the turbulence intensity and the turbulent heat flux that are caused by the combined action of the small-scale fluctuations are computed. The correlation length of the turbulence significantly depends on the strength and orientation of the magnetic field and the anisotropic behavior of the turbulence intensity induced by Coriolis and Lorentz force is considerably more pronounced for faster rotation. The development of isotropic behavior on the small scales -- as it is observed in pure rotating convection -- vanishes even for a weak magnetic field which results in a turbulent flow that is dominated by the vertical component. In the presence of a horizontal magnetic field the vertical turbulent heat flux slightly increases with increasing field strength, so that cooling of the rotating system is facilitated. Horizont...
The first turbulent combustion
Gibson, C H
2005-01-01
The first turbulent combustion arises in a hot big bang cosmological model Gibson (2004) where nonlinear exothermic turbulence permitted by quantum mechanics, general relativity, multidimensional superstring theory, and fluid mechanics cascades from Planck to strong force freeze out scales with gravity balancing turbulent inertial-vortex forces. Interactions between Planck scale spinning and non-spinning black holes produce high Reynolds number turbulence and temperature mixing with huge Reynolds stresses driving the rapid inflation of space. Kolmogorovian turbulent temperature patterns are fossilized as strong-force exponential inflation stretches them beyond the scale of causal connection ct where c is light speed and t is time. Fossil temperature turbulence patterns seed nucleosynthesis, and then hydro-gravitational structure formation in the plasma epoch, Gibson (1996, 2000). Evidence about formation mechanisms is preserved by cosmic microwave background temperature anisotropies. CMB spectra indicate hydr...
Spontaneous chiral symmetry breaking of Hall magnetohydrodynamic turbulence.
Meyrand, Romain; Galtier, Sébastien
2012-11-01
Hall magnetohydrodynamics (MHD) is investigated through three-dimensional direct numerical simulations. We show that the Hall effect induces a spontaneous chiral symmetry breaking of the turbulent dynamics. The normalized magnetic polarization is introduced to separate the right- (R) and left-handed (L) fluctuations. A classical k(-7/3) spectrum is found at small scales for R magnetic fluctuations which corresponds to the electron MHD prediction. A spectrum compatible with k(-11/3) is obtained at large-scales for the L magnetic fluctuations; we call this regime the ion MHD. These results are explained heuristically by rewriting the Hall MHD equations in a succinct vortex dynamical form. Applications to solar wind turbulence are discussed.
Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
Kritsuk, Alexei G; Collins, David; Padoan, Paolo; Norman, Michael L; Abel, Tom; Banerjee, Robi; Federrath, Christoph; Flock, Mario; Lee, Dongwook; Li, Pak Shing; Mueller, Wolf-Christian; Teyssier, Romain; Ustyugov, Sergey D; Vogel, Christian; Xu, Hao
2011-01-01
We employ simulations of supersonic super-Alfv\\'enic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high...
3D simulations of fluctuation spectra in the hall-MHD plasma.
Shaikh, Dastgeer; Shukla, P K
2009-01-30
Turbulent spectral cascades are investigated by means of fully three-dimensional (3D) simulations of a compressible Hall-magnetohydrodynamic (H-MHD) plasma in order to understand the observed spectral break in the solar wind turbulence spectra in the regime where the characteristic length scales associated with electromagnetic fluctuations are smaller than the ion gyroradius. In this regime, the results of our 3D simulations exhibit that turbulent spectral cascades in the presence of a mean magnetic field follow an omnidirectional anisotropic inertial-range spectrum close to k(-7/3). The latter is associated with the Hall current arising from nonequal electron and ion fluid velocities in our 3D H-MHD plasma model.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
Plasma Beta Dependence of Magnetic Compressibility in Solar Wind Turbulence
Chapman, S. C.; Hnat, B.; Kiyani, K. H.; Sahraoui, F.
2014-12-01
The turbulent signature of MHD scales in the near-Earth solar wind are known to be primarily incompressible which manifests itself in magnetic field fluctuation vector components to be aligned primarily perpendicular to the background magnetic field -- so-called "Variance Anisotropy". This, and other facts, have been seen as evidence for a majority Alfvenic turbulence cascade; with a small component (10%) of compressible fluctuations. When one approaches scales on the order of the ion-inertial length and the Larmor radius, this behaviour changes and it is now becoming increasingly evident that the spectral break at these scales is also accompanied by an increase in magnetic compressibility. This has been attributed to a phase change in the physics at these scales -- from fluid to kinetic -- and in particular to the dominant role of the Hall-effect at sub-ion scales. We will be presenting results from the Cluster mission to show how this increase in the compressibility is dependent on the ion plasma beta and what implications this has for the physics at sub-ion scales in the context of prominent theories and models for kinetic plasma turbulence.
Dissipation of Molecular Cloud Turbulence by Magnetohydrodynamic Shockwaves
Lehmann, Andrew; Wardle, Mark
2015-08-01
The character of star formation is intimately related to the supersonic magnetohydrodynamic (MHD) turbulent dynamics of the giant molecular clouds in which stars form. A significant amount of the turbulent energy dissipates in low velocity shock waves. These shocks cause molecular line cooling of the compressed and heated gas, and so their radiative signatures probe the nature of the turbulence. In MHD fluids the three distinct families of shocks—fast, intermediate and slow—differ in how they compress and heat the molecular gas, and so observational differences between them may also distinguish driving modes of turbulent regions.Here we use a two-fluid model to compare the characteristics of one-dimensional fast and slow MHD shocks. Fast MHD shocks are magnetically driven, forcing ion species to stream through the neutral gas ahead of the shock front. This magnetic precursor heats the gas sufficiently to create a large, warm transition zone where all the fluid variables only weakly change in the shock front. In contrast, slow MHD shocks are driven by gas pressure where neutral species collide with ion species in a thin hot slab that closely resembles an ordinary gas dynamic shock.We computed observational diagnostics for fast and slow shocks at velocities vs = 2-4 km/s and preshock Hydrogen nuclei densities n(H) = 102-4 cm-3. We followed the abundances of molecules relevant for a simple oxygen chemistry and include cooling by CO, H2 and H2O. Estimates of intensities of CO rotational lines show that high-J lines, above J = 6→5, are more strongly excited in slow MHD shocks. We discuss how these shocks could help interpret recently observed anomalously strong mid- and high-J CO lines emitted by warm gas in the Milky Way and external galaxies, and implications for simulations of MHD turbulence.
Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind.
Zhdankin, Vladimir; Boldyrev, Stanislav; Mason, Joanne; Perez, Jean Carlos
2012-04-27
Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.
Stochastic Particle Acceleration by Helical Turbulence in Solar Flares
Fleishman, Gregory D
2012-01-01
Flaring release of magnetic energy in solar corona is only possible if the magnetic field deviates from a potential one. We show that the linear MHD modes excited on top of the non-potential magnetic field possess a nonzero kinetic helicity. Accordingly, this necessarily results in a noticeable kinetic helicity of the turbulence, composed of these linear modes with various scales and random phases, generated at the flare site by the primary energy release, which may be important for many applications. In particular, a nonzero turbulence helicity has a potentially strong effect on the particle acceleration because the helical component of the turbulence induces a mean regular large-scale (DC) electric field capable of directly accelerating the charged particles in addition to the commonly considered stochastic turbulent electric field. In this paper, we derive the kinetic helicity density of the linear MHD modes excited on top of a twisted large-scale magnetic field, estimate the corresponding turbulence helic...
Tsallis statistics as a tool for studying interstellar turbulence
Esquivel, A
2009-01-01
We used magnetohydrodynamic (MHD) simulations of interstellar turbulence to study the probability distribution functions (PDFs) of increments of density, velocity, and magnetic field. We found that the PDFs are well described by a Tsallis distribution, following the same general trends found in solar wind and Electron MHD studies. We found that the PDFs of density are different in subsonic and supersonic turbulence. In order to extend this work to ISM observations we studied maps of column density obtained from 3D MHD simulations. From the column density maps we found the parameters that fit to Tsallis distributions and demonstrated that these parameters vary with the Mach and Alfvenic Mach numbers of turbulence. This opens avenues for using Tsallis distributions to study the dynamical and magnetic states of interstellar gas.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Magnetohydrodynamic (MHD) channel corner seal
Spurrier, Francis R.
1980-01-01
A corner seal for an MHD duct includes a compressible portion which contacts the duct walls and an insulating portion which contacts the electrodes, sidewall bars and insulators. The compressible portion may be a pneumatic or hydraulic gasket or an open-cell foam rubber. The insulating portion is segmented into a plurality of pieces of the same thickness as the electrodes, insulators and sidewall bars and aligned therewith, the pieces aligned with the insulator being of a different size from the pieces aligned with the electrodes and sidewall bars to create a stepped configuration along the corners of the MHD channel.
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory. Edge localised modes (ELMs), occurring in TCV Ohmic high-confinement mode discharges, were observed to be preceded by coherent magnetic oscillations. The detected poloidal and toroidal mode structures are consistent with a resonant flux surface close to the plasma edge. Unlike conventional MHD modes, these precursors start at a random toroidal location and then grow in amplitude and toroidal extent until they encompass the whole toroidal circumference. Thus, the asymmetry causing and maintaining the toroidal localisation of the ELM precursor must be intrinsic to the plasma. Soft X-ray measurements show that the localised precursor always coincides with a central m = 1 mode, which can usually be associated with the sawtooth pre- or postcursor mode. A comparison of the phases indicates a correlation with the maximum of the central mode preceding the toroidal location of the ELM precursor and, therefore, a hitherto unobserved coupling between central modes and ELMs. Highly elongated plasmas promise several advantages, among them higher current and beta limits. During TCV experiments dedicated to an increasing of the plasma elongation, a new disruptive current limit, at values well below the conventional current limit corresponding to q{sub a} > 2, was encountered for {kappa} > 2.3. This limit, which is preceded by a kink-type mode, is found to be consistent with ideal MHD stability calculations. The TCV observations, therefore, provide the first experimental confirmation of a deviation of the linear Troyon-scaling of the ideal beta limit with normalised current at high elongation, which was predicted over 10 years ago. Neoclassical tearing modes (NTMs), which have been observed to limit the achievable beta in a number of tokamaks, arise from a helical perturbation of the bootstrap current caused by an existing seed island. Neoclassical m/n = 2/1 tearing modes have been
Sub-Grid-Scale Description of Turbulent Magnetic Reconnection in Magnetohydrodynamics
Widmer, Fabien; Yokoi, Nobumitsu
2015-01-01
Magnetic reconnection requires, at least locally, a non-ideal plasma response. In collisionless space and astrophysical plasmas, turbulence could permit this instead of the too rare binary collisions. We investigated the influence of turbulence on the reconnection rate in the framework of a single fluid compressible MHD approach. The goal is to find out, whether unresolved, sub-grid for MHD simulations, turbulence can enhance the reconnection process in high Reynolds number astrophysical plasma. We solve, simultaneously with the grid-scale MHD equations, evolution equations for the sub-grid turbulent energy and cross helicity according to Yokoi's model (Yokoi (2013)) where turbulence is self-generated and -sustained through the inhomogeneities of the mean fields. Simulations of Harris and force free sheets confirm the results of Higashimori et al. (2013) and new results are obtained about the dependence on resistivity for large Reynolds number as well as guide field effects. The amount of energy transferred f...
Dust polarization and ISM turbulence
Caldwell, Robert R; Kamionkowski, Marc
2016-01-01
Perhaps the most intriguing result of Planck's dust-polarization measurements is the observation that the power in the E-mode polarization is twice that in the B mode, as opposed to pre-Planck expectations of roughly equal dust powers in E and B modes. Here we show how the E- and B-mode powers depend on the detailed properties of the fluctuations in the magnetized interstellar medium. These fluctuations are classified into the slow, fast, and Alfv\\'en magnetohydrodynamic (MHD) waves, which are determined once the ratio of gas to magnetic-field pressures is specified. We also parametrize models in terms of the power amplitudes and power anisotropies for the three types of waves. We find that the observed EE/BB ratio (and its scale invariance) and positive TE correlation cannot be easily explained in terms of favored models for MHD turbulence. The observed power-law index for temperature/polarization fluctuations also disfavors MHD turbulence. We thus speculate that the 0.1--30 pc length scales probed by these ...
Multiscale nature of the dissipation range in solar wind turbulence
Told, D; TenBarge, J M; Howes, G G; Hammett, G W
2015-01-01
Nonlinear energy transfer and dissipation in Alfv\\'en wave turbulence are analyzed in the first gyrokinetic simulation spanning all scales from the tail of the MHD range to the electron gyroradius scale. For typical solar wind parameters at 1 AU, about 30% of the nonlinear energy transfer close to the electron gyroradius scale is mediated by modes in the tail of the MHD cascade. Collisional dissipation occurs across the entire kinetic range $k_\\perp\\rho_i\\gtrsim 1$. Both mechanisms thus act on multiple coupled scales, which have to be retained for a comprehensive picture of the dissipation range in Alfv\\'enic turbulence.
Yoshizawa, Akira; Nisizima, Shoiti; Shimomura, Yutaka; Kobayashi, Hiromichi; Matsuo, Yuichi; Abe, Hiroyuki; Fujiwara, Hitoshi
2006-03-01
A new methodology for the Reynolds-averaged Navier-Stokes modeling is presented on the basis of the amalgamation of heuristic-modeling and turbulence-theory methods. A characteristic turbulence time scale is synthesized in a heuristic manner through the combination of several characteristic time scales. An algebraic model of turbulent-viscosity type for the Reynolds stress is derived from the Reynolds-stress transport equation with the time scale embedded. It is applied to the state of weak spatial and temporal nonequilibrium, and is compared with its theoretical counterpart derived by the two-scale direct-interaction approximation. The synthesized time scale is justified through the agreement of the two expressions derived by these entirely different methods. The derived model is tested in rotating isotropic, channel, and homogeneous-shear flows. It is extended to a nonlinear algebraic model and a supersonic model. The latter is shown to succeed in reproducing the reduction in the growth rate of a free-shear layer flow, without causing wrong effects on wall-bounded flows such as channel and boundary-layer flows.
Test-field method for mean-field coefficients with MHD background
Rheinhardt, M
2010-01-01
Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electr...
Standing Slow MHD Waves in Radiatively Cooling Coronal Loops
K. S. Al-Ghafri
2015-06-01
The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops, namely, thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function, that ensures the temperature evolution of the background plasma due to radiation, coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglecting the magnetic field perturbation and, eventually, reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale, much larger than the oscillation period that subsequently enables using the WKB theory to study the properties of standing wave. The governing equation describing the time-dependent amplitude of waves is obtained and solved analytically. The analytically derived solutions are numerically evaluated to give further insight into the evolution of the standing acoustic waves. We find that the plasma cooling gives rise to a decrease in the amplitude of oscillations. In spite of the reduction in damping rate caused by rising the cooling, the damping scenario of slow standing MHD waves strongly increases in hot coronal loops.
Motion stability of a suspended particle in a MHD flow
Shvarts, I.A.
1977-07-01
An examination is made of the motion instability of a suspended particle in a plane-parallel laminar flow with a velocity profile U(y,A) where A is certain parameter. An expression was obtained for the critical Reynolds number Re = ..cap alpha../delta/U/delta y/:the coefficient ..cap alpha.. is associated with dimensions and form of the particle. The results of the common theory are used for studying the motion instability of suspended spherical particle in Couette--Hartmann MHD flows. At large Hartmann numbers Re*/Ha was shown to be constant. This agrees well with experimental data on the hydrodynamic stability of the MHD flow itself. A definite correlation also takes place between Re/sub kr/(Ha) of a MHD flow and the Reynolds numbers that determine the stability of suspended particles when the Hartmann numbers are small. Thus, in a number of cases it is possible to examine the hydrodynamic stability of a MHD flow by the motion stability of solid particles introduced into the flow. 8 references, 2 illustrations.
Observational Diagnostics for Two-Fluid Turbulence in Molecular Clouds As Suggested by Simulations
Meyer, Chad D; Burkhart, Blakesely; Lazarian, Alex
2013-01-01
We present high resolution simulations of two-fluid (ion-neutral) MHD turbulence with resolutions as large as 512^3. The simulations are supersonic and mildly sub-Alfvenic, in keeping with the conditions present in molecular clouds. Such turbulence is thought to influence star formation processes in molecular clouds because typical cores form on length scales that are comparable to the dissipation scales of this turbulence in the ions. The simulations are motivated by the fact that recent studies of isophotologue lines in molecular clouds have found significant differences in the linewidth-size relationship for neutral and ion species. The goals of this paper are to explain those observations using simulations and analytic theory, present a new set of density-based diagnostics by drawing on similar diagnostics that have been obtained by studying single-fluid turbulence, and show that our two-fluid simulations play a vital role in reconciling alternative models of star formation. The velocity-dependent diagnos...
MHD control in burning plasmas MHD control in burning plasmas
Donné, Tony; Liang, Yunfeng
2012-07-01
Fusion physics focuses on the complex behaviour of hot plasmas confined by magnetic fields with the ultimate aim to develop a fusion power plant. In the future generation of tokamaks like ITER, the power generated by the fusion reactions substantially exceeds the external input power (Pfusion}/Pin >= 10). When this occurs one speaks of a burning plasma. Twenty per cent of the generated fusion power in a burning plasma is carried by the charged alpha particles, which transfer their energy to the ambient plasma in collisions, a process called thermalization. A new phenomenon in burning plasmas is that the alpha particles, which form a minority but carry a large fraction of the plasma kinetic energy, can collectively drive certain types of magneto-hydrodynamic (MHD) modes, while they can suppress other MHD modes. Both types of MHD modes can have desirable effects on the plasma, as well as be detrimental to the plasma. For example, the so-called sawtooth instability, on the one hand, is largely responsible for the transport of the thermalized alpha particles out of the core, but, on the other hand, may result in the loss of the energetic alphas before they have fully thermalized. A further undesirable effect of the sawtooth instability is that it may trigger other MHD modes such as neoclassical tearing modes (NTMs). These NTMs, in turn, are detrimental to the plasma confinement and in some cases may even lead to disruptive termination of the plasma. At the edge of the plasma, finally, so-called edge localized modes or ELMs occur, which result in extremely high transient heat and particle loads on the plasma-facing components of a reactor. In order to balance the desired and detrimental effects of these modes, active feedback control is required. An additional complication occurs in a burning plasma as the external heating power, which is nowadays generally used for plasma control, is small compared to the heating power of the alpha particles. The scientific challenge
Sahraoui, Fouad; Goldstein, Melvyn L.
2010-01-01
Over the past few decades, large-scales solar wind (SW) turbulence has been studied extensively, both theoretically and observationally. Observed power spectra of the low frequency turbulence, which can be described in the magnetohydrodynamic (MHD) limit, are shown to obey the Kolmogorov scaling, $k"{ -5/3 }$, down the local proton gyrofrequency ($C{ci} \\sim O.l$-Hz). Turbulence at frequencies above $C{ci}$ has not been thoroughly investigated and remains far less well understood. Above $C{ ci}$ the spectrum steepens to $\\sim f"{ -2.5}$ and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfven waves (KA W) or by whistler waves, before it is dissipated at small scales, In a case study Sahraoui et al., PRL (2009) have reported the first direct determination of the dissipation range of solar wind turbulence near the electron gyroscale using the high resolution Cluster magnetic and electric field data (up to $10"2$-Hz in the spacecraft reference frame). Above the Doppler-shifted proton scale $C{\\rho i}$ a new inertial range with a scaling $\\sim f"{ -2.3}$ has been evidenced and shown to remarkably agree with theoretical predictions of a quasi-two-dimensional cascade into KA W turbulence. Here, we use a wider sample of data sets of small scale SW turbulence under different plasma conditions, and investigate under which physical criteria the KA W (or the whistler) turbulence may be observed to carry out the cascade at small scales, These new observations/criteria are compared to the predictions on the cascade and the (kinetic) dissipation from the Vlasov theory. Implications of the results on the heating problem of the solar wind will be discussed.
Modelling the dynamics of turbulent floods
Mei, Z; Li, Z; Li, Zhenquan
1999-01-01
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical models for the evolution of the water depth and of vertically averaged flow velocity and turbulent parameters. This new model for the shallow water dynamics of turbulent flow: resolves the vertical structure of the flow and the turbulence; includes interaction between turbulence and long waves; and gives a rational alternative to classical models for turbulent environmental flows.
Magnetic levitation and MHD propulsion
Tixador, P.
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried out in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ...) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. Depuis quelques années nous assistons à un redémarrage de programmes concernant la lévitation et la propulsion supraconductrices. Différents systèmes supraconducteurs de lévitation et de propulsion seront décrits en examinant plus particulièrement l'aspect électromagnétique. Quelques programmes à travers le monde seront abordés. Les trains à sustentation magnétique pourraient constituer un nouveau mode de transport terrestre à vitesse élevée (500 km/h) pour le 21^e siècle. Les japonais n'ont cessé de s'intéresser à ce système avec bobine supraconductrice. Ils envisagent un stade préindustriel avec la construction d'une ligne de 43 km. En 1991 un programme américain pour une durée de six ans a été lancé pour évaluer les performances des systèmes à lévitation pour le transport aux Etats Unis. La MHD (Magnéto- Hydro-Dynamique) présente des avantages intéressants pour la propulsion navale et un regain d'intérêt apparaît à l'heure actuelle. Le japon se situe là encore à la pointe des d
Venaille, Antoine; Vallis, Geoffrey K
2014-01-01
We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel forced by an imposed unstable zonal mean flow, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization on the vertical. By contrast, in the limit of large bottom friction, the flow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these result by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the imposed mean flow appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the...
Temporal intermittency of energy dissipation in magnetohydrodynamic turbulence.
Zhdankin, Vladimir; Uzdensky, Dmitri A; Boldyrev, Stanislav
2015-02-13
Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheetlike coherent structures. Much less is known about intermittency in time, another fundamental aspect of turbulence which has great importance for observations of solar flares and other space or astrophysical phenomena. In this Letter, we investigate the temporal intermittency of energy dissipation in numerical simulations of MHD turbulence. We consider four-dimensional spatiotemporal structures, "flare events," responsible for a large fraction of the energy dissipation. We find that although the flare events are often highly complex, they exhibit robust power-law distributions and scaling relations. We find that the probability distribution of dissipated energy has a power-law index close to α≈1.75, similar to observations of solar flares, indicating that intense dissipative events dominate the heating of the system. We also discuss the temporal asymmetry of flare events as a signature of the turbulent cascade.
Integral Constraints and MHD Stability
Jensen, T. H.
2003-10-01
Determining stability of a plasma in MHD equilibrium, energetically isolated by a conducting wall, requires an assumption on what governs the dynamics of the plasma. One example is the assumption that the plasma obeys ideal MHD, leading to the well known ``δ W" criteria [I. Bernstein, et al., Proc. Roy. Soc. London A244, 17 (1958)]. A radically different approach was used by Taylor [J.B. Taylor, Rev. Mod. Phys. 58, 741 (1986)] in assuming that the dynamics of the plasma is restricted only by the requirement that helicity, an integral constant associated with the plasma, is conserved. The relevancy of Taylor's assumption is supported by the agreement between resulting theoretical results and experimental observations. Another integral constraint involves the canonical angular momentum of the plasma particles. One consequence of using this constraint is that tokamak plasmas have no poloidal current in agreement with some current hole tokamak observations [T.H. Jensen, Phys. Lett. A 305, 183 (2002)].
Birzvalk, Yu.
1978-01-01
The shunting ratio and the local shunting ratio, pertaining to currents induced by a magnetic field in a flow channel, are properly defined and systematically reviewed on the basis of the Lagrange criterion. Their definition is based on the energy balance and related to dimensionless parameters characterizing an MHD flow, these parameters evolving from the Hartmann number and the hydrodynamic Reynolds number as well as the magnetic Reynolds number, and the Lundquist number. These shunting ratios, of current density in the core of a stream (uniform) or equivalent mean current density to the short-circuit (maximum) current density, are given here for a slot channel with nonconducting or conducting walls, for a conduction channel with heavy side rails, and for an MHD-flow around bodies. 5 references, 1 figure.
Laboratory Plasma Source as an MHD Model for Astrophysical Jets
Mayo, Robert M.
1997-01-01
The significance of the work described herein lies in the demonstration of Magnetized Coaxial Plasma Gun (MCG) devices like CPS-1 to produce energetic laboratory magneto-flows with embedded magnetic fields that can be used as a simulation tool to study flow interaction dynamic of jet flows, to demonstrate the magnetic acceleration and collimation of flows with primarily toroidal fields, and study cross field transport in turbulent accreting flows. Since plasma produced in MCG devices have magnetic topology and MHD flow regime similarity to stellar and extragalactic jets, we expect that careful investigation of these flows in the laboratory will reveal fundamental physical mechanisms influencing astrophysical flows. Discussion in the next section (sec.2) focuses on recent results describing collimation, leading flow surface interaction layers, and turbulent accretion. The primary objectives for a new three year effort would involve the development and deployment of novel electrostatic, magnetic, and visible plasma diagnostic techniques to measure plasma and flow parameters of the CPS-1 device in the flow chamber downstream of the plasma source to study, (1) mass ejection, morphology, and collimation and stability of energetic outflows, (2) the effects of external magnetization on collimation and stability, (3) the interaction of such flows with background neutral gas, the generation of visible emission in such interaction, and effect of neutral clouds on jet flow dynamics, and (4) the cross magnetic field transport of turbulent accreting flows. The applicability of existing laboratory plasma facilities to the study of stellar and extragalactic plasma should be exploited to elucidate underlying physical mechanisms that cannot be ascertained though astrophysical observation, and provide baseline to a wide variety of proposed models, MHD and otherwise. The work proposed herin represents a continued effort on a novel approach in relating laboratory experiments to
Interstellar Turbulence II: Implications and Effects
Scalo, J
2004-01-01
Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small scale turbulence in the ionized medium, giving information about the power spe...
Variational approach to low-frequency kinetic-MHD in the current coupling scheme
Burby, Joshua W.; Tronci, Cesare
2017-04-01
Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which obeys a kinetic equation. In this work we apply Hamilton’s variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling schemes, in which energetic particle dynamics are expressed in either guiding center or gyrocenter coordinates. When guiding center theory is used to model the hot particles, we show how energy conservation requires corrections to the standard magnetization term. On the other hand, charge and momentum conservation in gyrokinetic-MHD lead to extra terms in the usual definition of the hot current density as well as modifications to conventional gyrocenter dynamics. All these new features arise naturally from the underlying variational structure of the proposed models.
Momentum Transport in DIII-D Discharges with and Without Magnetohydrodynamics (MHD) Activity
REN Qilong; J.M.PARK; J.S.DEGRASSIE; M.S.CHU; L.L.LAO; H.St.JOHN; R.LAHAYE; Y.M.JEON; ZHANG Cheng; ZHOU Deng; LI Guoqiang
2009-01-01
Two phases of a DIII-D discharge with and without magnetohydrodynamics(MHD)activity are analysed using ONETWO code.The toroidal momentum flux is extracted from experimental data and compared with the predictions by neoclassical theory,Gyro-Landau fluid transport model (GLF23) and Multi-Mode model(MMM95). It iS found that without MHD activities GLF23 and MMM95 provide a reasonable description while with MHD activity no model alone can fully describe the experimental momentum flux.For the phase with MHD activity a simple model of resonant magnetic drag is tested and it cannot fully explain the plasma slowing down observed in experiment.
Turbulent Velocity Structure in Molecular Clouds
Ossenkopf, V; Ossenkopf, Volker; Low, Mordecai-Mark Mac
2002-01-01
We compare velocity structure observed in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to the velocity structure of a suite of simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We examine different methods of characterising the structure, including a scanning-beam size-linewidth relation, structure functions, velocity and velocity difference probability distribution functions (PDFs), and the Delta-variance wavelet transform, and use them to compare models and observations. The Delta-variance is most sensitive in detecting characteristic scales and varying scaling laws, but is limited in the observational application by its lack of intensity weighting. We compare the true velocity PDF in our models to simulated observations of velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better. The observed velocity structure is consistent with supersonic turbulence showing a com...
Transition from 2D HD to 2D MHD turbulence
Seshasayanan, Kannabiran
2015-01-01
We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magneto-hydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions, cascades the energy to the large scales. The second process couples small scale magnetic fields to large scale flows transferring the energy back to the small scales via a non-local mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.
Simulations and Transport Models for Imbalanced Magnetohydrodynamic Turbulence
Ng, Chung-Sang; Dennis, T.
2016-10-01
We present results from a series of three-dimensional simulations of magnetohydrodynamic (MHD) turbulence based on reduced MHD equations. Alfven waves are launched from both ends of a long tube along the background uniform magnetic field so that turbulence develops due to collision between counter propagating Alfven waves in the interior region. Waves are launched randomly with specified correlation time Tc such that the length of the tube, L, is greater than (but of the same order of) VA *Tc such that turbulence can fill most of the tube. While waves at both ends are launched with equal power, turbulence generated is imbalanced in general, with normalized cross-helicity gets close to -1 at one end and 1 at the other end. This simulation setup allows easier comparison of turbulence properties with one-dimensional turbulence transport models, which have been applied rather successfully in modeling solar wind turbulence. However, direct comparison of such models with full simulations of solar wind turbulence is difficult due to much higher level of complexity involved. We will present our latest simulations at different resolutions with decreasing dissipation (resistivity and viscosity) levels and compare with model outputs from turbulence transport models. This work is supported by a NASA Grant NNX15AU61G.
Friedrich, J; Schäfer, T; Grauer, R
2016-01-01
We investigate the scaling behavior of longitudinal and transverse structure functions in homogeneous and isotropic magneto-hydrodynamic (MHD) turbulence by means of an exact hierarchy of structure function equations as well as by direct numerical simulations of two- and three-dimensional MHD turbulence. In particular, rescaling relations between longitudinal and transverse structure functions are derived and utilized in order to compare different scaling behavior in the inertial range. It is found that there are no substantial differences between longitudinal and transverse structure functions in MHD turbulence. This finding stands in contrast to the case of hydrodynamic turbulence which shows persistent differences even at high Reynolds numbers. We propose a physical picture that is based on an effective reduction of pressure contributions due to local regions of same magnitude and alignment of velocity and magnetic field fluctuations. Finally, our findings underline the importance of the pressure term for ...
Turbulence and Stochastic Processes
Celani, Antonio; Mazzino, Andrea; Pumir, Alain
sec:08-1In 1931 the monograph Analytical Methods in Probability Theory appeared, in which A.N. Kolmogorov laid the foundations for the modern theory of Markov processes [1]. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way". Ten years later, his article on fully developed turbulence provided the framework within which most, if not all, of the subsequent theoretical investigations have been conducted [2] (see e.g. the review by Biferale et al. in this volume [3]. Remarkably, the greatest advances made in the last few years towards a thorough understanding of turbulence developed from the successful marriage between the theory of stochastic processes and the phenomenology of turbulent transport of scalar fields. In this article we will summarize these recent developments which expose the direct link between the intermittency of transported fields and the statistical properties of particle trajectories advected by the turbulent flow (see also [4], and, for a more thorough review, [5]. We also discuss the perspectives of the Lagrangian approach beyond passive scalars, especially for the modeling of hydrodynamic turbulence.
Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades
Aluie, Hussein
2017-02-01
We formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales ℓ. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the ‘bare’ velocity and magnetic fields are ‘renormalized’ by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. Particular attention is given to the effects of these subscale terms on the balances of the quadratic invariants of ideal incompressible MHD—energy, cross-helicity and magnetic helicity. At large coarse-graining length-scales, the direct dissipation of the invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) is shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we prove a very strong version of the Woltjer-Taylor conjecture
Investigating prominence turbulence with Hinode SOT Dopplergrams
Hillier, Andrew; Ichimoto, Kiyoshi
2016-01-01
Quiescent prominences host a diverse range of flows, including Rayleigh-Taylor instability driven upflows and impulsive downflows, and so it is no surprise that turbulent motions also exist. As prominences are believed to have a mean horizontal guide field, investigating any turbulence they host could shed light on the nature of MHD turbulence in a wide range of astrophysical systems. In this paper we have investigated the nature of the turbulent prominence motions using structure function analysis on the velocity increments estimated from H$\\alpha$ Dopplergrams constructed with observational data from Hinode SOT. The pdf of the velocity increments shows that as we look at increasingly small spatial separations the distribution displays greater departure from a reference Gaussian distribution, hinting at intermittency in the velocity field. Analysis of the even order structure functions for both the horizontal and vertical separations showed the existence of two distinct regions displaying different exponents...
Extreme fluctuations and the finite lifetime of the turbulent state.
Goldenfeld, Nigel; Guttenberg, Nicholas; Gioia, Gustavo
2010-03-01
We argue that the transition to turbulence is controlled by large amplitude events that follow extreme distribution theory. The theory suggests an explanation for recent observations of the turbulent state lifetime which exhibit superexponential scaling behavior with Reynolds number.
Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence
Cho, Jungyeon
2013-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \\$b_+^2/b_-^2 \\propto (\\epsilon_+/\\epsilon_-)^n \\$ with n>2). These result...
Direct numerical simulations of helical dynamo action: MHD and beyond
D. O. Gómez
2004-01-01
Full Text Available Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.
Understanding Accretion Disks through Three Dimensional Radiation MHD Simulations
Jiang, Yan-Fei
I study the structures and thermal properties of black hole accretion disks in the radiation pressure dominated regime. Angular momentum transfer in the disk is provided by the turbulence generated by the magneto-rotational instability (MRI), which is calculated self-consistently with a recently developed 3D radiation magneto-hydrodynamics (MHD) code based on Athena. This code, developed by my collaborators and myself, couples both the radiation momentum and energy source terms with the ideal MHD equations by modifying the standard Godunov method to handle the stiff radiation source terms. We solve the two momentum equations of the radiation transfer equations with a variable Eddington tensor (VET), which is calculated with a time independent short characteristic module. This code is well tested and accurate in both optically thin and optically thick regimes. It is also accurate for both radiation pressure and gas pressure dominated flows. With this code, I find that when photon viscosity becomes significant, the ratio between Maxwell stress and Reynolds stress from the MRI turbulence can increase significantly with radiation pressure. The thermal instability of the radiation pressure dominated disk is then studied with vertically stratified shearing box simulations. Unlike the previous results claiming that the radiation pressure dominated disk with MRI turbulence can reach a steady state without showing any unstable behavior, I find that the radiation pressure dominated disks always either collapse or expand until we have to stop the simulations. During the thermal runaway, the heating and cooling rates from the simulations are consistent with the general criterion of thermal instability. However, details of the thermal runaway are different from the predictions of the standard alpha disk model, as many assumptions in that model are not satisfied in the simulations. We also identify the key reasons why previous simulations do not find the instability. The thermal
S. Dastgeer
2005-01-01
Full Text Available Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD fluctuations to density fluctuations through a 'pseudosound' relation within the context of 'nearly incompressible' (NI hydrodynamics (HD and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii the compressible ISM fluctuations form long scale flows and structures, and iii the density and the temperature fluctuations are anti-correlated.
Inverse scattering problem in turbulent magnetic fluctuations
Treumann, R A; Narita, Y
2016-01-01
We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gel$'$fand-Levitan-Marchenko equation of quantum mechanical scattering theory.
MHD stability limits in the TCV Tokamak
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
observed decrease of this limit with elongation is also in qualitative agreement with ideal MHD theory. Edge localised modes (ELMs), occurring in TCV Ohmic high-confinement mode discharges, were observed to be preceded by coherent magnetic oscillations. The detected poloidal and toroidal mode structures are consistent with a resonant flux surface close to the plasma edge. Unlike conventional MHD modes, these precursors start at a random toroidal location and then grow in amplitude and toroidal extent until they encompass the whole toroidal circumference. Thus, the asymmetry causing and maintaining the toroidal localisation of the ELM precursor must be intrinsic to the plasma. Soft X-ray measurements show that the localised precursor always coincides with a central m = 1 mode, which can usually be associated with the sawtooth pre- or postcursor mode. A comparison of the phases indicates a correlation with the maximum of the central mode preceding the toroidal location of the ELM precursor and, therefore, a hitherto unobserved coupling between central modes and ELMs. Highly elongated plasmas promise several advantages, among them higher current and beta limits. During TCV experiments dedicated to an increasing of the plasma elongation, a new disruptive current limit, at values well below the conventional current limit corresponding to q{sub a} > 2, was encountered for {kappa} > 2.3. This limit, which is preceded by a kink-type mode, is found to be consistent with ideal MHD stability calculations. The TCV observations, therefore, provide the first experimental confirmation of a deviation of the linear Troyon-scaling of the ideal beta limit with normalised current at high elongation, which was predicted over 10 years ago. Neoclassical tearing modes (NTMs), which have been observed to limit the achievable beta in a number of tokamaks, arise from a helical perturbation of the bootstrap current caused by an existing seed island. Neoclassical m/n = 2/1 tearing modes have been
MHD Driving of Relativistic Jets
Arieh Königl
2007-01-01
Full Text Available Paulatinamente se ha ido reconociendo que los campos magnéticos juegan un papel dominante en la producción y colimación de chorros astrofísicos. Demostramos aquí, usando soluciones semianalíticas exactas para las ecuaciones de MHD ideal en relatividad especial, que un disco de acreción altamente magnetizado (con un campo magnético principalmente poloidal o azimutal alrededor de un agujero negro es capaz de acelerar un flujo de protones y electrones a los factores de Lorentz y energías cinéticas asociadas a fuentes de destellos de rayos gama y nucleos activos de galaxias. También se discuten las contribuciones a la aceleración provenientes de efectos térmicos (por presión de radiación y pares electrón-positrón y de MHD no ideal. Notamos que la aceleración por MHD se caracteriza por ser extendida espacialmente, y esta propiedad se manifesta más claramente en flujos relativistas. Las indicaciones observacionales de que la aceleración de movimientos superlumínicos en chorros de radio ocurre sobre escalas mucho más grandes que las del agujero negro propiamente, apoyan la idea de que la producción de chorros es principalmente un fenómeno magnético. Presentamos resultados preliminares de un modelo global que puede utilizarse para probar esta interpretación.
Global MHD model of the earth's magnetosphere
Wu, C. C.
1983-01-01
A global MHD model of the earth's magnetosphere is defined. An introduction to numerical methods for solving the MHD equations is given with emphasis on the shock-capturing technique. Finally, results concerning the shape of the magnetosphere and the plasma flows inside the magnetosphere are presented.
An MHD model of the earth's magnetosphere
Wu, C. C.
1985-01-01
It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.
Turbulence and diffusion fossil turbulence
Gibson, C H
2000-01-01
Fossil turbulence processes are central to turbulence, turbulent mixing, and turbulent diffusion in the ocean and atmosphere, in astrophysics and cosmology, and in most other natural flows. George Gamov suggested in 1954 that galaxies might be fossils of primordial turbulence produced by the Big Bang. John Woods showed that breaking internal waves on horizontal dye sheets in the interior of the stratified ocean form highly persistent remnants of these turbulent events, which he called fossil turbulence. The dark mixing paradox of the ocean refers to undetected mixing that must exist somewhere to explain why oceanic scalar fields like temperature and salinity are so well mixed, just as the dark matter paradox of galaxies refers to undetected matter that must exist to explain why rotating galaxies don't fly apart by centrifugal forces. Both paradoxes result from sampling techniques that fail to account for the extreme intermittency of random variables involved in self-similar, nonlinear, cascades over a wide ra...
Coupled simulation of kinetic pedestal growth and MHD ELM crash
Park, G [Courant Institute of Mathematical Sciences, New York University (United States); Cummings, J [California Institute of Technology (United States); Chang, C S [Courant Institute of Mathematical Sciences, New York University (United States); Podhorszki, N [Univ. California at Davis (United States); Klasky, S [ORNL (United States); Ku, S [Courant Institute of Mathematical Sciences, New York University (United States); Pankin, A [Lehigh Univ. (United States); Samtaney, R [Princeton Plasma Physics Laboratory (United States); Shoshani, A [LBNL (United States); Snyder, P [General Atomics (United States); Strauss, H [Courant Institute of Mathematical Sciences, New York University (United States); Sugiyama, L [MIT (United States)
2007-07-15
Edge pedestal height and the accompanying ELM crash are critical elements of ITER physics yet to be understood and predicted through high performance computing. An entirely self-consistent first principles simulation is being pursued as a long term research goal, and the plan is planned for completion in time for ITER operation. However, a proof-of-principle work has already been established using a computational tool that employs the best first principles physics available at the present time. A kinetic edge equilibrium code XGC0, which can simulate the neoclassically dominant pedestal growth from neutral ionization (using a phenomenological residual turbulence diffusion motion superposed upon the neoclassical particle motion) is coupled to an extended MHD code M3D, which can perform the nonlinear ELM crash. The stability boundary of the pedestal is checked by an ideal MHD linear peeling-ballooning code, which has been validated against many experimental data sets for the large scale (type I) ELMs onset boundary. The coupling workflow and scientific results to be enabled by it are described.
Two-fluid MHD Regime of Drift Wave Instability
Yang, Shang-Chuan; Zhu, Ping; Xie, Jin-Lin; Liu, Wan-Dong
2015-11-01
Drift wave instabilities contribute to the formation of edge turbulence and zonal flows, and thus are believed to play essential roles in the anomalous transport processes in tokamaks. Whereas drift waves are generally assumed to be local and electrostatic, experiments have often found regimes where the spatial scales and the magnetic components of drift waves approach those of magnetohydrodynamic (MHD) processes. In this work we study such a drift wave regime in a cylindrical magnetized plasma using a full two-fluid MHD model implemented in the NIMROD code. The linear dependency of growth rates on resistivity and the dispersion relation found in the NIMROD calculations qualitatively agree with theoretical analysis. As the azimuthal mode number increases, the drift modes become highly localized radially; however, unlike the conventional local approximation, the radial profile of the drift mode tends to shift toward the edge away from the center of the density gradient slope, suggesting the inhomogeneity of two-fluid effects. Supported by National Natural Science Foundation of China Grant 11275200 and National Magnetic Confinement Fusion Science Program of China Grant 2014GB124002.
Turbulence measurements in fusion plasmas
Conway, G. D.
2008-12-01
Turbulence measurements in magnetically confined toroidal plasmas have a long history and relevance due to the detrimental role of turbulence induced transport on particle, energy, impurity and momentum confinement. The turbulence—the microscopic random fluctuations in particle density, temperature, potential and magnetic field—is generally driven by radial gradients in the plasma density and temperature. The correlation between the turbulence properties and global confinement, via enhanced diffusion, convection and direct conduction, is now well documented. Theory, together with recent measurements, also indicates that non-linear interactions within the turbulence generate large scale zonal flows and geodesic oscillations, which can feed back onto the turbulence and equilibrium profiles creating a complex interdependence. An overview of the current status and understanding of plasma turbulence measurements in the closed flux surface region of magnetic confinement fusion devices is presented, highlighting some recent developments and outstanding problems.
Feasibility of MHD submarine propulsion
Doss, E.D. (ed.) (Argonne National Lab., IL (United States)); Sikes, W.C. (ed.) (Newport News Shipbuilding and Dry Dock Co., VA (United States))
1992-09-01
This report describes the work performed during Phase 1 and Phase 2 of the collaborative research program established between Argonne National Laboratory (ANL) and Newport News Shipbuilding and Dry Dock Company (NNS). Phase I of the program focused on the development of computer models for Magnetohydrodynamic (MHD) propulsion. Phase 2 focused on the experimental validation of the thruster performance models and the identification, through testing, of any phenomena which may impact the attractiveness of this propulsion system for shipboard applications. The report discusses in detail the work performed in Phase 2 of the program. In Phase 2, a two Tesla test facility was designed, built, and operated. The facility test loop, its components, and their design are presented. The test matrix and its rationale are discussed. Representative experimental results of the test program are presented, and are compared to computer model predictions. In general, the results of the tests and their comparison with the predictions indicate that thephenomena affecting the performance of MHD seawater thrusters are well understood and can be accurately predicted with the developed thruster computer models.
Turbulent transport in hydromagnetic flows
Brandenburg, A; Del Sordo, F; Hubbard, A; Käpylä, P J; Rheinhardt, M
2010-01-01
The predictive power of mean-field theory is emphasized by comparing theory with simulations under controlled conditions. The recently developed test-field method is used to extract turbulent transport coefficients both in kinematic as well as nonlinear and quasi-kinematic cases. A striking example of the quasi-kinematic method is provided by magnetic buoyancy-driven flows that produce an alpha effect and turbulent diffusion.
Magnetohydrodynamic turbulent cascade of coronal loop magnetic fields.
Rappazzo, A F; Velli, M
2011-06-01
The Parker model for coronal heating is investigated through a high resolution simulation. An inertial range is resolved where fluctuating magnetic energy EMk[Please see symbol]) [Please see symbol] k[Please see symbol](-2.7) exceeds kinetic energy EK(k[Please see symbol])[Please see symbol]k[Please see symbol](-0.6). Increments scale as δbℓ ~/= ℓ(-0.85) and δuℓ ~/= ℓ(+0.2) with velocity increasing at small scales, indicating that magnetic reconnection plays a prime role in this turbulent system. We show that spectral energy transport is akin to standard magnetohydrodynamic (MHD) turbulence even for a system of reconnecting current sheets sustained by the boundary. In this new MHD turbulent cascade, kinetic energy flows are negligible while cross-field flows are enhanced, and through a series of "reflections" between the two fields, cascade more than half of the total spectral energy flow.
A renormalization group analysis of two-dimensional magnetohydrodynamic turbulence
Liang, Wenli Z.; Diamond, P. H.
1993-01-01
The renormalization group (RNG) method is used to study the physics of two-dimensional (2D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean-square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2D MHD system. A similar conclusion is reached for 2D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual-direction transfer.
On the energy spectrum of strong magnetohydrodynamic turbulence
Perez, Jean Carlos; Boldyrev, Stanislav; Cattaneo, Fausto
2012-01-01
The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of MHD turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048^3 mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state MHD turbulence to date. We study both the balanced case, where the energies associated with Alfv\\'en modes propagating in opposite directions along the guide field, E^+ and $E^-, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent -3/2 as the Reynolds number is increased, consistent with phenomenological models that include sc...
Turbulent mixing condensation nucleus counter
Mavliev, Rashid
The construction and operating principles of the Turbulent Mixing Condensation Nucleus Counter (TM CNC) are described. Estimations based on the semiempirical theory of turbulent jets and the classical theory of nucleation and growth show the possibility of detecting particles as small as 2.5 nm without the interference of homogeneous nucleation. This conclusion was confirmed experimentally during the International Workshop on Intercomparison of Condensation Nuclei and Aerosol Particle Counters (Vienna, Austria). Number concentration, measured by the Turbulent Mixing CNC and other participating instruments, is found to be essentially equal.
Subcritical excitation of plasma turbulence
Itoh, K.; Itoh, S.; Yagi, M.; Fukuyama, A.
1996-01-01
Theory of current-diffusive interchange mode turbulence in plasmas is developed in the presence of collisional transport. Double-valued amplitude of stationary fluctuations is expressed in terms of the pressure gradient. The backward bifurcation is shown to appear near the linear stability boundary. The subcritical nature of the turbulence is explicitly illustrated. Critical pressure gradient at which the transition from collisional transport to the turbulent one is to occur is predicted. This provides a prototype of the transport theory for nonlinear-non-equilibrium systems. (author).
Subcritical excitation of plasma turbulence
Itoh, Kimitaka [National Inst. for Fusion Science, Nagoya (Japan); Itoh, Sanae; Yagi, Masatoshi; Fukuyama, Atsushi
1996-09-01
Theory of current-diffusive interchange mode turbulence in plasmas in the presence of collisional transport is developed. Amplitude of stationary fluctuations is expressed in terms of the double-valued function of the pressure gradient. The backward bifurcation is shown to appear near the linear stability boundary. The subcritical nature of the turbulence is explicitly illustrated. The critical pressure gradient at which the transition from collisional transport to the turbulent one is to occur is predicted. This work provides a prototype of the transport theory for nonlinear-nonequilibrium systems. (author)
Vikhrev, V. V.; Baronova, E. O.
2006-01-01
Pinch dynamics is described, which takes into account generation of turbulent magnetic fields. Turbulent/chaotic magnetic fields (TMF) appear due to MHD and kinetic instabilities. It is shown, that TMF arises near the moment of maximal compression and essentially affects plasma dynamics at the expansion stage.
Extended MHD Modeling of Tearing-Driven Magnetic Relaxation
Sauppe, Joshua
2016-10-01
Driven plasma pinch configurations are characterized by the gradual accumulation and episodic release of free energy in discrete relaxation events. The hallmark of this relaxation in a reversed-field pinch (RFP) plasma is flattening of the parallel current density profile effected by a fluctuation-induced dynamo emf in Ohm's law. Nonlinear two-fluid modeling of macroscopic RFP dynamics has shown appreciable coupling of magnetic relaxation and the evolution of plasma flow. Accurate modeling of RFP dynamics requires the Hall effect in Ohm's law as well as first order ion finite Larmor radius (FLR) effects, represented by the Braginskii ion gyroviscous stress tensor. New results find that the Hall dynamo effect from / ne can counter the MHD effect from - in some of the relaxation events. The MHD effect dominates these events and relaxes the current profile toward the Taylor state, but the opposition of the two dynamos generates plasma flow in the direction of equilibrium current density, consistent with experimental measurements. Detailed experimental measurements of the MHD and Hall emf terms are compared to these extended MHD predictions. Tracking the evolution of magnetic energy, helicity, and hybrid helicity during relaxation identifies the most important contributions in single-fluid and two-fluid models. Magnetic helicity is well conserved relative to the magnetic energy during relaxation. The hybrid helicity is dominated by magnetic helicity in realistic low-beta pinch conditions and is also well conserved. Differences of less than 1 % between magnetic helicity and hybrid helicity are observed with two-fluid modeling and result from cross helicity evolution through ion FLR effects, which have not been included in contemporary relaxation theories. The kinetic energy driven by relaxation in the computations is dominated by velocity components perpendicular to the magnetic field, an effect that had not been predicted. Work performed at University of Wisconsin
MHD Instabilities Occurring Near/AT the Transport Barrier, Including Loss of Confinement in H-Modes
L. L. Lao
1999-09-01
In configurations with transport barriers the improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost. In this presentation, recent experimental and theoretical developments concerning MHD instabilities occurring near/at the edge and the core transport barriers are summarized emphasizing the dominant instabilities and the comparison with theory.
Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles
Qin, G.; Shalchi, A.
2016-05-01
Recently developed theories for perpendicular diffusion work remarkably well. The diffusion coefficients they provide agree with test-particle simulations performed for different turbulence setups ranging from slab and slab-like models to two-dimensional and noisy reduced MHD turbulence. However, such theories are still based on different analytical approximations. In the current paper we use a test-particle code to explore the different approximations used in diffusion theory. We benchmark different guiding center approximations, simplifications of higher-order correlations, and the Taylor-Green-Kubo formula. We demonstrate that guiding center approximations work very well as long as the particle's unperturbed Larmor radius is smaller than the perpendicular correlation length of the turbulence. Furthermore, the Taylor-Green-Kubo formula and the definition of perpendicular diffusion coefficients via mean square displacements provide the same results. The only approximation that was used in the past in nonlinear diffusion theory that fails is to replace fourth-order correlations by a product of two second-order correlation functions. In more advanced nonlinear theories, however, this type of approximation is no longer used. Therefore, we confirm the validity of modern diffusion theories as a result of the work presented in the current paper.
A mode filter for plasma waves in the Hall-MHD approximation
C. Vocks
Full Text Available A filter method is presented which allows a qualitative and quantitative identification of wave modes observed with plasma experiments on satellites. Hitherto existing mode filters are based on the MHD theory and thus they are restricted to low frequencies well below the ion cyclotron frequency. The present method is generalized to cover wave modes up to the characteristic ion frequencies. The spectral density matrix determined by the observations is decomposed using the eigenvectors of the linearized Hall-MHD equations. As the wave modes are dispersive in this formalism, a precise determination of the k->-vectors requires the use of multi-point measurements. Therefore the method is particularly relevant to multi-satellite missions. The method is tested using simulated plasma data. The Hall-MHD filter is able to identify the modes excited in the model plasma and to assign the correct energetic contributions. By comparison with the former method it is shown that the simple MHD filter leads to large errors if the frequency is not well below the ion cyclotron frequency. Further the range of validity of the linear theory is examined rising the simulated wave amplitudes.
Key words. Magnetospheric physics (MHD waves and instabilities; plasma waves and instabilities
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D; Abdelhamid, H M; Morrison, P J
2016-01-01
A comprehensive study of a reduced version of Lust's equations, the extended magnetohydrodynamic (XMHD) model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality, is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way energy conservation along with four families of Casimir invariants are naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Structure and computation of two-dimensional incompressible extended MHD
Grasso, D.; Tassi, E.; Abdelhamid, H. M.; Morrison, P. J.
2017-01-01
A comprehensive study of the extended magnetohydrodynamic model obtained from the two-fluid theory for electrons and ions with the enforcement of quasineutrality is given. Starting from the Hamiltonian structure of the fully three-dimensional theory, a Hamiltonian two-dimensional incompressible four-field model is derived. In this way, the energy conservation along with four families of Casimir invariants is naturally obtained. The construction facilitates various limits leading to the Hamiltonian forms of Hall, inertial, and ideal MHD, with their conserved energies and Casimir invariants. Basic linear theory of the four-field model is treated, and the growth rate for collisionless reconnection is obtained. Results from nonlinear simulations of collisionless tearing are presented and interpreted using, in particular, normal fields, a product of the Hamiltonian theory that gives rise to simplified equations of motion.
Alfven Wave Tomography for Cold MHD Plasmas
I.Y. Dodin; N.J. Fisch
2001-09-07
Alfven waves propagation in slightly nonuniform cold plasmas is studied by means of ideal magnetohydrodynamics (MHD) nonlinear equations. The evolution of the MHD spectrum is shown to be governed by a matrix linear differential equation with constant coefficients determined by the spectrum of quasi-static plasma density perturbations. The Alfven waves are shown not to affect the plasma density inhomogeneities, as they scatter off of them. The application of the MHD spectrum evolution equation to the inverse scattering problem allows tomographic measurements of the plasma density profile by scanning the plasma volume with Alfven radiation.
MHD Integrated Topping Cycle Project
1992-07-01
This seventeenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period August 1, 1991 to October 31, 1991. Manufacturing of the prototypical combustor pressure shell has been completed including leak, proof, and assembly fit checking. Manufacturing of forty-five cooling panels was also completed including leak, proof, and flow testing. All precombustor internal components (combustion can baffle and swirl box) were received and checked, and integration of the components was initiated. A decision was made regarding the primary and backup designs for the 1A4 channel. The assembly of the channel related prototypical hardware continued. The cathode wall electrical wiring is now complete. The mechanical design of the diffuser has been completed.
Cosmological AMR MHD with Enzo
Xu, Hao [Los Alamos National Laboratory; Li, Hui [Los Alamos National Laboratory; Li, Shengtai [Los Alamos National Laboratory
2009-01-01
In this work, we present EnzoMHD, the extension of the cosmological code Enzoto include magnetic fields. We use the hyperbolic solver of Li et al. (2008) for the computation of interface fluxes. We use constrained transport methods of Balsara & Spicer (1999) and Gardiner & Stone (2005) to advance the induction equation, the reconstruction technique of Balsara (2001) to extend the Adaptive Mesh Refinement of Berger & Colella (1989) already used in Enzo, though formulated in a slightly different way for ease of implementation. This combination of methods preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non cosmologjcal tests problems to demonstrate the quality of solution resulting from this combination of solvers.
Simulation of MHD collimation from differential rotation
Carey, Christopher
2005-10-01
Recent observations indicate that astrophysical outflows from active galactic nuclei are permeated with helical magnetic fields[1]. The most promising theory for the formation of the magnetic configurations in these magnetically driven jets is the coiling of an initial seed field by the differential rotation of the accretion disk surrounding the central object. We have begun simulations that are relevant to these Poynting jets using the NIMROD code[2]. To simulate dynamics on length scales that are significantly larger than the accretion disk, the non-relativistic MHD equations are evolved on a hemispherical logarithmic mesh. The accretion disk is treated as a condition on the lower boundary by applying a Keplerian velocity to the azimuthal component of the fluid velocity and a prescribed flux of mass through the boundary. The magnetic field configuration is initialized to a dipole like field. Formation of a jet outflow is observed later in time. The initial field is coiled up and collimated, driving a large current density on the axis of symmetry. Slipping of magnetic field lines due to non-ideal effects has been investigated. 1. Asada K. et. al., Pub. of the Astr. Soc. of Japan, 54, L39-L43, 2002 2. Sovinec C. et. al., J. Comp. Phys., 195, 355-386, 2004
Chomaz, J.M. [Ecole Polytechnique, LadHyX-CNRS, 91 - Palaiseau (France)
2004-06-01
Mixing layers, jets, wakes, boundary layers over wings or rotating disks, Poiseuille and Couette flows are examples of open shear flows encountered in many industrial or geophysical situations. These flows develop spatially under the combined action of advection and instabilities and eventually undergo a transition to turbulence. In the eighties, the linear concepts of absolute and convective instability succeeded in predicting some aspects of open shear flow dynamics, but a description of their spatio-temporal development including nonlinear effects and secondary instabilities was lacking and even the very fact that a linear criterion describes so well strongly nonlinear flows remains mysterious. The present work reports on very recent progress elucidating open shear flow dynamics. A fully nonlinear extension of the concepts of absolute and convective instability introduced by Chomaz (Phys. Rev. Lett. 69 (1992) 1931) is recalled in connection with the broader problem of front and pattern selection. These new ideas are first illustrated on simple amplitude equations. Then the fully nonlinear concepts are applied to actual flows such as wakes and mixing layers. Furthermore, new scenarios involving secondary absolute instability are proposed and compared to the dynamics of the rotating disk and mixing layers experiment. (author)
Theorem of turbulent intensity and macroscopic mechanism of the turbulence development
2007-01-01
Turbulence is one of the most common nature phenomena in everyday experience, but that is not adequately understood yet. This article reviews the history and present state of development of the turbulence theory and indicates the necessity to probe into the turbulent features and mechanism with the different methods at different levels. Therefore this article proves a theorem of turbulent transpor- tation and a theorem of turbulent intensity by using the theory of the nonequilibrium thermodynamics, and that the Reynolds turbulence and the Rayleigh-Bénard turbulence are united in the theorems of the turbulent intensity and the turbulent transportation. The macroscopic cause of the development of fluid turbulence is a result from shearing effect of the velocity together with the temperature, which is also the macroscopic cause of the stretch and fold of trajectory in the phase space of turbulent field. And it is proved by the observed data of atmosphere that the phenomenological coefficient of turbulent in- tensity is not only a function of the velocity shear but also a function of temperature shear, viz the sta- bility of temperature stratification, in the atmosphere. Accordingly, authenticity of the theorem, which is proved by the theory of nonequilibrium thermodynamics, of turbulent intensity is testified by the facts of observational experiment.
Horton, W. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Hu, G. [Globalstar LP, San Jose, CA (United States)
1998-07-01
The origin of plasma turbulence from currents and spatial gradients in plasmas is described and shown to lead to the dominant transport mechanism in many plasma regimes. A wide variety of turbulent transport mechanism exists in plasmas. In this survey the authors summarize some of the universally observed plasma transport rates.
EuHIT, Collaboration
2015-01-01
As a member of the EuHIT (European High-Performance Infrastructures in Turbulence - see here) consortium, CERN is participating in fundamental research on turbulence phenomena. To this end, the Laboratory provides European researchers with a cryogenic research infrastructure (see here), where the first tests have just been performed.
Testing assumptions and predictions of star-formation theories
González-Samaniego, Alejandro; González, Ricardo F; Kim, Jongsoo
2013-01-01
We present numerical simulations of isothermal, MHD, supersonic turbulence, designed to test various hypotheses frequently assumed in star formation(SF) theories. We consider three simulations, each with a different combination of physical size, rms sonic Mach number, and Jeans parameter, but chosen as to give the same value of the virial parameter and to conform with Larson's scaling relations. As in the non-magnetic case: we find no simultaneously subsonic and super-Jeans structures in our MHD simulations. We find that the fraction of small-scale super-Jeans structures increases when self gravity is turned on, and that the production of gravitationally unstable dense cores by turbulence alone is very low. This implies that self-gravity is in general necessary not only to induce the collapse of Jeans-unstable cores, but also to form them. We find that denser regions tend to have more negative values of the velocity divergence, implying a net inwards flow towards the regions' centers. We compare the results f...
Characteristics of laminar MHD fluid hammer in pipe
Huang, Z.Y.; Liu, Y.J., E-mail: yajun@scut.edu.cn
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
Equations of state for self-excited MHD generator studies
Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K.
1980-02-26
We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range.
Are "EIT Waves" Fast-Mode MHD Waves?
Wills-Davey, M J; Stenflo, J O
2007-01-01
We examine the nature of large-scale, coronal, propagating wave fronts (``EIT waves'') and find they are incongruous with solutions using fast-mode MHD plane-wave theory. Specifically, we consider the following properties: non-dispersive single pulse manifestions, observed velocities below the local Alfven speed, and different pulses which travel at any number of constant velocities, rather than at the ``predicted'' fast-mode speed. We discuss the possibility of a soliton-like explanation for these phenomena, and show how it is consistent with the above-mentioned aspects.
Turbulence-driven Polar Winds from T Tauri Stars Energized by Magnetospheric Accretion
Cranmer, Steven R
2008-01-01
Pre-main-sequence stars are observed to be surrounded by both accretion flows and some kind of wind or jet-like outflow. Recent work by Matt and Pudritz has suggested that if classical T Tauri stars exhibit stellar winds with mass loss rates about 0.1 times their accretion rates, the wind can carry away enough angular momentum to keep the stars from being spun up unrealistically by accretion. This paper presents a preliminary set of theoretical models of accretion-driven winds from the polar regions of T Tauri stars. These models are based on recently published self-consistent simulations of the Sun's coronal heating and wind acceleration. In addition to the convection-driven MHD turbulence (which dominates in the solar case), we add another source of wave energy at the photosphere that is driven by the impact of plasma in neighboring flux tubes undergoing magnetospheric accretion. This added energy, determined quantitatively from the far-field theory of MHD wave generation, is sufficient to produce T Tauri-l...
Revisiting Acceleration of Charged Grains in Magnetohydrodynamic Turbulence
Hoang, Thiem; Schlickeiser, R
2011-01-01
We study the acceleration of charged grains by magnetohydrodynamics (MHD) turbulence in the interstellar medium (ISM). We begin with revisiting gyroresonance acceleration by taking into account fluctuations of the grain guiding center along a uniform magnetic field (i.e. non-linear theory, NLT). We calculate grain velocity due to gyroresonance acceleration by fast modes using the NLT for different phases of the ISM, and compare with results obtained using quasi-linear theory (QLT). We find that the fluctuations of the grain guiding center reduce the grain velocity by less than 15 percent, but large grains are still accelerated to super-Alfvenic speed. For such super-Alfvenic grains, we investigate the effect of transit time damping (TTD) by fast modes. We find that due to the broadening of resonance condition in the NLT, the TTD acceleration is not only important for the cosine pitch angle $\\mu>V_{A}/v$, but also for $\\mu
Testing a missing spectral link in turbulence
Kellay, H.; Tran, A.T.; Goldburg, W.; Goldenfeld, N.; Gioia, G.; Chakraborty, P.
2012-01-01
Although the cardinal attribute of turbulence is the velocity fluctuations, these fluctuations have been ignored in theories of the frictional drag of turbulent flows. Our goal is to test a new theory that links the frictional drag to the spectral exponent , a property of the velocity fluctuations i
Open Boundary Conditions for Dissipative MHD
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Black Hole Variability in MHD: A Numerical Test of the Propagating Fluctuations Model
Hogg, J. Drew; Reynolds, Christopher S.
2017-08-01
The variability properties of accreting black hole systems offer a crucial probe of the accretion physics providing the angular momentum transport and enabling the mass accretion. A few of the most telling signatures are the characteristic log-normal flux distributions, linear RMS-flux relations, and frequency-dependent time lags between energy bands. These commonly observed properties are often interpreted as evidence of inward propagating mass accretion rate fluctuations where fluctuations in the accretion flow combine multiplicatively. We present recent results from a long, semi-global MHD simulation of a thin (h/r=0.1) accretion disk that naturally reproduces this phenomenology. This bolsters the theoretical underpinnings of the “propagating fluctuations” model and demonstrates the viability of this process manifesting in MHD turbulence driven by the magnetorotational instability. We find that a key ingredient to this model is the modulation of the effective α parameter by the magnetic dynamo.
Plunian, Franck; Stepanov, Rodion
2010-10-01
A phenomenology of isotropic magnetohydrodynamic (MHD) turbulence subject to both rotation and applied magnetic field is presented. It is assumed that the triple correlation decay time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and the Alfvén wave period. For Pm=1 it leads to four kinds of piecewise spectra, depending on four parameters: injection rate of energy, magnetic diffusivity, rotation rate, and applied field. With a shell model of MHD turbulence (including rotation and applied magnetic field), spectra for Pm ≤ 1 are presented, together with the ratio between magnetic and viscous dissipations.
Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics.
Busse, Angela; Müller, Wolf-Christian; Gogoberidze, Grigol
2010-12-01
For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations τ(ac) and the associated cascade time scale τ(cas). Thus, the Lagrangian energy spectrum can serve to identify weak (τ(ac) ≪ τ(cas)) and strong (τ(ac) ∼ τ(cas)) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.
Turbulent Transport in a Three-dimensional Solar Wind
Shiota, D.; Zank, G. P.; Adhikari, L.; Hunana, P.; Telloni, D.; Bruno, R.
2017-03-01
Turbulence in the solar wind can play essential roles in the heating of coronal and solar wind plasma and the acceleration of the solar wind and energetic particles. Turbulence sources are not well understood and thought to be partly enhanced by interaction with the large-scale inhomogeneity of the solar wind and the interplanetary magnetic field and/or transported from the solar corona. To investigate the interaction with background inhomogeneity and the turbulence sources, we have developed a new 3D MHD model that includes the transport and dissipation of turbulence using the theoretical model of Zank et al. We solve for the temporal and spatial evolution of three moments or variables, the energy in the forward and backward fluctuating modes and the residual energy and their three corresponding correlation lengths. The transport model is coupled to our 3D model of the inhomogeneous solar wind. We present results of the coupled solar wind-turbulence model assuming a simple tilted dipole magnetic configuration that mimics solar minimum conditions, together with several comparative intermediate cases. By considering eight possible solar wind and turbulence source configurations, we show that the large-scale solar wind and IMF inhomogeneity and the strength of the turbulence sources significantly affect the distribution of turbulence in the heliosphere within 6 au. We compare the predicted turbulence distribution results from a complete solar minimum model with in situ measurements made by the Helios and Ulysses spacecraft, finding that the synthetic profiles of the turbulence intensities show reasonable agreement with observations.
Simulation and modeling of turbulent flows
Gatski, Thomas B; Lumley, John L
1996-01-01
This book provides students and researchers in fluid engineering with an up-to-date overview of turbulent flow research in the areas of simulation and modeling. A key element of the book is the systematic, rational development of turbulence closure models and related aspects of modern turbulent flow theory and prediction. Starting with a review of the spectral dynamics of homogenous and inhomogeneous turbulent flows, succeeding chapters deal with numerical simulation techniques, renormalization group methods and turbulent closure modeling. Each chapter is authored by recognized leaders in their respective fields, and each provides a thorough and cohesive treatment of the subject.
Turbulence in Natural Environments
Banerjee, Tirtha
Problems in the area of land/biosphere-atmosphere interaction, hydrology, climate modeling etc. can be systematically organized as a study of turbulent flow in presence of boundary conditions in an increasing order of complexity. The present work is an attempt to study a few subsets of this general problem of turbulence in natural environments- in the context of neutral and thermally stratified atmospheric surface layer, the presence of a heterogeneous vegetation canopy and the interaction between air flow and a static water body in presence of flexible protruding vegetation. The main issue addressed in the context of turbulence in the atmospheric surface layer is whether it is possible to describe the macro-states of turbulence such as mean velocity and turbulent velocity variance in terms of the micro-states of the turbulent flow, i.e., a distribution of turbulent kinetic energy across a multitude of scales. This has been achieved by a `spectral budget approach' which is extended for thermal stratification scenarios as well, in the process unifying the seemingly different and unrelated theories of turbulence such as Kolmogorov's hypothesis, Heisenberg's eddy viscosity, Monin Obukhov Similarity Theory (MOST) etc. under a common framework. In the case of a more complex scenario such as presence of a vegetation canopy with edges and gaps, the question that is addressed is in what detail the turbulence is needed to be resolved in order to capture the bulk flow features such as recirculation patterns. This issue is addressed by a simple numerical framework and it has been found out that an explicit prescription of turbulence is not necessary in presence of heterogeneities such as edges and gaps where the interplay between advection, pressure gradients and drag forces are sufficient to capture the first order dynamics. This result can be very important for eddy-covariance flux calibration strategies in non-ideal environments and the developed numerical model can be
Basu, Abhik; Naji, Ali; Pandit, Rahul
2014-01-01
We generalize the method of A. M. Polyakov, [Phys. Rev. E 52, 6183 (1995), 10.1103/PhysRevE.52.6183] for obtaining structure-function relations in turbulence in the stochastically forced Burgers equation, to develop structure-function hierarchies for turbulence in three models for magnetohydrodynamics (MHD). These are the Burgers analogs of MHD in one dimension [Eur. Phys. J. B 9, 725 (1999), 10.1007/s100510050817], and in three dimensions (3DMHD and 3D Hall MHD). Our study provides a convenient and unified scheme for the development of structure-function hierarchies for turbulence in a variety of coupled hydrodynamical equations. For turbulence in the three sets of MHD equations mentioned above, we obtain exact relations for third-order structure functions and their derivatives; these expressions are the analogs of the von Kármán-Howarth relations for fluid turbulence. We compare our work with earlier studies of such relations in 3DMHD and 3D Hall MHD.
A simplified MHD model of capillary Z-Pinch compared with experiments
Shapolov, A.A.; Kiss, M.; Kukhlevsky, S.V. [Institute of Physics, University of Pecs (Hungary)
2016-11-15
The most accurate models of the capillary Z-pinches used for excitation of soft X-ray lasers and photolithography XUV sources currently are based on the magnetohydrodynamics theory (MHD). The output of MHD-based models greatly depends on details in the mathematical description, such as initial and boundary conditions, approximations of plasma parameters, etc. Small experimental groups who develop soft X-ray/XUV sources often use the simplest Z-pinch models for analysis of their experimental results, despite of these models are inconsistent with the MHD equations. In the present study, keeping only the essential terms in the MHD equations, we obtained a simplified MHD model of cylindrically symmetric capillary Z-pinch. The model gives accurate results compared to experiments with argon plasmas, and provides simple analysis of temporal evolution of main plasma parameters. The results clarify the influence of viscosity, heat flux and approximations of plasma conductivity on the dynamics of capillary Z-pinch plasmas. The model can be useful for researchers, especially experimentalists, who develop the soft X-ray/XUV sources. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
MHD activity in the ISX-B tokamak: experimental results and theoretical interpretation
Carreras, B.A.; Dunlap, J.L.; Bell, J.D.; Charlton, L.A.; Cooper, W.A.; Dory, R.A.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.
1982-01-01
The observed spectrum of MHD fluctuations in the ISX-B tokamak is clearly dominated by the n=1 mode when the q=1 surface is in the plasma. This fact agrees well with theoretical predictions based on 3-D resistive MHD calculations. They show that the (m=1; n=1) mode is then the dominant instability. It drives other n=1 modes through toroidal coupling and n>1 modes through nonlinear couplings. These theoretically predicted mode structures have been compared in detail with the experimentally measured wave forms (using arrays of soft x-ray detectors). The agreement is excellent. More detailed comparisons between theory and experiment have required careful reconstructions of the ISX-B equilibria. The equilibria so constructed have permitted a precise evaluation of the ideal MHD stability properties of ISX-B. The present results indicate that the high ..beta.. ISX-B equilibria are marginally stable to finite eta ideal MHD modes. The resistive MHD calculations also show that at finite ..beta.. there are unstable resistive pressure driven modes.
D. Falceta-Gonçalves
2011-01-01
Full Text Available The Interstellar Medium (ISM is a complex, multi-phase system, where the history of the stars occurs. The processes of birth and death of stars are strongly coupled to the dynamics of the ISM. The observed chaotic and diffusive motions of the gas characterize its turbulent nature. Understanding turbulence is crucial for understanding the star-formation process and the energy-mass feedback from evolved stars. Magnetic fields, threading the ISM, are also observed, making this effort even more difficult. In this work, I briefly review the main observations and the characterization of turbulence from these observable quantities. Following on, I provide a review of the physics of magnetized turbulence. Finally, I will show the main results from theoretical and numerical simulations, which can be used to reconstruct observable quantities, and compare these predictions to the observations.
Hanratty, Thomas J.
1980-01-01
This paper gives an account of research on the structure of turbulence close to a solid boundary. Included is a method to study the flow close to the wall of a pipe without interferring with it. (Author/JN)
Trunev A. P.
2014-05-01
Full Text Available In this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed
On the Nature of Magnetic Turbulence in Rotating, Shearing Flows
Walker, Justin; Boldyrev, Stanislav
2015-01-01
The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to $k^{-2}$, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While the spectrum of the fluctuations is universal, the outer-scale characteristics of the turbulence are not; they depend on the parameters of the system, such as the net magnetic flux. However, there is remarkable universality among the allowed turbulent states -- their intensity $v_0$ and their outer scale $\\lambda_0$ satisfy the balance condition $v_0/\\lambda_0\\sim \\mathrm d\\Omega/\\mathrm d\\ln r$, where $\\mathrm d\\Omega/\\mathrm d\\l...
MHD Jets in inhomogeneous media
S. O´Sullivan
2002-01-01
Full Text Available Presentamos simulaciones de la propagaci on de jets moleculares no-adiab aticos en un medio ambiente inhomog eneo. Los jets tienen condiciones descritos por un modelo de jet MHD en el cual la forma de las l neas magn eticas se prescribe cerca de la fuente. Per les de densidad ambiental fueron elegidos para representar la zona de transici on entre las regiones exteriores de una nube molecular y el medio interestelar. Escalamos las tasas de enfriamiento at omico y molecular a niveles apropriados para resolver todas las escalas espaciales apropriadas. Con la inclusi on de variabilidad de la fuente, las simulaciones reproducen varias caracter sticas observacionales de jets moleculares, entre ellas las cavidades moleculares. Adicionalmente, encontramos similitudes entre teor a y observaci on para la fracci on de ionizaci on a lo largo del jet. Encontramos que la extensi on lateral de las super cies de trabajo internas son sensibles al medio ambiente. Tambi en presentamos resultados preliminares para un m etodo de calcular mapas de emisi on en l neas usando solamente variables fundamentales de estado que parecen reproducir la emisi on lamentosa de Balmer en frentes de choque.
MHD Integrated Topping Cycle Project
1992-02-01
This fourteenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period November 1, 1990 to January 31, 1991. Testing of the High Pressure Cooling Subsystem electrical isolator was completed. The PEEK material successfully passed the high temperature, high pressure duration tests (50 hours). The Combustion Subsystem drawings were CADAM released. The procurement process is in progress. An equipment specification and RFP were prepared for the new Low Pressure Cooling System (LPCS) and released for quotation. Work has been conducted on confirmation tests leading to final gas-side designs and studies to assist in channel fabrication.The final cathode gas-side design and the proposed gas-side designs of the anode and sidewall are presented. Anode confirmation tests and related analyses of anode wear mechanisms used in the selection of the proposed anode design are presented. Sidewall confirmation tests, which were used to select the proposed gas-side design, were conducted. The design for the full scale CDIF system was completed. A test program was initiated to investigate the practicality of using Avco current controls for current consolidation in the power takeoff (PTO) regions and to determine the cause of past current consolidation failures. Another important activity was the installation of 1A4-style coupons in the 1A1 channel. A description of the coupons and their location with 1A1 channel is presented herein.
Vorticity, Shocks and Magnetic Fields in Subsonic, ICM-like Turbulence
Porter, David H; Ryu, Dongsu
2015-01-01
We analyze high resolution simulations of compressible, MHD turbulence with properties resembling conditions in galaxy clusters. The flow is driven to turbulence Mach number $\\mathcal{M}_t \\sim 1/2$ in an isothermal medium with an initially very weak, uniform seed magnetic field ($\\beta = P_g/P_B = 10^6$). Since cluster turbulence is likely to result from a mix of sheared (solenoidal) and compressive forcing processes, we examine the distinct turbulence properties for both cases. In one set of simulations velocity forcing is entirely solenoidal ($\
Scale invariance and superfluid turbulence
Sen, Siddhartha, E-mail: siddhartha.sen@tcd.ie [CRANN, Trinity College Dublin, Dublin 2 (Ireland); R.K. Mission Vivekananda University, Belur 711 202, West Bengal (India); Ray, Koushik, E-mail: koushik@iacs.res.in [Department of Theoretical Physics, Indian Association for the Cultivation of Science, Calcutta 700 032 (India)
2013-11-11
We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot–Savart interaction between the observed filament excitations of the system as well.
Chiral Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence
Banerjee, Supratik
2016-01-01
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous (non-isotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with non-zero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e. the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations while the magnetic helicity cascade is linked to the right polarized fluctuations.
Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence.
Banerjee, Supratik; Galtier, Sébastien
2016-03-01
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants, which are the magnetic helicity and the generalized helicity. Exact relations are derived for homogeneous (nonisotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with nonzero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e., the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations, while the magnetic helicity cascade is linked to the right polarized fluctuations.
GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
Trunev A. P.
2015-03-01
Full Text Available The article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory
Polymer Stretching by Turbulence
Chertkov, M
2000-01-01
The stretching of a polymer chain by a large scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is quantitatively described, i.e. the dependency on the flow parameters (Lyapunov exponent statistics) and the chain characteristics (the number of beads and the inter-bead elastic potential) is made explicit. Implications for the drag reduction theory are discussed.
Random functions and turbulence
Panchev, S
1971-01-01
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random
Coherence in Turbulence: New Perspective
Levich, Eugene
2009-07-01
It is claimed that turbulence in fluids is inherently coherent phenomenon. The coherence shows up clearly as strongly correlated helicity fluctuations of opposite sign. The helicity fluctuations have cellular structure forming clusters that are actually observed as vorticity bands and coherent structures in laboratory turbulence, direct numerical simulations and most obviously in atmospheric turbulence. The clusters are named BCC - Beltrami Cellular Clusters - because of the observed nearly total alignment of the velocity and vorticity fields in each particular cell, and hence nearly maximal possible helicity in each cell; although when averaged over all the cells the residual mean helicity in general is small and does not play active dynamical role. The Beltrami like fluctuations are short-lived and stabilize only in small and generally contiguous sub-domains that are tending to a (multi)fractal in the asymptotic limit of large Reynolds numbers, Re → ∞. For the model of homogeneous isotropic turbulence the theory predicts the leading fractal dimension of BCC to be: DF = 2.5. This particular BCC is responsible for generating the Kolmogorov -5/3 power law energy spectrum. The most obvious role that BCC play dynamically is that the nonlinear interactions in them are relatively reduced, due to strong spatial alignment between the velocity field v(r, t) and the vorticity field ω(r, t) = curlv(r, t), while the physical quantities typically best characterizing turbulence intermittency, such as entrophy, vorticity stretching and generation, and energy dissipation are maximized in and near them. The theory quantitatively relates the reduction of nonlinear inter-actions to the BCC fractal dimension DF and subsequent turbulence intermittency. It is further asserted that BCC is a fundamental feature of all turbulent flows, e.g., wall bounded turbulent flows, atmospheric and oceanic flows, and their leading fractal dimension remains invariant and universal in these flows
Rani, Sarma; Dhariwal, Rohit; Koch, Donald
2016-11-01
In an earlier work, we derived closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary.The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large scale eddies. Two diffusivity expressions were obtained based on whether the pair center of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. A quantitative analysis of the stochastic theory is performed through a comparison of the pair statistics obtained using Langevin simulations with those from DNS. Langevin simulations of particle pair dispersion were performed using the diffusivity closures for four particle Stokes numbers based on the Kolmogorov time-scale, Stη = 10 , 20 , 40 , 80 and at two Taylor micro-scale Reynolds numbers Reλ = 76 , 131 . Statistics such as RDF, PDF, variance and kurtosis of particle-pair relative velocities were computed using both Langevin and DNS runs, and compared.
A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
Mininni, P D; Pouquet, A G
2004-01-01
We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl number...
Smith, D. R.; Fonck, R. J.; McKee, G. R.; Thompson, D. S. [Department of Engineering Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States); Bell, R. E.; Diallo, A.; Guttenfelder, W.; Kaye, S. M.; LeBlanc, B. P.; Podesta, M. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States)
2013-05-15
The spherical torus edge region is among the most challenging regimes for plasma turbulence simulations. Here, we measure the spatial and temporal properties of ion-scale turbulence in the steep gradient region of H-mode pedestals during edge localized mode-free, MHD quiescent periods in the National Spherical Torus Experiment. Poloidal correlation lengths are about 10 ρ{sub i}, and decorrelation times are about 5 a/c{sub s}. Next, we introduce a model aggregation technique to identify parametric dependencies among turbulence quantities and transport-relevant plasma parameters. The parametric dependencies show the most agreement with transport driven by trapped-electron mode, kinetic ballooning mode, and microtearing mode turbulence, and the least agreement with ion temperature gradient turbulence. In addition, the parametric dependencies are consistent with turbulence regulation by flow shear and the empirical relationship between wider pedestals and larger turbulent structures.
Planetary turbulence: survey of Cassini data in the Saturn's magnetosheath
Hadid, Lina; Sahraoui, Fouad; Kiyani, Khurom; Modolo, Ronan; Retino, Alessandro; Canu, Patrick; Masters, Adam; Dougherty, Michele K.; Gurnett, Donald A.
2015-04-01
Turbulence is one of the most important yet not fully understood topics of modern physics. Understanding turbulence is collisionless plasmas, where kinetic effects mediate interactions between fields and charged particles play, is crucial to apprehend many dynamical processes such as particle heating and acceleration. Among others, one key open issue of plasma turbulence is how the energy associated to magnetic and electric fields is converted, and eventually dissipated, into kinetic and internal energy of the plasma. The planets' magnetosheath present a high level of turbulence that involves both nonlinear stochastic processes and a rich variety of wave phenomena. In comparison with turbulence in the solar wind and in the terrestrial magnetosheath, turbulence around other planets is far less explored. Here, we expand our knowledge in plasma turbulence by exploring the properties of turbulence in the Kronian magnetosheath using the Cassini spacecraft data. These properties include the magnetic field energy spectra, the magnetic compressibility and intermittency at both MHD and kinetic scales. The analysis is based on in-situ data provided by the Fluxgate Magnetometer of the MAG instrument, which measures the magnetic field data with 32ms time resolution and the plasma data from the CAPS/IMS (Cassini Plasma Spectrometer) and the Electron Spectrometer (ELS), during 39 shock-crossings between 2004 and 2005. Similarities and differences with the solar wind were found, in particular about the nature of the turbulence and its scaling laws, as well as the dependence of those properties on the topology of the bow shock.
Theorem of turbulent intensity and macroscopic mechanism of the turbulence development
HU YinQiao; CHEN JinBei; ZUO HongChao
2007-01-01
Turbulence is one of the most common nature phenomena in everyday experience, but that is not adequately understood yet. This article reviews the history and present state of development of the turbulence theory and indicates the necessity to probe into the turbulent features and mechanism with the different methods at different levels. Therefore this article proves a theorem of turbulent transportation and a theorem of turbulent intensity by using the theory of the nonequilibrium thermodynamics,turbulent intensity and the turbulent transportation. The macroscopic cause of the development of fluid turbulence is a result from shearing effect of the velocity together with the temperature, which is also the macroscopic cause of the stretch and fold of trajectory in the phase space of turbulent field. And it is proved by the observed data of atmosphere that the phenomenological coefficient of turbulent intensity is not only a function of the velocity shear but also a function of temperature shear, viz the stability of temperature stratification, in the atmosphere. Accordingly, authenticity of the theorem, which is proved by the theory of nonequilibrium thermodynamics, of turbulent intensity is testified by the facts of observational experiment.
Turbulence and turbulent mixing in natural fluids
Gibson, Carl H
2010-01-01
Turbulence and turbulent mixing in natural fluids begins with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretion on a spinning pair releases 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscosity and negative turbulence stresses work against gravity, creating mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until a quark-gluon strong-force SF freeze-out. Gluon-viscosity anti-gravity ({\\Lambda}SF) exponentially inflates the fireball to preserve big bang turbulence information at scales larger than ct as the first fossil turbulence. Cosmic microwave background CMB temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered (10^12 s) as plasma viscous forces permit gravitational fragmentation on supercluster to galaxy mass scales (10^13 s). Turbulent morphologies and viscous-turbulent lengths a...
PREFACE: Theory of Fusion Plasmas, 13th Joint Varenna-Lausanne International Workshop (2012)
Garbet, Xavier; Sauter, Olivier
2012-12-01
The 2012 joint Varenna-Lausanne international workshop on the theory of fusion plasmas has been very fruitful. A broad variety of topics were addressed, as usual covering turbulence, MHD, edge physic, RF wave heating and a taste of astrophysics. Moreover the scope of the meeting was extended this year to include the physics of materials and diagnostics for burning plasmas. This evolution reflects the complexity of problems at hand in fusion, in particular in the context of ITER construction. Long-standing problems without immediate consequences have sometimes become an urgent matter in that context. One may quote for instance the choice of plasma facing components or the design of control systems. Another characteristic of the meeting is the interplay between various domains of plasma physics. For instance MHD modes are now currently investigated with gyrokinetic codes, kinetic effects are more and more included in MHD stability analysis, and turbulence is now accounted for in wave propagation problems. This is the proof of cross-fertilization and it is certainly a healthy sign in our community. Finally introducing some novelty in the programme does not prevent us from respecting the traditions of the meeting. As usual a good deal of the presentations were dedicated to numerical simulations. Combining advanced numerical techniques with elaborated analytical theory is certainly a trademark of the Varenna-Lausanne conference, which was respected again this year. The quality and size of the scientific production is illustrated by the 26 papers which appear in the present volume of Journal of Physics: Conference Series, all refereed. We would also like to mention another set of 20 papers to be published in Plasma Physics and Controlled Fusion. We hope the readers will enjoy this special issue of JPCS and the one to come in PPCF. Xavier Garbet and Olivier Sauter October 26, 2012
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
Grete, Philipp; Schmidt, Wolfram; Schleicher, Dominik R G; Federrath, Christoph
2015-01-01
Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pre...
Magnetic Flux Transport by turbulent reconnection in astrophysical flows
Pino, Elisabete M de Gouveia Dal; Santos-Lima, Reinaldo; Guerrero, Gustavo; Kowal, Grzegorz; Lazarian, Alex
2011-01-01
The role of MHD turbulence in astrophysical environments is still highly debated. An important question that permeates this debate is the transport of magnetic flux. This is particularly important, for instance, in the context of star formation. When clouds collapse gravitationally to form stars, there must be some magnetic flux transport. otherwise the new born stars would have magnetic fields several orders of magnitude larger than the observed ones. Also, the magnetic flux that is dragged in the late stages of the formation of a star can remove all the rotational support from the accretion disk that grows around the protostar. The efficiency of the mechanism which is often invoked to allow the transport of magnetic fields in the different stages of star formation, namely, the ambipolar diffusion, has been lately put in check. We here discuss an alternative mechanism for magnetic flux transport which is based on turbulent fast magnetic reconnection. We review recent results obtained from 3D MHD numerical si...
Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence
Linkmann, Moritz F; McKay, Mairi E; Jäger, Julia
2015-01-01
Spectral transfer processes in magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for nonhelical magnetic fields is shown to be possible. Fu...
Joos, Marc; Ciardi, Andrea; Fromang, Sebastien
2013-01-01
[Abridged] Theoretical and numerical studies of star formation have shown that magnetic field (B) has a strong influence on both disk formation and fragmentation; even a relatively low B can prevent these processes. However, very few studies investigated the combined effects of B and turbulence. We study the effects of turbulence in magnetized core collapse, focusing on the magnetic diffusion, the orientation of the angular momentum (J) of the protostellar core, and on its consequences on disk formation, fragmentation and outflows. We perform 3D, AMR, MHD simulations of magnetically supercritical collapsing dense cores of 5 Msun using the MHD code RAMSES. A turbulent velocity field is imposed as initial conditions, characterised by a Kolmogorov power spectrum. Different levels of turbulence and magnetization are investigated, as well as 3 realisations for the turbulent velocity field. Magnetic diffusion, orientation of the rotation axis with respect to B, transport of J, disk formation, fragmentation and outf...
Radiation-driven MHD systems for space applications
Lee, J. H.; Jalufka, N. W.
High-power radiation such as concentrated solar or high-power laser radiation is considered as a driver for magnetohydrodynamic (MHD) systems which could be developed for efficient power generation and propulsion in space. Eight different systems are conceivable since the MHD systems can be classified in two: plasma and liquid-metal MHD's. Each of these systems is reviewed and solar- (or laser-) driven MHD thrusters are proposed.
Simulation of wave interactions with MHD
Batchelor, D; Bernholdt, D; Berry, L; Elwasif, W; Jaeger, E; Keyes, D; Klasky, S [Oak Ridge National Laboratory, Oak Ridge, TN 37331 (United States); Alba, C; Choi, M [General Atomics, San Diego, CA 92186 (United States); Bateman, G [Lehigh University, Bethlehem, PA 18015 (United States); Bonoli, P [Plasma Science and Fusion Center, MTT, Cambridge, MA 02139 (United States); Bramley, R [Indiana University, Bloomington, IN 47405 (United States); Breslau, J; Chance, M; Chen, J; Fu, G; Jardin, S [Princeton Plasma Physics Laboratory, Princeton, NJ 08543 (United States); Harvey, R [CompX, Del Mar, CA 92014 (United States); Jenkins, T [University of Wisconsin, Madison, WI 53706 (United States); Kruger, S [Tech-X, Boulder, CO 80303 (United States)], E-mail: batchelordb@ornl.gov (and others)
2008-07-15
The broad scientific objectives of the SWIM (Simulation 01 Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RP effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Simulation of wave interactions with MHD
Batchelor, Donald B [ORNL; Abla, G [General Atomics, San Diego; Bateman, Glenn [Lehigh University, Bethlehem, PA; Bernholdt, David E [ORNL; Berry, Lee A [ORNL; Bonoli, P. [Massachusetts Institute of Technology (MIT); Bramley, R [Indiana University; Breslau, J. [Princeton Plasma Physics Laboratory (PPPL); Chance, M. [Princeton Plasma Physics Laboratory (PPPL); Chen, J. [Princeton Plasma Physics Laboratory (PPPL); Choi, M. [General Atomics; Elwasif, Wael R [ORNL; Fu, GuoYong [Princeton Plasma Physics Laboratory (PPPL); Harvey, R. W. [CompX, Del Mar, CA; Jaeger, Erwin Frederick [ORNL; Jardin, S. C. [Princeton Plasma Physics Laboratory (PPPL); Jenkins, T [University of Wisconsin; Keyes, David E [Columbia University; Klasky, Scott A [ORNL; Kruger, Scott [Tech-X Corporation; Ku, Long-Poe [Princeton Plasma Physics Laboratory (PPPL); Lynch, Vickie E [ORNL; McCune, Douglas [Princeton Plasma Physics Laboratory (PPPL); Ramos, J. [Massachusetts Institute of Technology (MIT); Schissel, D. [General Atomics; Schnack, [University of Wisconsin; Wright, J. [Massachusetts Institute of Technology (MIT)
2008-07-01
The broad scientific objectives of the SWIM (Simulation of Wave Interaction with MHD) project are twofold: (1) improve our understanding of interactions that both radio frequency (RF) wave and particle sources have on extended-MHD phenomena, and to substantially improve our capability for predicting and optimizing the performance of burning plasmas in devices such as ITER: and (2) develop an integrated computational system for treating multiphysics phenomena with the required flexibility and extensibility to serve as a prototype for the Fusion Simulation Project. The Integrated Plasma Simulator (IPS) has been implemented. Presented here are initial physics results on RF effects on MHD instabilities in tokamaks as well as simulation results for tokamak discharge evolution using the IPS.
Principal Component Analysis studies of turbulence in optically thick gas
Correia, Caio; Burkhart, Blakesley; Pogosyan, Dmitri; De Medeiros, José Renan
2015-01-01
In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes of fractional Brownian motion (fBm) and magnetohydrodynamics (MHD) simulations, post processed to include radiative transfer effects from CO. We find that PCA analysis is very different from the tools based on the traditional power spectrum of PPV data cubes. Our major finding is that PCA is also sensitive to the phase information of PPV cubes and this allows PCA to detect the changes of the underlying velocity and density spectra at high opacities, where the spectral analysis of the maps provides the universal -3 spectrum in accordance with the predictions of Lazarian \\& Pogosyan (2004) theory. This makes PCA potentially a valuable tool for studies of turbulence at high opacities provided that the proper gauging of the PCA index is made. The later, however, we found t...
PRINCIPAL COMPONENT ANALYSIS STUDIES OF TURBULENCE IN OPTICALLY THICK GAS
Correia, C.; Medeiros, J. R. De [Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970, Natal (Brazil); Lazarian, A. [Astronomy Department, University of Wisconsin, Madison, 475 N. Charter St., WI 53711 (United States); Burkhart, B. [Harvard-Smithsonian Center for Astrophysics, 60 Garden St, MS-20, Cambridge, MA 02138 (United States); Pogosyan, D., E-mail: caioftc@dfte.ufrn.br [Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, ON (Canada)
2016-02-20
In this work we investigate the sensitivity of principal component analysis (PCA) to the velocity power spectrum in high-opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic position–position–velocity (PPV) cubes of fractional Brownian motion and magnetohydrodynamics (MHD) simulations, post-processed to include radiative transfer effects from CO. We find that PCA analysis is very different from the tools based on the traditional power spectrum of PPV data cubes. Our major finding is that PCA is also sensitive to the phase information of PPV cubes and this allows PCA to detect the changes of the underlying velocity and density spectra at high opacities, where the spectral analysis of the maps provides the universal −3 spectrum in accordance with the predictions of the Lazarian and Pogosyan theory. This makes PCA a potentially valuable tool for studies of turbulence at high opacities, provided that proper gauging of the PCA index is made. However, we found the latter to not be easy, as the PCA results change in an irregular way for data with high sonic Mach numbers. This is in contrast to synthetic Brownian noise data used for velocity and density fields that show monotonic PCA behavior. We attribute this difference to the PCA's sensitivity to Fourier phase information.
Criticality and turbulence in a resistive magnetohydrodynamic current sheet.
Klimas, Alexander J; Uritsky, Vadim M
2017-02-01
Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.
Criticality and turbulence in a resistive magnetohydrodynamic current sheet
Klimas, Alexander J.; Uritsky, Vadim M.
2017-02-01
Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.
Turbulence and turbulent mixing in natural fluids
2010-01-01
Turbulence and turbulent mixing in natural fluids begins with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair releases 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until str...
Santos-Lima, R; Falceta-Gonçalves, D A; Nakwacki, M S; Kowal, G
2016-01-01
Statistical analysis of Faraday Rotation Measure (RM) maps of the intracluster medium (ICM) of galaxy clusters provides a unique tool to evaluate some spatial features of the magnetic fields there. Its combination with numerical simulations of magnetohydrodynamic (MHD) turbulence allows the diagnosis of the ICM turbulence. Being the ICM plasma weakly collisional, the thermal velocity distribution of the particles naturally develops anisotropies as a consequence of the large scale motions and the conservation of the magnetic moment of the charged particles. A previous study (Paper I) analyzed the impact of large scale thermal anisotropy on the statistics of RM maps synthesized from simulations of turbulence; these simulations employed a collisionless MHD model which considered a tensor pressure with uniform anisotropy. In the present work, we extend that analysis to a collisionless MHD model in which the thermal anisotropy develops according to the conservation of the magnetic moment of the thermal particles. ...
Gauthier, Serge; Keane, Christopher J.; Niemela, Joseph J.; Abarzhi, Snezhana I.
2013-07-01
. Chernyak et al consider compressible gas flows in a gravity field above a homogeneous surface in a shallow water approximation within the Riemann invariants form. Fukumoto and Mie develop a weakly nonlinear stability theory for a rotating flow confined in a cylinder of elliptic cross-section. Karelsky and Petrosyan further expand the use of the shallow-water approximation and Riemann invariants to study the problem of a steady-state flow over a step. Meshram and Sahu employ the Lewis-Kraichnan space-time version of the Hopf functional formalism to investigate MHD turbulence. Nepomnyashchy and Volpert study particle growth due to sub-diffusion (described by an equation with fractional derivatives) of a dissolved component. Stochastic processes and probabilistic description. Two research papers are dedicated to this theme. Abarzhi et al present a stochastic model of statistically unsteady RT mixing with uniform and non-uniform accelerations. Within the framework of non-equilibrium thermodynamics, Klimenko considers the combustion problem and interprets it as a competitive mixing. Advanced numerical methods. Seven research papers are dedicated to advanced numerical methods and numerical simulations. Denisenko and Oparina study the stability of the laminar flow between two rotating cylinders (the Taylor-Couette flow) by means of numerical simulations based on the compressible inviscid Euler equations. Fortova investigates spectral characteristics of the vortex cascades in a shear flow. Ghods and Herrmann present a consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using the level set methods. Kaman et al provide an overview on recent progress in turbulent mixing. Koppula et al report the development of a universal realizable anisotropic and pre-stress closure model and illustrate the model application in shear flows. Kozlov and Eriklintsev carry out numerical simulation of countercurrent flow and diffusion processes
Wave turbulence buildup in a vibrating plate
Auliel, Maria Ines; Mordant, Nicolas
2015-01-01
We report experimental and numerical results on the buildup of the energy spectrum in wave turbulence of a vibrating thin elastic plate. Three steps are observed: first a short linear stage, then the turbulent spectrum is constructed by the propagation of a front in wave number space and finally a long time saturation due to the action of dissipation. The propagation of a front at the second step is compatible with scaling predictions from the Weak Turbulence Theory.
Euler potentials for the MHD Kamchatnov-Hopf soliton solution
Semenov, VS; Korovinski, DB; Biernat, HK
2002-01-01
In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invarian
Safety and reliability in superconducting MHD magnets
Laverick, C.; Powell, J.; Hsieh, S.; Reich, M.; Botts, T.; Prodell, A.
1979-07-01
This compilation adapts studies on safety and reliability in fusion magnets to similar problems in superconducting MHD magnets. MHD base load magnet requirements have been identified from recent Francis Bitter National Laboratory reports and that of other contracts. Information relevant to this subject in recent base load magnet design reports for AVCO - Everett Research Laboratories and Magnetic Corporation of America is included together with some viewpoints from a BNL workshop on structural analysis needed for superconducting coils in magnetic fusion energy. A summary of design codes used in large bubble chamber magnet design is also included.
Explosively-driven magnetohydrodynamic (MHD) generator studies
Agee, F.J.; Lehr, F.M. [Phillips Lab., Kirtland AFB, NM (United States); Vigil, M.; Kaye, R. [Sandia National Labs., Albuquerque, NM (United States); Gaudet, J.; Shiffler, D. [New Mexico Univ., Albuquerque, NM (United States)
1995-08-01
Plasma jet generators have been designed and tested which used an explosive driver and shocktube with a rectangular cross section that optimize the flow velocity and electrical conductivity. The latest in a series of designs has been tested using a reactive load to diagnose the electrical properties of the MHD generator/electromagnet combination. The results of these tests indicate that the plasma jet/MHD generator design does generate a flow velocity greater than 25 km/s and produces several gigawatts of pulsed power in a very small package size. A larger, new generator design is also presented.
Electron magnetohydrodynamics: dynamics and turbulence.
Lyutikov, Maxim
2013-11-01
We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k(1)=k(2) do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade [proportionality]k(-2). The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.
Ju, Wenhua; Zhu, Zhaohuan
2016-01-01
We present results from the first global 3D MHD simulations of accretion disks in Cataclysmic Variable (CV) systems in order to investigate the relative importance of angular momentum transport via turbulence driven by the magnetorotational instability (MRI) compared to that driven by spiral shock waves. Remarkably, we find that even with vigorous MRI turbulence, spiral shocks are an important component to the overall angular momentum budget, at least when temperatures in the disk are high (so that Mach numbers are low). In order to understand the excitation, propagation, and damping of spiral density waves in our simulations more carefully, we perform a series of 2D global hydrodynamical simulations with various equation of states and both with and without mass inflow via the Lagrangian point (L1). Compared with previous similar studies, we find the following new results. 1) Linear wave dispersion relation fits the pitch angles of spiral density waves very well. 2) We demonstrate explicitly that mass accreti...
Investigating Magnetic Activity in the Galactic Centre by Global MHD Simulation
Suzuki, Takeru K; Torii, Kazufumi; Machida, Mami; Matsumoto, Ryoji; Kakiuchi, Kensuke
2016-01-01
By performing a global magnetohydrodynamical (MHD) simulation for the Milky Way with an axisymmetric gravitational potential, we propose that spatially dependent amplification of magnetic fields possibly explains the observed noncircular motion of the gas in the Galactic centre (GC) region. The radial distribution of the rotation frequency in the bulge region is not monotonic in general. The amplification of the magnetic field is enhanced in regions with stronger differential rotation, because magnetorotational instability and field-line stretching are more effective. The strength of the amplified magnetic field reaches >~ 0.5 mG, and radial flows of the gas are excited by the inhomogeneous transport of angular momentum through turbulent magnetic field that is amplified in a spatially dependent manner. As a result, the simulated position-velocity diagram exhibits a time-dependent asymmetric parallelogram-shape owing to the intermittency of the magnetic turbulence; the present model provides a viable alternati...
Magnetohydrodynamic dynamo: global flow generation in plasma turbulence
Yokoi, Nobumitsu; Yoshizawa, Akira [Tokyo Univ. (Japan). Inst. of Industrial Science; Itoh, Kimitaka; Itoh, Sanae-I.
1999-07-01
Generation mechanism of the spontaneous plasma rotation observed in an improved confinement mode in tokamak's is examined from the viewpoint of the turbulent magnetohydrodynamic (MHD) dynamo. A dynamo model, where the concept of cross helicity (velocity/magnetic-field correlation) plays a key role, is applied to the reversed shear (RS) modes. The concave electric-current profile occurred in the RS modes is shown to be a cause of the global plasma rotation through a numerical simulation of the cross-helicity turbulence model. (author)
Sunspot Modeling: From Simplified Models to Radiative MHD Simulations
Rolf Schlichenmaier
2011-09-01
Full Text Available We review our current understanding of sunspots from the scales of their fine structure to their large scale (global structure including the processes of their formation and decay. Recently, sunspot models have undergone a dramatic change. In the past, several aspects of sunspot structure have been addressed by static MHD models with parametrized energy transport. Models of sunspot fine structure have been relying heavily on strong assumptions about flow and field geometry (e.g., flux-tubes, "gaps", convective rolls, which were motivated in part by the observed filamentary structure of penumbrae or the necessity of explaining the substantial energy transport required to maintain the penumbral brightness. However, none of these models could self-consistently explain all aspects of penumbral structure (energy transport, filamentation, Evershed flow. In recent years, 3D radiative MHD simulations have been advanced dramatically to the point at which models of complete sunspots with sufficient resolution to capture sunspot fine structure are feasible. Here overturning convection is the central element responsible for energy transport, filamentation leading to fine-structure and the driving of strong outflows. On the larger scale these models are also in the progress of addressing the subsurface structure of sunspots as well as sunspot formation. With this shift in modeling capabilities and the recent advances in high resolution observations, the future research will be guided by comparing observation and theory.
Molecular Tracers of Turbulent Shocks in Giant Molecular Clouds
Pon, A; Kaufman, M J
2012-01-01
Giant molecular clouds contain supersonic turbulence and simulations of MHD turbulence show that these supersonic motions decay in roughly a crossing time, which is less than the estimated lifetimes of molecular clouds. Such a situation requires a significant release of energy. We run models of C-type shocks propagating into gas with densities around 10^3 cm^(-3) at velocities of a few km / s, appropriate for the ambient conditions inside of a molecular cloud, to determine which species and transitions dominate the cooling and radiative energy release associated with shock cooling of turbulent molecular clouds. We find that these shocks dissipate their energy primarily through CO rotational transitions and by compressing pre-existing magnetic fields. We present model spectra for these shocks and by combining these models with estimates for the rate of turbulent energy dissipation, we show that shock emission should dominate over emission from unshocked gas for mid to high rotational transitions (J >5) of CO. ...
Distributed chaos and isotropic turbulence
Bershadskii, A
2015-01-01
Power spectrum of the distributed chaos can be represented by a weighted superposition of the exponential functions which is converged to a stretched exponential $\\exp-(k/k_{\\beta})^{\\beta }$. An asymptotic theory has been developed in order to estimate the value of $\\beta$ for the isotropic turbulence. This value has been found to be $\\beta =3/4$. Excellent agreement has been established between this theory and the data of direct numerical simulations not only for the velocity field but also for the passive scalar and energy dissipation fields. One can conclude that the isotropic turbulence emerges from the distributed chaos.
Complexity induced solar wind turbulence and evolution
Chang, T.
2003-04-01
"Complexity" has become a hot topic in nearly every field of modern physics. Solar wind plasmas are of no exception. Recently, Chang [2002], in analogy with theories developed for phenomena observed in the magnetotail and the auroral zone [Chang, 1999; 2001], demonstrated that the sporadic and localized interactions of magnetic coherent structures arising from plasma resonances could be the origin of "complexity" of nonresonant pseudo-2D spatiotemporal fluctuations in solar wind turbulence and in the coronal hole base. Such nonresonant fluctuations were shown to exist in the solar wind by Matthaeus et al. [1990] in terms of the two-dimensional correlation as a function of distance parallel and perpendicular to the mean magnetic field based on the ISEE-3 magnetometer data. Other evidences indicating the existence of such type of fluctuations in the solar wind have been reported by Tu et al. [1989], Tu and Marsch [1990, 1991], Bruno and Bavassano [1991], Bavassano and Bruno [1992], Bruno et al. [2001], and others. These results explain [Tu and Marsch, 1991] why the Alfvén ratio (a quantitative measure of Alfvénicity) is often found to be less than one in the solar wind [Belcher and Davis 1971, Solodyna et al., 1977, Bruno et al, 1985, Roberts et al., 1990], particularly for the space range farther than 0.3 AU. The above observational results are also consistent with the conclusions obtained from 2D MHD numerical simulations [Matthaeus and Larkin, 1986, Roberts and Goldstein, 1988, Goldstein et al., 1989, Roberts et al., 1991, and Roberts, 1992]. Such findings have led Chang [2002] to suggest the following evolutional scenario for the plasma turbulence in the generic fast solar wind. In and near the coronal hole base, the turbulent fluctuations are predominantly nonresonantly generated by pseudo-2D nonlinear interactions. As the fluctuations emerge from the coronal hole base, they propagate resonantly in the field-aligned direction primarily as Alfvén waves
The generation, destination, and astrophysical applications of magnetohydrodynamic turbulence
Xu, Siyao; Lazarian, Alex; Zhang, Bing
2017-01-01
The ubiquitous turbulence in the interstellar medium (ISM) participates in astrophysical processes over a huge dynamic range of scales. Understanding the turbulence properties in the multiphase, magnetized, partially ionized, and compressible ISM is the fundamental step prior to the studies of the ISM physics and other fields of astrophysics. I feel that a triad of analytical, numerical and observational efforts provides a winning combination to understand this complex system and solve long-standing puzzles. I have intensively studied the fundamental physics of magnetohydrodynamic (MHD) turbulence, and focused on two primary domains, dynamo and dissipation, which concern the origin of strong magnetic fields and the destination of turbulence, respectively. I further applied my theoretical studies in interpreting numerical results and observational data in various astrophysical contexts. The advanced analyses of MHD turbulence enable me to address a number of challenging astrophysical problems, e.g. the importance of magnetic fields for star formation in the early and present-day universe, new methods of measuring magnetic fields, the density distribution in the Galaxy and the host galaxy of a fast radio burst, the diffusion and acceleration of cosmic rays in partially ionized ISM phases.
Turbulent reconnection and its implications
Lazarian, A.; Eyink, G.; Vishniac, E.; Kowal, G.
2015-01-01
Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes happening in magnetized plasmas. In most astrophysical environments, the Reynolds numbers corresponding to plasma flows are large and therefore the transition to turbulence is inevitable. This turbulence, which can be pre-existing or driven by magnetic reconnection itself, must be taken into account for any theory of magnetic reconnection that attempts to describe the process in the aforementioned environments. This necessity is obvious as three-dimensional high-resolution numerical simulations show the transition to the turbulence state of initially laminar reconnecting magnetic fields. We discuss ideas of how turbulence can modify reconnection with the focus on the Lazarian & Vishniac (Lazarian & Vishniac 1999 Astrophys. J. 517, 700–718 ()) reconnection model. We present numerical evidence supporting the model and demonstrate that it is closely connected to the experimentally proven concept of Richardson dispersion/diffusion as well as to more recent advances in understanding of the Lagrangian dynamics of magnetized fluids. We point out that the generalized Ohm's law that accounts for turbulent motion predicts the subdominance of the microphysical plasma effects for reconnection for realistically turbulent media. We show that one of the most dramatic consequences of turbulence is the violation of the generally accepted notion of magnetic flux freezing. This notion is a cornerstone of most theories dealing with magnetized plasmas, and therefore its change induces fundamental shifts in accepted paradigms, for instance, turbulent reconnection entails reconnection diffusion process that is essential for understanding star formation. We argue that at sufficiently high Reynolds numbers the process of tearing reconnection should transfer to turbulent reconnection. We discuss flares that are predicted by turbulent reconnection and relate this process to
Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E.
2017-01-01
This paper examines the behavior of the dimensionless dissipation rate Cɛ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for Cɛ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote Cɛ ,∞ lie between 0.193 ≤Cɛ ,∞≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure Cɛ ,∞=0.223 .
Signatures of fast and slow magnetohydrodynamic shocks in turbulent molecular clouds
Lehmann, Andrew
2015-01-01
The character of star formation is intimately related to the supersonic magnetohydrodynamic (MHD) turbulent dynamics of the giant molecular clouds in which stars form. A significant amount of the turbulent energy dissipates in low-velocity shock waves. These shocks cause molecular line cooling of the compressed and heated gas, and so their radiative signatures probe the nature of the turbulence. In MHD fluids the three distinct families of shocks---fast, intermediate and slow---differ in how they compress and heat the molecular gas, and so observational differences between them may also distinguish driving modes of turbulent regions. Here we use a two-fluid model to compare the characteristics of one-dimensional fast and slow MHD shocks propagating at low speeds (a few km/s) in molecular clouds. Fast MHD shocks are magnetically driven, forcing ion species to stream through the neutral gas ahead of the shock front. This magnetic precursor heats the gas sufficiently to create a large, warm transition zone where...
Structure and modeling of turbulence
Novikov, E.A. [Univ. of California, San Diego, La Jolla, CA (United States)
1995-12-31
The {open_quotes}vortex strings{close_quotes} scale l{sub s} {approximately} LRe{sup -3/10} (L-external scale, Re - Reynolds number) is suggested as a grid scale for the large-eddy simulation. Various aspects of the structure of turbulence and subgrid modeling are described in terms of conditional averaging, Markov processes with dependent increments and infinitely divisible distributions. The major request from the energy, naval, aerospace and environmental engineering communities to the theory of turbulence is to reduce the enormous number of degrees of freedom in turbulent flows to a level manageable by computer simulations. The vast majority of these degrees of freedom is in the small-scale motion. The study of the structure of turbulence provides a basis for subgrid-scale (SGS) models, which are necessary for the large-eddy simulations (LES).
Turbulence optimisation in stellarator experiments
Proll, Josefine H.E. [Max-Planck/Princeton Center for Plasma Physics (Germany); Max-Planck-Institut fuer Plasmaphysik, Wendelsteinstr. 1, 17491 Greifswald (Germany); Faber, Benjamin J. [HSX Plasma Laboratory, University of Wisconsin-Madison, Madison, WI 53706 (United States); Helander, Per; Xanthopoulos, Pavlos [Max-Planck/Princeton Center for Plasma Physics (Germany); Lazerson, Samuel A.; Mynick, Harry E. [Plasma Physics Laboratory, Princeton University, P.O. Box 451 Princeton, New Jersey 08543-0451 (United States)
2015-05-01
Stellarators, the twisted siblings of the axisymmetric fusion experiments called tokamaks, have historically suffered from confining the heat of the plasma insufficiently compared with tokamaks and were therefore considered to be less promising candidates for a fusion reactor. This has changed, however, with the advent of stellarators in which the laminar transport is reduced to levels below that of tokamaks by shaping the magnetic field accordingly. As in tokamaks, the turbulent transport remains as the now dominant transport channel. Recent analytical theory suggests that the large configuration space of stellarators allows for an additional optimisation of the magnetic field to also reduce the turbulent transport. In this talk, the idea behind the turbulence optimisation is explained. We also present how an optimised equilibrium is obtained and how it might differ from the equilibrium field of an already existing device, and we compare experimental turbulence measurements in different configurations of the HSX stellarator in order to test the optimisation procedure.
1991-10-01
and complexity of thermochemistry . Accordingly a practical viewpoint is required to meet near-term work required for use in advanced CFD codes...teachers the opportunity to learn/explore/ teach turbulence issues. While such a product could be an invaluable eductaional tool (university), it also
Prediction of turbulent shear layers in turbomachines
Bradshaw, P.
1974-01-01
The characteristics of turbulent shear layers in turbomachines are compared with the turbulent boundary layers on airfoils. Seven different aspects are examined. The limits of boundary layer theory are investigated. Boundary layer prediction methods are applied to analysis of the flow in turbomachines.
Physical and Chemical Processes in Turbulent Flames
2015-06-23
DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR)/ RTE Arlington, Virginia 22203 Air Force Research...two-year subject program, conducted through tight coupling between experiment, theory and computation, and reported in high impact journal articles ...The thrust for this program constitutes of three major areas of turbulent combustion: (1) Flame surface statistics , (2) Flame-turbulence interaction
Fully Parallel MHD Stability Analysis Tool
Svidzinski, Vladimir; Galkin, Sergei; Kim, Jin-Soo; Liu, Yueqiang
2015-11-01
Progress on full parallelization of the plasma stability code MARS will be reported. MARS calculates eigenmodes in 2D axisymmetric toroidal equilibria in MHD-kinetic plasma models. It is a powerful tool for studying MHD and MHD-kinetic instabilities and it is widely used by fusion community. Parallel version of MARS is intended for simulations on local parallel clusters. It will be an efficient tool for simulation of MHD instabilities with low, intermediate and high toroidal mode numbers within both fluid and kinetic plasma models, already implemented in MARS. Parallelization of the code includes parallelization of the construction of the matrix for the eigenvalue problem and parallelization of the inverse iterations algorithm, implemented in MARS for the solution of the formulated eigenvalue problem. Construction of the matrix is parallelized by distributing the load among processors assigned to different magnetic surfaces. Parallelization of the solution of the eigenvalue problem is made by repeating steps of the present MARS algorithm using parallel libraries and procedures. Results of MARS parallelization and of the development of a new fix boundary equilibrium code adapted for MARS input will be reported. Work is supported by the U.S. DOE SBIR program.
Application of ADER Scheme in MHD Simulation
ZHANG Yanyan; FENG Xueshang; JIANG Chaowei; ZHOU Yufen
2012-01-01
The Arbitrary accuracy Derivatives Riemann problem method（ADER） scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions： （ⅰ） Brio-Wu shock tube problem,（ⅱ） Dai-Woodward shock tube problem,（ⅲ） Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
Principal characteristics of SFC type MHD generator
Kayukawa, Naoyuki; Oikawa, Shun-ichi; Aoki, Yoshiaki; Seidou, Tadashi; Okinaka, Noriyuki
1988-02-01
This paper describes the experimental and analytical results obtained for an MHD channel with a two dimensionally shaped magnetic field configuration called 'the SFC-type'. The power generating performance was examined under various load conditions and B-field intensities with a 2 MWt shock tunnel MHD facility. It is demonstrated that the power output performance and the enthalpy extraction scaling law of the conventional uniform B-field MHD generator (UFC-type) were significantly improved by the SFC-design of the spatial distribution of the magnetic field. The arcing processes were also examined by a high speed camera and the post-test observation of arc spot traces on electrodes. Further, the characteristic frequencies of each of the so-called micro and constricted arcs were clarified by spectral analyses. The critical current densities, which define the transient conditions of each from the diffuse-to micro arc, and from the micro-to constricted arc modes could be clearly obtained by the present spectral analysis method. We also investigated the three-dimensional behavior under strong magnetic field based on the coupled electrical and hydrodynamical equations for both of the middle scale SFC-and UFC-type generators. Finally, it is concluded from the above mentioned various aspects that the shaped 2-D magnetic field design will offer a most useful means for the realization of a compact, high efficiency and a long duration open-cycle MHD generator.
Pseudo-reconnection in MHD numerical simulation
无
2000-01-01
A class of pseudo-reconnections caused by a shifted mesh in magnetohydrodynamics (MHD) simulations is reported. In terms of this mesh system, some non-physical results may be obtained in certain circumstances, e.g. magnetic reconnection occurs without resistivity. After comparison, another kind of mesh is strongly recommended.
MHD equilibrium and stability in heliotron plasmas
Ichiguchi, Katsuji [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-09-01
Recent topics in the theoretical magnetohydrodynamic (MHD) analysis in the heliotron configuration are overviewed. Particularly, properties of three-dimensional equilibria, stability boundary of the interchange mode, effects of the net toroidal current including the bootstrap current and the ballooning mode stability are focused. (author)
Realistic Modeling of Multi-Scale MHD Dynamics of the Solar Atmosphere
Kitiashvili, Irina; Mansour, Nagi N.; Wray, Alan; Couvidat, Sebastian; Yoon, Seokkwan; Kosovichev, Alexander
2014-01-01
Realistic 3D radiative MHD simulations open new perspectives for understanding the turbulent dynamics of the solar surface, its coupling to the atmosphere, and the physical mechanisms of generation and transport of non-thermal energy. Traditionally, plasma eruptions and wave phenomena in the solar atmosphere are modeled by prescribing artificial driving mechanisms using magnetic or gas pressure forces that might arise from magnetic field emergence or reconnection instabilities. In contrast, our 'ab initio' simulations provide a realistic description of solar dynamics naturally driven by solar energy flow. By simulating the upper convection zone and the solar atmosphere, we can investigate in detail the physical processes of turbulent magnetoconvection, generation and amplification of magnetic fields, excitation of MHD waves, and plasma eruptions. We present recent simulation results of the multi-scale dynamics of quiet-Sun regions, and energetic effects in the atmosphere and compare with observations. For the comparisons we calculate synthetic spectro-polarimetric data to model observational data of SDO, Hinode, and New Solar Telescope.
Driver gas flow with fluctuations. [shock tube turbulent bursts
Johnson, J. A., III; Jones, W. R.; Santiago, J.
1980-01-01
A shock tube's driver gas can apparently provide flow with turbulent bursts. The fluctuations are interpreted using a boundary layer model of contact surface flow and results form a kinetic theory of turbulence. With this, a lower limit of 4 on the ratio of maximum to minimum turbulent intensities in contact surface instabilities has been estimated.
Collisionless magnetic reconnection under anisotropic MHD approximation
Hirabayashi, Kota; Hoshino, Masahiro
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless magneto-hydro-dynamic (MHD) simulations based on the double adiabatic approximation, which is an important step to bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. According to our results, a pair of slow shocks does form in the reconnection layer. The resultant shock waves, however, are quite weak compared with those in an isotropic MHD from the point of view of the plasma compression and the amount of the magnetic energy released across the shock. Once the slow shock forms, the downstream plasma are heated in highly anisotropic manner and a firehose-sense (P_{||}>P_{⊥}) pressure anisotropy arises. The maximum anisotropy is limited by the marginal firehose criterion, 1-(P_{||}-P_{⊥})/B(2) =0. In spite of the weakness of the shocks, the resultant reconnection rate is kept at the same level compared with that in the corresponding ordinary MHD simulations. It is also revealed that the sequential order of propagation of the slow shock and the rotational discontinuity, which appears when the guide field component exists, changes depending on the magnitude of the guide field. Especially, when no guide field exists, the rotational discontinuity degenerates with the contact discontinuity remaining at the position of the initial current sheet, while with the slow shock in the isotropic MHD. Our result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere.
Numerical Validation and Comparison of Three Solar Wind Heating Methods by the SIP-CESE MHD Model
YANG Li-Ping; FENG Xue-Shang; XIANG Chang-Qing; JIANG Chao-Wei
2011-01-01
We conduct simulations using the three-dimensional(3D) solar-interplanetary conservation element/solution element(SIP-CESE) maguetohydrodynamic(MHD) model and magnetogram data from a Carrington rotation (CR) 1897 to compare the three commonly used heating methods, I.e. The Wentzel-Kramers-Brillouin(WKB)Alfvén wave heating method, the turbulence heating method and the volumetric heating method. Our results show that all three heating models can basically reproduce the bimodal structure of the solar wind observed near the solar minimum. The results also demonstrate that the major acceleration interval terminates about 4Rs for the turbulence heating method and 1ORs for both the WKB Alfvén wave heating method and the volumetric heating method. The turbulence heating and the volumetric heating methods can capture the observed changing trends by the WIND satellite, while the WKB Alfvén wave heating method does not.