Generation of Synthetic Turbulence in Arbitrary Domains
Gilling, Lasse; Nielsen, Søren R.K.; Sørensen, Niels
A new method for generating synthetic turbulence is presented. The method is intended for generating a turbulent velocity field with a fine spatial resolution but only covering a small moving part of the rotor area of a wind turbine. For this application the Mann and Sandia methods cannot be used...... because of the very high requirements for computer memory. In the present method the auto- and cross-correlation in all three directions is computed from analytical or empirical expressions and the auto- and cross-spectra are determined by using the Wiener-Khinchin relation. From the auto- and cross......-spectra a realization of a velocity field is determined by factorization and Fourier transform as in the Sandia method....
Yang-Mills Spectrum with an Arbitrary Simple Gauge Algebra
The mass spectrum of pure Yang-Mills theory in 3 + 1 dimensions is discussed for an arbitrary simple gauge algebra within a quasi gluon picture. The general structure of the low-lying gluelump and glueball spectrum is shown to be common to all algebras, excepted the lightest C = - glueballs that only exist when the gauge algebra is Ar≥2. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and finally, the obtained results are shown to be consistent with existing lattice data in the large-N limit of an su(N) gauge algebra. (author)
Spectrum of resistivity gradient driven turbulence
The resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity gradient driven turbulence are calculated analytically and compared to the results of three dimensional numerical calculations. Resistivity gradient driven turbulence is characterized by effective Reynolds' numbers of order unity. Steady-state solution of the renormalized spectrum equations yields an electrostatic potential spectrum (circumflex phi2)/sub ktheta/ approx. k/sub theta//sup -3.25/. Agreement of the analytically calculated potential spectrum and mean-square radial velocity with the results of multiple helicity numerical calculations is excellent. This comparison constitutes a quantitative test of the analytical turbulence theory used. The spectrum of magnetic fluctuations is also calculated, and agrees well with that obtained from the numerical computations. 13 refs., 8 figs
Generating Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum
Walton, Z D; Saleh, B E A; Teich, M C; Walton, Zachary D.; Sergienko, Alexander V.; Saleh, Bahaa E. A.; Teich, Malvin C.
2004-01-01
We present a scheme for generating polarization-entangled photons pairs with arbitrary joint spectrum. Specifically, we describe a technique for spontaneous parametric down-conversion in which both the center frequencies and the bandwidths of the down-converted photons may be controlled by appropriate manipulation of the pump pulse. The spectral control offered by this technique permits one to choose the operating wavelengths for each photon of a pair based on optimizations of other system parameters (loss in optical fiber, photon counter performance, etc.). The combination of spectral control, polarization control, and lack of group-velocity matching conditions makes this technique particularly well-suited for a distributed quantum information processing architecture in which integrated optical circuits are connected by spans of optical fiber.
The spatio-temporal spectrum of turbulent flows
di Leoni, P Clark; Mininni, P D
2015-01-01
Identification and extraction of vortical structures and of waves in a disorganized flow is a mayor challegen in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyze the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of random sweeping. For rotating and for stratified turbulence, the spectrum allows identification of the waves, quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplit...
Energy spectrum of buoyancy-driven turbulence
Kumar, Abhishek
2014-08-25
Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Πu, we demonstrate that, for stably stratified flows, the kinetic energy spectrum Eu(k)∼k-11/5, the potential energy spectrum Eθ(k)∼k-7/5, and Πu(k)∼k-4/5 are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence Eu(k) follows Kolmogorov\\'s spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Πu(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Πu(k) and Eu(k)∼k-5/3 for a narrow band of wave numbers. © 2014 American Physical Society.
Residual Energy Spectrum of Solar Wind Turbulence
Chen, C H K; Salem, C S; Maruca, B A
2013-01-01
It has long been known that the energy in velocity and magnetic field fluctuations in the solar wind is not in equipartition. In this paper, we present an analysis of 5 years of Wind data at 1 AU to investigate the reason for this. The residual energy (difference between energy in velocity and magnetic field fluctuations) was calculated using both the standard magnetohydrodynamic (MHD) normalization for the magnetic field and a kinetic version, which includes temperature anisotropies and drifts between particle species. It was found that with the kinetic normalization, the fluctuations are closer to equipartition, with a mean normalized residual energy of sigma_r = -0.19 and mean Alfven ratio of r_A = 0.71. The spectrum of residual energy, in the kinetic normalization, was found to be steeper than both the velocity and magnetic field spectra, consistent with some recent MHD turbulence predictions and numerical simulations, having a spectral index close to -1.9. The local properties of residual energy and cros...
The temperature spectrum generated by frictional heating in isotropic turbulence
Bos, Wouter
2014-01-01
In every turbulent flow with non-zero viscosity, heat is generated by viscous friction. This heat is then mixed by the velocity field. We consider how heat fluctuations generated this way are injected and distributed over length scales in isotropic turbulence. A triadic closure is derived and numerically integrated. It is shown how the heat fluctuation spectrum depends on the Reynolds and Prandtl numbers.
The theoretical model of atmospheric turbulence spectrum in surface layer
Liu, Shida; Liu, Shikuo; Xin, Guojun; Liang, Fuming
1994-12-01
It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv—Burgers equation lies between —5/3 and—2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov's isotropic turbulence and Frisch's intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the equation, the 1 / R e corresponds to dissipative coefficient v, R /2 t to dispersive coefficient β, then ( v/2 β)2 corresponds to 1 / R 2 e • Ri. We prove that the wave number corresponding to maximum energy spectrum S(k) decreases with the decrease of stability (i.e., the increase of ( v / 2 β)2 in eddy—containing region. And the spectrim amplitude decreases with the increase of ( v / 2 β)2 (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.
Time frequency spectrum of atmospheric turbulence and sweeping hypothesis
无
2011-01-01
The present study is focused on the structure of time frequency spectrum.A scaling law for Eulerian time frequency spectrum and the corresponding temporal structure function are calculated from the sweeping hypothesis and Kolmogorov's similarity law regarding spatial structure function.An experiment is designed to study this scaling law in the atmospheric turbulent boundary layer.The results well support the conclusion derived from relevant theoretical analysis.
Energy Spectrum of Buoyancy-Driven Turbulence
Kumar, Abhishek; Chatterjee, Anando G.; Verma, Mahendra K.
2014-01-01
Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $\\Pi_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k) \\sim k^{-11/5}$, the entropy spectrum $E_\\theta(k) \\sim k^{-7/5}$, and $\\Pi_u(k) \\sim k^{-4/5}$, consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence $E_u(k)$ follo...
Quantum Turbulence: Vortex Bundle Collapse and Kolmogorov Spectrum
Nemirovskii, Sergey K.
2015-12-01
The statement of problem is motivated by the idea of modeling the classical turbulence with a set of chaotic quantized vortex filaments in superfluids. Among various arguments supporting the idea of quasi-classic behavior of quantum turbulence, the strongest, probably, is the k dependence of the spectra of energy, E(k)∝ k^{-5/3} obtained in numerical simulations and experiments. At the same time, the mechanism of classical vs. quantum turbulence is not clarified and the source of the k^{-5/3} dependence is unclear. In this work, we concentrated on the nonuniform vortex bundles. This choice is related to the actively discussed question concerning a role of collapses in the vortex dynamics in formation of turbulent spectra. We demonstrate that the nonuniform vortex bundles, which appear in result of nonlinear vortex dynamics, generates an energy spectrum which is close to the Kolmogorov dependence ∝ k^{-5/3}.
Energy Spectrum of Buoyancy-driven Turbulence
Verma, Mahendra K; Chatterjee, Anando G
2014-01-01
Using direct numerical simulation we demonstrate that stably stratified flows with large Richardson number follow Bolgiano-Obukhov scaling, i.e, the kinetic energy spectrum $E_u(k) \\sim k^{-11/5}$, the entropy spectrum $E_\\theta(k) \\sim k^{-7/5}$, and kinetic energy flux $\\Pi_u(k) \\sim k^{-4/5}$. This is due to the conversion of kinetic energy to potential energy because of buoyancy. We also demonstrate that $E_u(k) \\sim k^{-5/3}$ for stratified flow with weaker buoyancy or smaller Richardson number. We argue that due to the positive energy supply by buoyancy and non-decreasing $\\Pi_u(k)$, Rayleigh B\\'{e}nard convection should follow Kolmogorov-Obukhov scaling ($E_u(k) \\sim k^{-5/3}$).
Energy spectrum of stably-stratified and convective turbulent flows
Verma, Mahendra; Kumar, Abhishek
2015-11-01
In the inertial range of fluid turbulence, the energy flux is constant, while the energy spectrum scales as k - 5 / 3 (k=wavenumber). The buoyancy however could change the phenomenology dramatically. Bolgiano and Obukhov (1959) had conjectured that stably stratified flows (as in atmosphere) exhibits a decrease in the energy flux as k - 4 / 5 due to the conversion of kinetic energy to the potential energy, consequently, the energy spectrum scales as k - 11 / 5. We show using detailed numerical analysis that the stably stratified flows indeed exhibit k - 11 / 5 energy spectrum for Froude numbers Fr near unity. The flow becomes anisotropic for small Froude numbers. For weaker buoyancy (large Fr), the kinetic energy follows Kolmogorov's spectrum with a constant energy flux. However, in convective turbulence, the energy flux is a nondecreasing function of wavenumber since the buoyancy feeds positively into the kinetic energy. Hence, the kinetic energy spectrum is Kolmogorov-like (k - 5 / 3) or shallower. We also demonstrate the above scaling using a shell model of buoyancy-driven turbulence.
Turbulent kinetic energy spectrum in very anisothermal flows
Serra, Sylvain, E-mail: sylvain_serra@bbox.fr [PROcedes, Materiaux et Energie Solaire, UPR CNRS 8521, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan (France); Toutant, Adrien, E-mail: adrien.toutant@univ-Perp.fr [PROcedes, Materiaux et Energie Solaire, UPR CNRS 8521, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan (France); Bataille, Françoise, E-mail: francoise.bataille@promes.cnrs.fr [PROcedes, Materiaux et Energie Solaire, UPR CNRS 8521, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan (France); Zhou, Ye, E-mail: yezhou@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94550 (United States)
2012-10-01
In this Letter, we find that the Kolmogorov scaling law is no longer valid when the flow is submitted to strong dilatational effects caused by high temperature gradients. As a result, in addition to the nonlinear time scale, there is a much shorter “temperature gradients” time scale. We propose a model that estimates the time scale of the triple decorrelation incorporating the influences of the temperature gradient. The model agrees with the results from the thermal large-eddy simulations of different Reynolds numbers and temperature gradients. This Letter provides a better understanding of the very anisothermal turbulent flow. -- Highlights: ► Turbulent flows subject to high temperature gradients are considered. ► The new “temperature gradients” time scale is determined. ► A generalized energy spectrum is developed to incorporate the effects of temperature gradient.
Turbulent kinetic energy spectrum in very anisothermal flows
In this Letter, we find that the Kolmogorov scaling law is no longer valid when the flow is submitted to strong dilatational effects caused by high temperature gradients. As a result, in addition to the nonlinear time scale, there is a much shorter “temperature gradients” time scale. We propose a model that estimates the time scale of the triple decorrelation incorporating the influences of the temperature gradient. The model agrees with the results from the thermal large-eddy simulations of different Reynolds numbers and temperature gradients. This Letter provides a better understanding of the very anisothermal turbulent flow. -- Highlights: ► Turbulent flows subject to high temperature gradients are considered. ► The new “temperature gradients” time scale is determined. ► A generalized energy spectrum is developed to incorporate the effects of temperature gradient.
The Turbulence Power Spectrum in Optically Thick Interstellar Clouds
Burkhart, Blakesley; Ossenkopf, V; Stutzki, J
2013-01-01
The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic turbulence in the interstellar medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should saturate to -3 for an optically thick medium and many observations exist in support of their prediction. However, there have not been any numerical studies to-date testing these results. We analyze the spatial power spectrum of MHD simulations with a wide range of sonic and Alfv\\'enic Mach numbers, which include radiative transfer effects of the $^{13}$CO transition. We confirm numerically the predictions of Lazarian & Pogosyan (2004) that the spectral slope of line intensity maps of an optically thick medium saturates to -3. Furthermore, for very optically thin supersonic CO gas, where the density or CO abundance values are too low to excite emission in all but the densest shock compressed gas, we find that the spectral slope is shallower than expected from the column density....
Zamek, Steve; Yitzhaky, Yitzhak
2006-08-01
In remote sensing, atmospheric turbulence and aerosols limit the image quality. For many practical cases turbulence is shown to be dominant, especially for horizontal close-to-earth imaging in hot environments. In a horizontal long-range imaging it is usually impractical to measure path-averaged refractive index structure constant C n2 (which characterizes the turbulence strength) with conventional equipment. In this paper we propose a method for estimation of C n2 based just on the available recorded turbulence-degraded image sequence. The method exploits the turbulence-induced image "dancing". C n2 is extracted from the estimated image shifts variance. Experimental comparison with C n2 measurements using a scintillometer shows reliable estimation results. We also estimate image motion with sub-pixel accuracy for the purpose of obtaining a high-resolution image by applying a simple super-resolution procedure. Results of super-resolution for real imagery are presented.
On the technique for the recovery of the spectrum of turbulence in astrophysical discs
Bisikalo, D. V.; Kurbatov, E. P.; Pavlyuchenkov, Ya. N.; Zhilkin, A. G.; Kaygorodov, P. V.
2016-06-01
We present a method that can be used to recover the spectrum of turbulence from observations of optically thin emission lines formed in astrophysical discs. Within this method, we analyse how line intensity fluctuations depend on the angular resolution of the instrument, used for the observations. The method allows us to restore the slope of the power spectrum of velocity turbulent pulsations and estimate the upper boundary of the turbulence scale.
We study the acceleration of charged particles by the variable magnetic field. The study is based on the determination of spectrum of accelerated particles and the spectrum of hydro magnetic turbulence. We plan the self-consistent system of equation and we also find out the solution of the system for the spectrum of particles and hydro magnetic turbulence with the conditions of effective acceleration in the cosmic space of solar system. (author)
Wei, W.; Schmitt, F. G.; Huang, Y. X.; Zhang, H. S.
2016-05-01
Turbulent characteristics in the atmospheric surface layer are investigated using a data-driven method, Hilbert spectral analysis. The results from empirical mode decomposition display a set of intrinsic mode functions whose characteristic scales suggest a dyadic filter-bank property. It can be concluded from the joint probability density function of the intrinsic mode functions that the turbulent properties are totally different under different stratifications: the amplitudes (or energies) are arranged according to the stability parameter [InlineEquation not available: see fulltext.] for stable conditions, but tend to cluster randomly for unstable cases. The intermittency analyses reveal that second-order Hilbert marginal spectra display a power-law behaviour in the inertial subrange, and that the scaling exponent functions deviate from the theoretical values due to the strong intermittency in the stable boundary layer.
THE POWER SPECTRUM OF TURBULENCE IN NGC 1333: OUTFLOWS OR LARGE-SCALE DRIVING?
Is the turbulence in cluster-forming regions internally driven by stellar outflows or the consequence of a large-scale turbulent cascade? We address this question by studying the turbulent energy spectrum in NGC 1333. Using synthetic 13CO maps computed with a snapshot of a supersonic turbulence simulation, we show that the velocity coordinate spectrum method of Lazarian and Pogosyan provides an accurate estimate of the turbulent energy spectrum. We then apply this method to the 13CO map of NGC 1333 from the COMPLETE database. We find that the turbulent energy spectrum is a power law, E(k) ∝ k -β, in the range of scales 0.06 pc ≤l ≤ 1.5 pc, with slope β = 1.85 ± 0.04. The estimated energy injection scale of stellar outflows in NGC 1333 is linj ∼ 0.3 pc, well resolved by the observations. There is no evidence of the flattening of the energy spectrum above the scale linj predicted by outflow-driven simulations and analytical models. The power spectrum of integrated intensity is also a nearly perfect power law in the range of scales 0.16 pc inj. We conclude that the observed turbulence in NGC 1333 does not appear to be driven primarily by stellar outflows.
Transition from thermal to turbulent equilibrium with a resulting electromagnetic spectrum
A recent paper [Ziebell et al., Phys. Plasmas 21, 010701 (2014)] discusses a new type of radiation emission process for plasmas in a state of quasi-equilibrium between the particles and enhanced Langmuir turbulence. Such a system may be an example of the so-called “turbulent quasi-equilibrium.” In the present paper, it is shown on the basis of electromagnetic weak turbulence theory that an initial thermal equilibrium state (i.e., only electrostatic fluctuations and Maxwellian particle distributions) transitions toward the turbulent quasi-equilibrium state with enhanced electromagnetic radiation spectrum, thus demonstrating that the turbulent quasi-equilibrium discussed in the above paper correctly describes the weakly turbulent plasma dynamically interacting with electromagnetic fluctuations, while maintaining a dynamical steady-state in the average sense
GE Huiliang; HE Zuoyong; BAO Xuemei
2001-01-01
The point power spectrum density and the wavenumber frequency spectrum density of turbulent-boundary-layer fluctuation pressure were measured in water-tunnel by use of a φ8 mm hydrophone and a 20-element array, respectively. The non-dimensional representation of measured point power spectrum coincides with the measured results by Bull M. K. et. al. in wind tunnel. The convection peak can be seen clearly in the measured wavenumber frequencyspectrum and the convection velocity can be calculated from the location of the convection peak.The response spectrum of a polyvinylidence fluoride (PVDF) hydrophone, which receiving area is 100 mm × 60 mm, was also measured. By comparing it with the response spectrum of the φ8 mm hydrophone, it is shown that the PVDF hyrdophone has a strong wavenumber filtering effect on turbulent-boundary-layer pressure fluctuation.
Investigations of the Turbulent Energy Spectrum in an Oscillating Grid Experiment
Hall, Stephen C.; Honey, Rose E.; Donnelly, Russell J.
1998-03-01
We report a novel technique to investigate the turbulent energy spectrum generated by an oscillating grid in water. We suspend tubes of a variety of diameters below the oscillating grid and measure the steady state position in the tube of the turbulent front. This position decreases (becomes closer to the grid) as the tube diameter is decreased. We present a model, in which the tubes act as low-pass filters that exclude eddies larger than the tube diameter, to explain the observations and discuss the implications for the turbulent energy spectrum. We estimate the effect of boundary layers formed on the tubes. due to viscosity before the larger ones. The energy spectrum in cross-sections further and further from the grid is contained in an increasingly narrow range of eddy sizes towards the larger eddies. The tubes, acting as low-pass filters, exclude eddies of size larger than the tube diameter and are only filled with eddies smaller than the tube. Therefore, the turbulence in a smaller tube is expected to decay away before turbulence in a larger tube which contains more larger, longer lived eddies.
Phase noise effects on turbulent weather radar spectrum parameter estimation
Lee, Jonggil; Baxa, Ernest G., Jr.
1990-01-01
Accurate weather spectrum moment estimation is important in the use of weather radar for hazardous windshear detection. The effect of the stable local oscillator (STALO) instability (jitter) on the spectrum moment estimation algorithm is investigated. Uncertainty in the stable local oscillator will affect both the transmitted signal and the received signal since the STALO provides transmitted and reference carriers. The proposed approach models STALO phase jitter as it affects the complex autocorrelation of the radar return. The results can therefore by interpreted in terms of any source of system phase jitter for which the model is appropriate and, in particular, may be considered as a cumulative effect of all radar system sources.
Spectrum and Anisotropy of Turbulence from Multi-Frequency Measurement of Synchrotron Polarization
Lazarian, Alex
2015-01-01
We consider turbulent synchrotron emitting media that also exhibits Faraday rotation and provide a statistical description of synchrotron polarization fluctuations. In particular, we consider these fluctuations as a function of the spatial separation of the direction of measurements and as a function of wavelength for the same line-of-sight. On the basis of our general analytical approach, we introduce several measures that can be used to obtain the spectral slopes and correlation scales of both the underlying magnetic turbulence responsible for emission and the spectrum of the Faraday rotation fluctuations. We show the synergetic nature of these measures and discuss how the study can be performed using sparsely sampled interferometric data. We also discuss how additional characteristics of turbulence can be obtained, including the turbulence anisotropy, the three dimensional direction of the mean magnetic field. We consider both cases when the synchrotron emission and Faraday rotation regions coincide and wh...
Gaston, Laurence; Kamara, Alima; Bellet, Michel
2000-01-01
This is the pre-peer reviewed version of the following article : An arbitrary Lagrangian-Eulerian finite element approach to non-steady state turbulent fluid flow with application to mould filling in casting, Gaston L., Kamara A., Bellet M. International Journal for Numerical Methods in Fluids 34, 4 (2000) pages 341-369, which has been published in final form at http://dx.doi.org/10.1002/1097-0363(20001030)34:4%3C341::AID-FLD64%3E3.0.CO;2-K International audience This paper presents a t...
Coherent structures and turbulent spectrum in solar wind plasmas
Sharma, R. P.; Yadav, N.; Kumari, Anju [Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi-110016 (India)
2013-08-15
The present paper investigates the localization of a uniform plane kinetic Alfvén wave (KAW) due to the coupling with the density/magnetic field fluctuations associated with a magnetosonic wave propagating in the transverse direction, i.e., perpendicular to the background magnetic field. To gain the physical insight into this evolution, a simplified analytical model based on the Mathieu equation has also been studied. Numerical method has also been used to analyse the evolution of KAW. The magnetic fluctuation spectrum follows Kolmogorovian scaling above the proton gyroradius scalelength, which is regarded as the inertial range. Below this scale, a steepened spectrum has been obtained in the dispersive range with power law index ∼−2.5, which continues up to the dissipation range. Our results reveal that the proposed mechanism may be an interesting physical mechanism for transferring the energy from larger lengthscales to smaller lengthscales in the solar wind plasmas. Relevance of the present study with Cluster spacecraft observations has also been discussed.
Chandran
2000-11-27
Scattering rates for a Goldreich-Sridhar (GS) spectrum of anisotropic, incompressible, magnetohydrodynamic turbulence are calculated in the quasilinear approximation. Because the small-scale fluctuations are constrained to have wave vectors nearly perpendicular to the background magnetic field, scattering is too weak to provide either the mean-free paths commonly used in Galactic cosmic-ray propagation models or the mean-free paths required for acceleration of cosmic rays at quasiparallel shocks. Where strong pitch-angle scattering occurs, it is due to fluctuations not described by the GS spectrum, such as fluctuations generated by streaming cosmic rays. PMID:11082620
Roman-Duval, Julia; Federrath, Christoph; Brunt, Christopher; Heyer, Mark; Jackson, James; Klessen, Ralf
2011-01-01
Turbulence plays a major role in the formation and evolution of molecular clouds. The problem is that turbulent velocities are convolved with the density of an observed region. To correct for this convolution, we investigate the relation between the turbulence spectrum of model clouds, and the statistics of their synthetic observations obtained from Principal Component Analysis (PCA). We apply PCA to spectral maps generated from simulated density and velocity fields, obtained from hydrodynami...
For the temperature fields in rod clads of experimental assemblies a good agreement have been got with use of prior calculations by subchannel code COBRA-IV-I, from results of which an additional information about δt/δX3 distribution was taken. The method of definition the local fields of velocity, turbulent kinetic energy, temperature and eddy diffusivities for one-phase axial stabilized fluids in arbitrary formed rod bundle assemblies with invariable upward geometry was developed. According to this model the AGURA code was worked out to calculate local thermal hydraulic problems in combination with temperature fields in fuel rods and constructive elements of fuel assemblies. The method does not use any prior geometric scales and is based only on invariant local flow parameters: turbulent kinetic energy, velocity field deformation tensor and specific work of inner friction. Verification of this method by available experimental data showed a good agreement of calculation data and findings of velocity and t.k.e. fields, when the secondary flows have not a substantial influence to a balance of axial momentum and turbulent kinetic energy. (author)
Spectrum and Anisotropy of Turbulence from Multi-frequency Measurement of Synchrotron Polarization
Lazarian, A.; Pogosyan, D.
2016-02-01
We consider turbulent synchrotron-emitting media that also exhibit Faraday rotation and provide a statistical description of synchrotron polarization fluctuations. In particular, we consider these fluctuations as a function of the spatial separation of the direction of the measurements and as a function of wavelength for the same line of sight. On the basis of our general analytical approach, we introduce several measures that can be used to obtain the spectral slopes and correlation scales of both the underlying magnetic turbulence responsible for emission and the spectrum of the Faraday rotation fluctuations. We show the synergetic nature of these measures and discuss how the study can be performed using sparsely sampled interferometric data. We also discuss how additional characteristics of turbulence can be obtained, including the turbulence anisotropy and the three-dimensional direction of the mean magnetic field. In addition, we consider the cases when the synchrotron emission and Faraday rotation regions are spatially separated. Appealing to our earlier study, we explain that our new results are applicable to a wide range of spectral indexes of relativistic electrons responsible for synchrotron emission. We expect wide application of our techniques, both with existing synchrotron data sets and with big forthcoming data sets from LOFAR and SKA.
Gotoh, Toshiyuki
2012-11-01
Spectrum of passive scalar variance at very high Schmidt number up to 1000 in isotropic steady turbulence has been studied by using very high resolution DNS. Gaussian random force and scalar source which are isotropic and white in time are applied at low wavenumber band. Since the Schmidt number is very large, the system was integrated for 72 large eddy turn over time for the system to forgot the initial state. It is found that the scalar spectrum attains the asymptotic k-1 spectrum in the viscous-convective range and the constant CB is found to be 5.7 which is larger than 4.9 obtained by DNS under the uniform mean scalar gradient. Reasons for the difference are inferred as the Reynolds number effect, anisotropy, difference in the scalar injection, duration of time average, and the universality of the constant is discussed. The constant CB is also compared with the prediction by the Lagrangian statistical theory for the passive scalar. The scalar spectrum in the far diffusive range is found to be exponential, which is consistent with the Kraichnan's spectrum. However, the Kraichnan spectrum was derived under the assumption that the velocity field is white in time, therefore theoretical explanation of the agreement needs to be explored. Grant-in-Aid for Scientific Research No. 21360082, Ministry of Education, Culture, Sports, Science and Technology of Japan.
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.
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.
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results
Localization of Dispersive Alfvén Wave in Solar wind plasmas and Turbulent Spectrum
Sharma, Swati; Sharma, R. P.
2016-07-01
Solar wind turbulence at large inertial scales is well known for decades and believed to consist of Alfvén cascade. The inertial range of Solar wind turbulence can be described by a magnetohydrodynamic model. But at small scales the MHD description is not valid. At scales of the order of proton inertial length, Alfvén cascade excites kinetic Alfvén wave or fast wave or whistler wave that carries wave energy to smaller scales. On the other hand, parallel propagating right(R) and left(L) circularly polarized Alfvén/ ion cyclotron wave in the framework of Hall MHD are also thought to be essential ingredients of the solar wind turbulence. Recently, He et.al[1] have used the magnetic field data from the STEREO spacecraft to calculate the magnetic helicities in the solar wind turbulence and reported the possible existence of Alfvén -cyclotron waves and their coexistence with the right handed polarized fluctuations. In the present article we intend to study the right circularly polarized dispersive Alfvén wave (DAW) and their role in the solar wind turbulence. The inclusion of the Hall term causes the dispersion of the AW which, in the present study, is considered on account of the finite frequency (frequency comparable to ion gyro frequency) of the pump wave. Filamentation instability has been reported to occur for the case of circularly polarized dispersive Alfvén wave (DAW) propagating parallel to ambient magnetic field. In the present study, the instability arises on account of the transverse density perturbations of the acoustic wave that may couple nonlinearly with the Alfvén wave and the driven ponderomotive force sequentially leads to growth of density perturbations. Numerical simulation involves finite difference method for the time domain and pseudo spectral method for the spatial domain. The power spectrum is investigated which shows a steepening for scales larger than the proton inertial length. These findings have been reported by Alexandrova et al
Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence
Johnson, Perry L., E-mail: pjohns86@jhu.edu; Meneveau, Charles [Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, The Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218 (United States)
2015-08-15
One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume
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...
Marschalkó, G
2014-01-01
A simple analytical relation of form {\\alpha} = 2 {\\kappa} -1 between the magnetic energy spectral exponent {\\alpha} of the turbulent magnetic field in the solar photosphere and its magnetic flux cancellation exponent {\\kappa}, valid under certain restrictive assumptions, is tested and extended outside its range of validity in a series of Monte Carlo simulations. In these numerical tests artificial "magnetograms" are constructed in 1D and 2D by superposing a discrete set of Fourier modes of the magnetic field distribution with amplitudes following a power law spectrum and measuring the cancellation function on these simulated magnetograms. Our results confirm the validity of the analytical relation and extend it to the domain {\\alpha} 0 as {\\alpha} ---> - infinity. The observationally derived upper limit of 0.38 on {\\kappa} implies {\\alpha} < -0.24 in the granular size range, apparently at odds with a small scale dynamo driven in the inertial range.
Shaping the X-ray spectrum of galaxy clusters with AGN feedback and turbulence
Gaspari, M; Ruszkowski, M
2014-01-01
The hot plasma filling galaxy clusters emits copious radiation in the X-ray band. The classic unheated and unperturbed cooling flow model predicts dramatic cooling rates and an isobaric X-ray spectrum with constant differential luminosity distribution, $dL_{\\rm x}/dT \\propto (T/T_{\\rm hot})^0$. Combining past observations, it is however clear that the cores of clusters (and groups) show a strong deficit of emission increasing toward the soft X-ray band: $dL_{\\rm x}/dT \\propto (T/T_{\\rm hot})^{\\alpha=2\\pm1}$. Using 3D hydrodynamic simulations, we show that the deficit arises from the competition of thermal instability condensation and AGN outflow injection. During tight self-regulated feedback, the average luminosity distribution slope is $\\alpha\\approx2$, oscillating within the observed $18$), while pure cooling drives a too shallow slope, $\\alpha<1$. We disentangle the role of heating and turbulence via controlled experiments. Distributed heating alone induces a declining X-ray spectrum with $1<\\alpha&...
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.
An evaluation method of the neutron fluence and mean spectrum with which samples have been irradiated is proposed. The principle is based on measuring the change of the isotopic abundance ratios of arbitrary pairs of nuclides having different neutron absorption cross sections for both thermal and intermediate neutrons. Advantages of the method are as follows, although sensitivity is lower than that of the ordinary activation method in a short irradiation period. i) Any sample can be used irrespective of irradiation history. ii) Nuclides present as impurities in samples can be used as detectors. iii) Neutron fluences and mean spectra with which samples have been heavily irradiated can be measured with reasonable accuracy, thus making it possible to offer the direct information to radiation damage studies. The present study deals with the principle and applicability of the method. (author)
Sharp vorticity gradients in two-dimensional turbulence and the energy spectrum
Kuznetsov, E.A.; Naulin, Volker; Nielsen, Anders Henry;
2010-01-01
Formation of sharp vorticity gradients in two-dimensional (2D) hydrodynamic turbulence and their influence on the turbulent spectra are considered. The analog of the vortex line representation as a transformation to the curvilinear system of coordinates moving together with the di-vorticity lines...
Stephen Phillips
2013-09-01
Full Text Available States have international obligations to ensure that all deprivations of an individual’s liberty are consistent with international human rights law. The majority of provisions in the international human rights law instruments that deal with such deprivations of liberty contain the term ‘arbitrary’, yet there is no clear definition of what this entails. Arbitrariness is defined differently by different supervisory bodies in different cases, and in different contexts; understanding it requires awareness of the different factors affecting how individual deprivations of liberty are examined and understood.A longer version of this article can be found at:http://tinyurl.com/HRD-arbitrary-August2013
Engelbrecht, N. E.; Burger, R. A.
2015-12-01
In this study, a novel ab initio cosmic ray (CR) modulation code that solves a set of stochastic transport equations equivalent to the Parker transport equation, and that uses output from a turbulence transport code as input for the diffusion tensor, is introduced. This code is benchmarked with a previous approach to ab initio modulation. The sensitivity of computed galactic CR proton spectra at Earth to assumptions made as to the low-wavenumber behavior of the two-dimensional (2D) turbulence power spectrum is investigated using perpendicular mean free path expressions derived from two different scattering theories. Constraints on the low-wavenumber behavior of the 2D power spectrum are inferred from the qualitative comparison of computed CR spectra with spacecraft observations at Earth. Another key difference from previous studies is that observed and inferred CR intensity spectra at 73 AU are used as boundary spectra instead of the usual local interstellar spectrum. Furthermore, the results presented here provide a tentative explanation as to the reason behind the unusually high galactic proton intensity spectra observed in 2009 during the recent unusual solar minimum.
Stephen Phillips
2013-01-01
States have international obligations to ensure that all deprivations of an individual’s liberty are consistent with international human rights law. The majority of provisions in the international human rights law instruments that deal with such deprivations of liberty contain the term ‘arbitrary’, yet there is no clear definition of what this entails. Arbitrariness is defined differently by different supervisory bodies in different cases, and in different contexts; understanding it requires ...
Fujita, Yutaka; Kimura, Shigeo S
2016-01-01
It has often been thought that the northern radio relic in the galaxy cluster CIZA J2242.8+5301 (the "Sausage" Cluster) is associated with cosmic-ray (CR) electrons that are accelerated at a shock through diffusive shock acceleration (DSA) mechanism. However, recent radio observations have shown that the radio spectrum is curved, which is inconsistent with the prediction of a simple DSA model. Moreover, the CR electron spectrum before being affected by radiative cooling seems to be too hard for the DSA. In this study, we show that these facts are natural consequences if the electrons are reaccelerated in turbulence in the downstream of the shock. In this model, the DSA is not the main mechanism to generate high-energy electrons. We find that the mean free path of the electrons should be much shorter than the Coulomb mean free path for efficient reacceleration. The scale of the turbulent eddies must be smaller than the width of the relic. We also predict hard X-ray spectra of inverse Compton scattering of phot...
Liu, Yu
2015-09-01
The spectral characteristics of combustion noise are dictated by the temporal correlation of the overall change of heat release rate fluctuations which has not received sufficient attention in prior studies. In this work, the two-time correlation of the volumetric heat release rate fluctuations within the flame brush and its role in modeling combustion noise spectrum are investigated by analyzing direct numerical simulation (DNS) data of turbulent premixed V-flames. This two-time correlation can be well represented by Gaussian-type functions and it captures the slow global variation of the fluctuating heat release rate and hence the low-frequency noise sources of unsteady combustion. The resulting correlation model is applied to predict the far-field noise spectrum from test open flames, and different reference time scales are used to scale this correlation from the DNS data to the test flames. The comparison between predictions and measurements indicates that the correlation models of all reference time scales are capable of reproducing the essential spectral shape including the low- and high-frequency dependencies. Reasonable agreement in the peak frequency, peak sound pressure level, and the Strouhal number scaling of peak frequency is also achieved for two turbulent time scales. A promising convective time scale shows great potential for characterizing the spectral features, yet its predictive capabilities are to be further verified through a longer DNS signal of a bounded flame configuration.
Fujita, Yutaka; Akamatsu, Hiroki; Kimura, Shigeo S.
2016-06-01
It has often been thought that the northern radio relic in the galaxy cluster CIZA J2242.8+5301 (the "Sausage" Cluster) is associated with cosmic ray (CR) electrons that are accelerated at a shock through the diffusive shock acceleration (DSA) mechanism. However, recent radio observations have shown that the radio spectrum is curved, which is inconsistent with the prediction of a simple DSA model. Moreover, the CR electron spectrum before being affected by radiative cooling seems to be too hard for DSA. In this study, we show that these facts are natural consequences if the electrons are reaccelerated in turbulence downstream of the shock. In this model, DSA is not the main mechanism for generating high-energy electrons. We find that the mean free path of the electrons should be much shorter than the Coulomb mean free path for efficient reacceleration. The scale of the turbulent eddies must be smaller than the width of the relic. We also predict hard X-ray spectra of inverse Compton scattering of photons.
Turbulence-induced vibration is an important concern in the design of the spacer grids of nuclear power plants. This study addresses numerically and statistically the effects of random pressures due to turbulent flows upon the fluctuating responses to the power spectrum density in one-dimensional nuclear fuel rod supported simply by the spacer grids. The dynamic forces produced by the pressure fluctuation on the rod surface are calculated by the 3-dimensional large eddy simulation turbulent model in Fluent-6 to simulate the flow field in the same as being measured empirically via pressure transducers. To acquire response to fluctuating pressure, the mode response equation of vibration is used in case of a cylindrical rod in one-dimensional case. The first modal longitudinal joint acceptance integral including a coherence function is also an important parameter affecting the displacement in the form of the root-mean-square of modal responses along with the damping ratio. The root mean square of the lateral displacement in addition to the natural frequency is studied using the power spectral density (PSD) and the longitudinal joint acceptance integral in a fundamental mode. The PSD random pressure on the middle point of the rod shows the typical turbulence pattern: the PSD energy decreases slightly in a low frequency region, but decreases rapidly and linearly with frequency as the frequency exceeds a certain value. The PSD in a very high frequency region is obtained assuming the slope is constant in a logarithmic graph after smoothing the PSD. It turns out that the root-mean-square of displacement ranges from 15 to 40 micro-meter at the maximum value using the mode response equation under the modal damping ratio ranging from 0.01 to 0.05. (authors)
Morlino, G.; P. Blasi(INAF Arcetri); Vietri, M.
2007-01-01
We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of energy exchange between the electron and proton thermal components downstream, and the effect of generation of a turbulent magnetic field in the downstream plasma. The slope of the spectrum turns out to be appreciably affected by all these phenomena, especially ...
Zhou Qi
2012-01-01
To a large degree,language is arbitrary. But there are exceptions to prove that language is not always arbitrary. However,non-arbitrariness is itself inevitably arbitrary. In fact,arbitrariness and non-arbitrariness work together to complete a language. It seems that they contradict to each other, but they actually coexist as a whole in the same unity.
Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum.
Callies, Jörn; Ferrari, Raffaele; Bühler, Oliver
2014-12-01
Midlatitude fluctuations of the atmospheric winds on scales of thousands of kilometers, the most energetic of such fluctuations, are strongly constrained by the Earth's rotation and the atmosphere's stratification. As a result of these constraints, the flow is quasi-2D and energy is trapped at large scales—nonlinear turbulent interactions transfer energy to larger scales, but not to smaller scales. Aircraft observations of wind and temperature near the tropopause indicate that fluctuations at horizontal scales smaller than about 500 km are more energetic than expected from these quasi-2D dynamics. We present an analysis of the observations that indicates that these smaller-scale motions are due to approximately linear inertia-gravity waves, contrary to recent claims that these scales are strongly turbulent. Specifically, the aircraft velocity and temperature measurements are separated into two components: one due to the quasi-2D dynamics and one due to linear inertia-gravity waves. Quasi-2D dynamics dominate at scales larger than 500 km; inertia-gravity waves dominate at scales smaller than 500 km. PMID:25404349
Quenching the X-ray spectrum of hot halos with AGN outflows and turbulence
Gaspari, M.
2016-06-01
I highlight recent advancements in the astrophysics of AGN outflow feedback and diffuse hot gas. Thanks to XMM RGS resolution, we know that the X-ray cores of clusters, groups, and massive galaxies have a strong deficit of soft X-ray emission compared with the classic cooling flow prediction: dL_{x}/dT ∝ (T/T_{hot})^{2±1}. Using 3D hydrodynamic simulations, I show that such deficit arises from the tight self-regulation between thermal instability condensation and AGN outflow feedback. Multiphase filaments condense out of the hot plasma, they rain onto the central SMBH, and boost the AGN outflows via chaotic cold accretion. The sub-relativistic outflows thermalize in the core via shocks and turbulence, releasing more heat in the inner cooler phase, thus inducing the observed soft X-ray decline. I discuss how we can leverage XMM capabilities in the next decade by probing turbulence, conduction, AGN accretion and outflows via the information contained in X-ray spectra and surface brightness. I focus on the importance of selecting a few objects with Ms exposure and how we can unveil multiphase halos through the synergy between simulations and multiwavelength observations.
Ornigotti, Marco; Conti, Claudio; Szameit, Alexander
2015-10-01
We report on the dependence of the carrier frequency of a nondiffracting optical pulse on the amount of orbital angular momentum it carries. We provide a unified universal form of such a dependence for the cases of both scalar and vector pulses with arbitrary frequency spectra. For the case of paraxial optical pulses we consider two different examples, namely, pulses with exponentially decaying spectra and Gaussian spectra.
Infrared properties of the energy spectrum in freely decaying isotropic turbulence
McComb, W. D.
2016-01-01
The low wave number expansion of the energy spectrum takes the well known form E (k ,t ) =E2(t ) k2+E4(t ) k4+⋯ , where the coefficients are weighted integrals against the correlation function C (r ,t ) . We show that expressing E (k ,t ) in terms of the longitudinal correlation function f (r ,t ) immediately yields E2(t ) =0 by cancellation. We verify that the same result is obtained using the correlation function C (r ,t ) , provided only that f (r ,t ) falls off faster than r-3 at large values of r . As power-law forms are widely studied for the purpose of establishing bounds, we consider the family of model correlations f (r ,t ) =αn(t ) r-n , for positive integer n , at large values of the separation r . We find that for the special case n =3 , the relationship connecting f (r ,t ) and C (r ,t ) becomes indeterminate, and (exceptionally) E2≠0 , but that this solution is unphysical in that the viscous term in the Kármán-Howarth equation vanishes. Lastly, we show that E4(t ) is independent of time, without needing to assume the exponential decrease of correlation functions at large distances.
The infrared properties of the energy spectrum in freely decaying isotropic turbulence
McComb, W D
2014-01-01
The low wavenumber expansion of the energy spectrum takes the well known form: $ E(k,t) = E_2(t) k^2 + E_4(t) k^4 + ... $, where the coefficients are weighted integrals against the correlation function $C(r,t)$. We show that expressing $E(k,t)$ in terms of the longitudinal correlation function $f(r,t)$ immediately yields $E_2(t)=0$ by cancellation. We verify that the same result is obtained using the correlation function $C(r,t)$, provided only that $f(r,t)$ falls off faster than $r^{-3}$ at large values of $r$. As power-law forms are widely studied for the purpose of establishing bounds, we consider the family of model correlations $f(r,t)=\\alpha_n(t)r^{-n}$, for positive integer $n$, at large values of the separation $r$. We find that for the special case $n=3$, the relationship connecting $f(r,t)$ and $C(r,t)$ becomes indeterminate, and (exceptionally) $E_2 \
Baluev, Roman V.; Shaidulin, Vakhit Sh.
2015-01-01
We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. We consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\\sin i$, giving a clo...
FIV(fluid-induced vibration) is an important concern in power and process plants especially in nuclear industry subject to high axial and cross flow causing serious problems. This study addresses the effects of random pressures due to turbulent flows upon the vibrational responses to PSD(power spectrum density) in one dimensional rod supported simply at both ends. Though TIV(turbulenceinduced vibration) takes place under parallel flows where axial flow-induced vibration is a much smaller problem than cross-flow vibration, FIV in axial flow generates random pressure fluctuations due to turbulence mainly around the rod surfaces forcing them vibrate randomly. Dynamic forces produced by the total pressure fluctuating on the rod surface are calculated by the 3 dimensional LES (large eddy simulation) turbulent model in FLUENT 6 to simulate the flow field in CFD code. To acquire response to fluctuating pressure, the response equation of vibration is used in case of a cylindrical rod in one dimensional case. The first modal longitudinal joint acceptance integral including coherence function is an important parameter affecting the vibrational responses in the form of root mean square modal response along with the damping ratio. And the fluctuating stagnation pressure PSD at the wall via FFT transformation in turbulent boundary layer is a key to increasing CHF(critical heat flux). The main goal is not only to enhance the CHF but also to reduce FIV simultaneously, and to apply to designing fuel rods and spacer grid assembly including mixing vanes
Dimotakis, Paul E.
2005-01-01
The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach o...
Nazarenko, Sergey [Warwick Univ., Coventry (United Kingdom). Mathematics Inst.
2011-07-01
Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as ''frozen'' turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field. (orig.)
Molodij, Guillaume
2011-08-01
A general expression of the spatial correlation functions of quantities related to the phase fluctuations of a wave that have propagated through the atmospheric turbulence are derived. A generalization of the method to integrand containing the product of an arbitrary number of hypergeometric functions is presented. The formalism is able to give the coefficients of phase-expansion functions orthogonal over an arbitrary circularly symmetric weighting function for an isotropic turbulence spectrum, as well as to describe the effect of the finite outer and inner scales of the turbulence and to describe the spherical propagation or to derive the effects of the analytical operators acting on the phase such as the derivatives of any order. The derivation of the generalized integrals with multiparameters is based on the Mellin transforms integration method. PMID:21811336
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...
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
A generalization of a transformation due to Kurskov and Ozernoi is used to rewrite the usual equations governing subsonic turbulence in Robertson-Walker cosmological models as Navier-Stokes equations with a time-dependent viscosity. This paper first rederives some well-known results in a very simple way by means of this transformation. The main result however is that the establishment of a Kolmogorov spectrum at recombination appears to be incompatible with subsonic turbulence. The conditions after recombination are also discussed briefly. (author)
Solar conjunction of Mars on 1976 November 25 occurred very near the beginning of solar cycle 21, about 4 months after the first Viking spacecraft arrived at the planet. Radio wave scattering data were collected at 3.6 and 13 cm wavelengths, using the radio link between the Viking orbiters and the Earth. These data allow measurements of solar wind properties over a range of heliocentric radial distance from approx.6 to 44 R/sub sun/ with solar latitudes ranging from -170 to +70. Observations with Mariner 10 during a period of moderate solar activity in 1974 cover from 6 to 24 R/sub sun/ and from approx.200 to near 900. We have found that the temporal frequency variance spectrum of amplitude fluctuations is useful for characterizing the bulk motion of the plasma. This spectrum has an approximately constant low frequency plateau and a power-law high frequency asymptote; the plateau-asymptote intersection frequency provides a measure of the solar wind velocity V. We also obtain the spectral index p of electron density turbulence, Phi/sub N/approx.kappa/sup -p/, where kappa is spatial wavenumber. These results apply to a cylindrical region oriented with its axis along the radio ray path and its center at the point of closest approach to the Sun. The measurements of V and p cover some 78/sup d/ for Viking and 492 for Mariner 10 and show the combined effects of changing heliocentric distance rho, solar latitude theta, and solar longitude Psi, as well as solar activity. The Viking results can be regarded as a function primary of rho and Psi since the observations are concentrated in the equatorial regions when solar activity was near minimum. For Mariner 10, rho, theta, and Psi variations were important. The Viking results show an abrupt change in V(rho) and the turbulence spectral index at approx.15 R/sub sun/
Shell Model for Buoyancy-driven Turbulence
Kumar, Abhishek
2014-01-01
In this paper we construct shell models for convective turbulence, e.g., Rayleigh B\\'{e}nard convection, and stably-stratified turbulence. We simulate these models in the turbulent regime and show that the convective turbulence exhibits Kolmogorov spectrum for the kinetic energy, while the stably-stratified turbulence show Bolgiano-Obukhbov scaling.
Laser induced fluorescence is used to obtain data for determining magnitudes and fluctuation spectra of local electric fields within a turbulent plasma. A 600 keV, 15 ka, 1 μs, 50 ns risetime electron beam is injected into a 20 cm diameter, 60 cm long polycarbonate drift tube containing 10/sup 13/ cm /sup -3/ hydrogen or helium plasmas, constrained by a 2 kgauss axial magnetic field. The transfer of beam kinetic energy to resonant plasma modes is accompanied by large, local electric fields, the average magnitude and fluctuation spectra of which cannot be measured by physical probes. A small plasma gun containing alkaline earth carbonates is used to create plasma doped with appropriate ions, or a small 10 kV electron source is used to ionize 1 mtorr of helium gas in the drift tube. The doping ions or the helium atoms and ions are then excited by laser photons to levels sensitive to the Stark effect or to levels that yield electric field stimulated optical transitions in the vicinity of forbidden lines. A 20 MW, 20 ns XeCl excimer laser is used to pump various dyes to achieve the necessary wavelengths and photon fluxes for these experiments
Dynamics of the modulational instability of a broad Langmuir wave spectrum
Modulational instability of a Langmuir turbulence spectrum is considered in which the wave group velocities are great compared with the velocity of ion sound. A dispersion equation is obtained which yields the instability threshold and increment for an arbitrary relation between the modulation space scale and the characteristic Langmuir oscillation wavelength. An equation describing the nonlinear stage of instability of one-dimensional longwave perturbations for the case of a small excess over the threshold is derived and solved by the method of the inverse scattering problem. It is found that the transition of the instability to a nonlinear regime resembles the hard excitation of turbulence in hydrodynamics
Multi-scale theory of rotating turbulence
Leprovost, Nicolas; Kim, Eun-Jin
2007-01-01
We consider turbulence induced by an arbitrary forcing and derive turbulence amplitude and turbulent transport coefficients, first by using a quasi-linear theory and then by using a multi-scale renormalisation analysis. With an isotropic forcing, the quasi-linear theory gives that the turbulent transport coefficients, both parallel and perpendicular to the rotation vector, have the asymptotic scaling $\\Omega^{-1}$ for rapid rotation (i.e. when the rotation rate $\\Omega$ is larger than the inv...
Arbitrary Spin Galilean Oscillator
Hagen, C R
2014-01-01
The so-called Dirac oscillator was proposed as a modification of the free Dirac equation which reproduces many of the properties of the simple harmonic oscillator but accompanied by a strong spin-orbit coupling term. It has yet to be extended successfully to the arbitrary spin S case primarily because of the unwieldiness of general spin Lorentz invariant wave equations. It is shown here using the formalism of totally symmetric multispinors that the Dirac oscillator can, however, be made to accommodate spin by incorporating it into the framework of Galilean relativity. This is done explicitly for spin zero and spin one as special cases of the arbitrary spin result. For the general case it is shown that the coefficient of the spin-orbit term has a 1/S behavior by techniques which are virtually identical to those employed in the derivation of the g-factor carried out over four decades ago.
Universal statistics of density of inertial particles sedimenting in turbulence
Fouxon, Itzhak; Lee, Changhoon
2014-01-01
We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio $Fr$ of acceleration of fluid particles to acceleration of gravity $g$. The particles are driven by linear drag and have arbitrary inertia. We demonstrate that independently of the particles' size or density the particles distribute over fractal set with log-normal statistics determined completely by the Kaplan-Yorke dimension $D_{KY}$. When inertia is not small $D_{KY}$ is proportional to the ratio of integral of spectrum of turbulence multiplied by wave-number and $g$. This ratio is independent of properties of particles so that the particles concentrate on fractal with universal, particles-independent statistics. We find Lyapunov exponents and confirm predictions numerically. The considered case includes typical situation of water droplets in clouds.
Baluev, Roman V
2015-01-01
We present an attempt to improve models of the Rossiter-McLaughlin effect by relaxing several restrictive assumptions. For our main model of the Doppler anomaly, we consider the entire multiline stellar spectrum rather than just a single line, use no assumptions about the shape of the lines profiles, and allow arbitrary size ratio for the star and its eclipser. However, we neglect the effect of macro-turbulence and differential rotation. We construct our model as a power series in the stellar rotation velocity, $V\\sin i$, giving a closed set of analytic formulae for up to three terms, and assuming quadratic limb-darkening law. We consider three major approaches of determining the Doppler shift: cross-correlation with a predefined template, cross-correlation with an out-of-transit stellar spectrum, and parametric modelling of the spectrum. We reveal that the Doppler anomaly has an additional first-order (in $V\\sin i$) correction term, while previous works primarily deal with only a second-order correction. Thi...
Stirring turbulence with turbulence
Cekli, Hakki Ergun; Joosten, René; van de Water, Willem
2015-12-01
We stir wind-tunnel turbulence with an active grid that consists of rods with attached vanes. The time-varying angle of these rods is controlled by random numbers. We study the response of turbulence on the statistical properties of these random numbers. The random numbers are generated by the Gledzer-Ohkitani-Yamada shell model, which is a simple dynamical model of turbulence that produces a velocity field displaying inertial-range scaling behavior. The range of scales can be adjusted by selection of shells. We find that the largest energy input and the smallest anisotropy are reached when the time scale of the random numbers matches that of the largest eddies of the wind-tunnel turbulence. A large mismatch of these times creates a highly intermittent random flow with interesting but quite anomalous statistics.
Invariants of free turbulent decay
Llor, Antoine
2006-01-01
In practically all turbulent flows, turbulent energy decay is present and competes with numerous other phenomena. In Kolmogorov's theory, decay proceeds by transfer from large energy-containing scales towards small viscous scales through the "inertial cascade." Yet, this description cannot predict an actual decay rate, even in the simplest case of homogeneous isotropic turbulence (HIT). As empirically observed over 50 years, the steepness of the "infrared" spectrum - at scales larger than ene...
Stecker, F. W.; Puget, J. L.
1972-01-01
Following the big-bang baryon symmetric cosmology of Omnes, the redshift was calculated to be on the order of 500-600. It is show that, at these redshifts, annihilation pressure at the boundaries between regions of matter and antimatter drives large scale supersonic turbulence which can trigger galaxy formation. This picture is consistent with the gamma-ray background observations discussed previously. Gravitational binding of galaxies then occurs at a redshift of about 70, at which time vortical turbulent velocities of about 3 x 10 to the 7th power cm/s lead to angular momenta for galaxies comparable with measured values.
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 $\\beta=4/7$.
Arbitrary shape surface Fresnel diffraction
Shimobaba, Tomoyoshi; Masuda, Nobuyuki; Ito, Tomoyoshi
2012-01-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to $O(N^2)$ in one dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of sampling points. However, the calculation cost ...
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.
Generalised turbulence spectra for broadband noise predictions with the Random Particle Mesh method
Wohlbrandt, Attila; Guerin, Sebastien; Ewert, Roland
2015-01-01
For better comparison to fan broadband noise experiments the Random Particle Mesh (RPM) method is extended to generalised turbulence spectra. The RPM method synthesises turbulent fluctuations by filtering white noise with a Gaussian filter kernel, which in turn gives a Gaussian spectrum. The Gaussian function is smooth and its derivatives and antiderivatives are again Gaussian functions; the Gaussian filter is efficient and finds wide-spread applications in stochastic signal processing. However in many applications Gaussian spectra are not matching physical spectra. E.g. in turbo-machines, the von Karman, Liepmann, and modified von Karman spectra are the most relevant model spectra. In the current paper we show how to analytically derive weighting functions to realise arbitrary spectra which are isotropic and solenoidal using a superposition of weighted Gaussian spectra of differing length scales. The analytic weighting functions for the von Karman , the Liepmann , and the modified von Karman spectra are deri...
Magnetohydrodynamic turbulence
Biskamp, Dieter
2003-01-01
This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressi
Classifying Serre subcategories via atom spectrum
Kanda, Ryo
2011-01-01
In this paper, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian category. Moreover we show that the atom spectrum of a locally noetherian Grothendieck category is homeomorphic to its Ziegler spectrum.
Bell inequalities for arbitrary situations
We present a simple way based on the joint global probability distribution to derive CHSH inequalities. Inspired by this derivation we develop a simple method that gives a set of conditions which are necessary for a model to be a local variable theory. This method generates candidate Bell inequalities for models of arbitrary situations in which there are an arbitrary number of particles, measurements and outcomes. With the help of a type of distribution it will be clear that all necessary conditions are Bell inequalities. This work gives a unified way to write Bell inequalities for arbitrary situations. - Highlights: • Constructing CHSH inequalities based on joint global probability distribution. • Constructing conditions which are necessary for a model to be local and realistic. • Bell inequalities for general situations
Non-linear diffusion of charged particles in a turbulent magnetoplasma
A unified theory is presented which describes non-linear effects on relative and absolute diffusion of charged particles in a magnetoplasma, in analogy with analogous methods used for diffusion studies of pollutants in the environment. Explicit results are obtained for non-linear diffusion of test particles represented by their guiding centers in a turbulent energy spectrum in K-1 and K-3, which corresponds to recent measurements in the T.F.R. Tokamak. As expected, a BOHM scaling of the absolute diffusion coefficient is obtained for frozen turbulence. The growth of an initially small cloud of particles in an arbitrary turbulent medium corresponds to the process of relative diffusion. It is described by a generalization of the Brownian motion, including a first stage of very slow initial relative diffusion, followed by a stage of rapid expansion of the cloud up to the final stage in which particles become uncorrelated, and Brownian diffusion is reached asymptotically. The stage of exponential growth, observed in fluid turbulence corresponds to the clump effect in plasma turbulence. It is entirely due to the effect of trajectory correlations. The LJAPUNOV exponent of this exponential separation is obtained analytically. Numerical solutions of the diffusion equation are presented for the effective radius of the cloud as function of time in the case of a model spectrum of drift-wave turbulence. When compared with classical Brownian diffusion of uncorrelated particles, the effective ''diffusion coefficient'' for correlated particles is found to be reduced by orders of magnitude for rather long times. Practical implications for experimental situations are also discussed (Barium clouds released in the ionosphere, pellet injection in e.g. Tokamaks)
Arbitrary shape surface Fresnel diffraction.
Shimobaba, Tomoyoshi; Masuda, Nobuyuki; Ito, Tomoyoshi
2012-04-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to O(N²) in one dimensional or O(N⁴) in two dimensional cases, where N is the number of sampling points. However, the calculation cost of the proposed method is O(N log N) in one dimensional or O(N² log N) in two dimensional cases using non-uniform fast Fourier transform. PMID:22513646
Arbitrary shape surface Fresnel diffraction
Shimobaba, Tomoyoshi; Ito, Tomoyoshi
2012-01-01
Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to $O(N^2)$ in one dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of sampling points. However, the calculation cost of the proposed method is $O(N \\log N)$ in one dimensional or $O(N^2 \\log N)$ in two dimensional cases using non-uniform fast Fourier transform.
The Interpretation of Saussure’s Arbitrariness
王艳
2015-01-01
According to Saussure,The arbitrary nature of language is"first principle of linguistic".With the development of cognitive science,some exaggerate the importance of iconicity;some even suggest iconicity should replace arbitrariness.What leads to this extreme view is the misunderstanding of arbitrariness.The paper aims at advocating an overall and objective view towards the arbitrary nature of language,putting forward that arbitrariness and iconicity are not incompatible but complementary.
Spectrum Analysis of Wind Profiling Radar Measurements
阮征; 慕瑞琪; 魏鸣; 葛润生
2014-01-01
Unlike previous studies on wind turbulence spectrum in the planetary boundary layer, this investigation focuses on high-altitude (1-5 km) wind energy spectrum and turbulence spectrum under various weather conditions. A fast Fourier transform (FFT) is used to calculate the wind energy and turbulence spectrum density at high altitudes (1-5 km) based on wind profiling radar (WPR) measurements. The turbulence spectrum under stable weather conditions at high altitudes is expressed in powers within a frequency range of 2 × 10-5-10-3 s-1, and the slope b is between -0.82 and -1.04, indicating that the turbulence is in the transition from the energetic area to the inertial sub-range. The features of strong weather are reflected less obviously in the wind energy spectrum than in the turbulence spectrum, with peaks showing up at different heights in the latter spectrum. Cold windy weather appears over a period of 1.5 days in the turbulence spectrum. Wide-range rainstorms exhibit two or three peaks in the spectrum over a period of 15-20 h, while in severe convective weather conditions, there are two peaks at 13 and 9 h. The results indicate that spectrum analysis of wind profiling radar measurements can be used as a supplemental and helpful method for weather analysis.
Forced fluid dynamics from gravity in arbitrary dimensions
We consider long wavelength solutions to the Einstein-dilaton system with negative cosmological constant which are dual, under the AdS/CFT correspondence, to solutions of the conformal relativistic Navier-Stokes equations with a dilaton-dependent forcing term. Certain forced fluid flows are known to exhibit turbulence; holographic duals of forced fluid dynamics are therefore of particular interest as they may aid efforts towards an explicit model of holographic steady state turbulence. In recent work, Bhattacharyya et al. have constructed long wavelength asymptotically locally AdS5 bulk spacetimes with a slowly varying boundary dilaton field which are dual to forced fluid flows on the 4−dimensional boundary. In this paper, we generalise their work to arbitrary spacetime dimensions; we explicitly compute the dual bulk metric, the fluid dynamical stress tensor and Lagrangian to second order in a boundary derivative expansion
Turbulence and galactic structure
Elmegreen, Bruce G
2004-01-01
Interstellar turbulence is driven over a wide range of scales by processes including spiral arm instabilities and supernovae, and it affects the rate and morphology of star formation, energy dissipation, and angular momentum transfer in galaxy disks. Star formation is initiated on large scales by gravitational instabilities which control the overall rate through the long dynamical time corresponding to the average ISM density. Stars form at much higher densities than average, however, and at much faster rates locally, so the slow average rate arises because the fraction of the gas mass that forms stars at any one time is low, ~10^{-4}. This low fraction is determined by turbulence compression, and is apparently independent of specific cloud formation processes which all operate at lower densities. Turbulence compression also accounts for the formation of most stars in clusters, along with the cluster mass spectrum, and it gives a hierarchical distribution to the positions of these clusters and to star-forming...
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...
Bulk Comptonization by Turbulence in Accretion Disks
Kaufman, J
2016-01-01
Radiation pressure dominated accretion discs around compact objects may have turbulent velocities that greatly exceed the electron thermal velocities within the disc. Bulk Comptonization by the turbulence may therefore dominate over thermal Comptonization in determining the emergent spectrum. Bulk Comptonization by divergenceless turbulence is due to radiation viscous dissipation only. It can be treated as thermal Comptonization by solving the Kompaneets equation with an equivalent "wave" temperature, which is a weighted sum over the power present at each scale in the turbulent cascade. Bulk Comptonization by turbulence with non-zero divergence is due to both pressure work and radiation viscous dissipation. Pressure work has negligible effect on photon spectra in the limit of optically thin turbulence, and in this limit radiation viscous dissipation alone can be treated as thermal Comptonization with a temperature equivalent to the full turbulent power. In the limit of extremely optically thick turbulence, ra...
Scintillation index in strong oceanic turbulence
Baykal, Yahya
2016-09-01
Scintillation index of spherical wave in strongly turbulent oceanic medium is evaluated. In the evaluation, modified Rytov solution and our recent formulation that expresses the oceanic turbulence parameters by the atmospheric turbulence structure constant, are employed. Variations of the scintillation index in strong oceanic turbulence are examined versus the oceanic turbulence parameters such as the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, viscosity, wavelength, the link length, and the ratio of temperature to salinity contributions to the refractive index spectrum.
Turbulence patterns and neutrino flavor transitions in high-resolution supernova models
During the shock-wave propagation in a core-collapse supernova (SN), matter turbulence may affect neutrino flavor conversion probabilities. Such effects have been usually studied by adding parametrized small-scale random fluctuations (with arbitrary amplitude) on top of coarse, spherically symmetric matter density profiles. Recently, however, two-dimensional (2D) SN models have reached a space resolution high enough to directly trace anisotropic density profiles, down to scales smaller than the typical neutrino oscillation length. In this context, we analyze the statistical properties of a large set of SN matter density profiles obtained in a high-resolution 2D simulation, focusing on a post-bounce time (2 s) suited to study shock-wave effects on neutrino propagation on scales as small as O(100) km and possibly below. We clearly find the imprint of a broken (Kolmogorov-Kraichnan) power-law structure, as generically expected in 2D turbulence spectra. We then compute the flavor evolution of SN neutrinos along representative realizations of the turbulent matter density profiles, and observe no or modest damping of the neutrino crossing probabilities on their way through the shock wave. In order to check the effect of possibly unresolved fluctuations at scales below O(100) km, we also apply a randomization procedure anchored to the power spectrum calculated from the simulation, and find consistent results within ± 1σ fluctuations. These results show the importance of anchoring turbulence effects on SN neutrinos to realistic, fine-grained SN models
Bass, J; Agostini, L
1955-01-01
The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum.
Elastic wave turbulence and intermittency
Chibbaro, Sergio; Josserand, Christophe
2016-07-01
We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by d cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only.
Fragmentation in turbulent primordial gas
Glover, S C O; Klessen, R S; Bromm, V
2010-01-01
We report results from numerical simulations of star formation in the early universe that focus on the role of subsonic turbulence, and investigate whether it can induce fragmentation of the gas. We find that dense primordial gas is highly susceptible to fragmentation, even for rms turbulent velocity dispersions as low as 20% of the initial sound speed. The resulting fragments cover over two orders of magnitude in mass, ranging from 0.1 to 40 solar masses. However, our results suggest that the details of the fragmentation depend on the local properties of the turbulent velocity field and hence we expect considerable variations in the resulting stellar mass spectrum in different halos.
Two-dimensional elastic turbulence
Berti, S; Boffetta, G; Celani, A; Musacchio, S; 10.1103/PhysRevE.77.055306
2010-01-01
We investigate the effect of polymer additives on a two-dimensional Kolmogorov flow at very low Reynolds numbers by direct numerical simulations of the Oldroyd-B viscoelastic model. We find that above the elastic instability threshold the flow develops the elastic turbulence regime recently observed in experiments. We observe that both the turbulent drag and the Lyapunov exponent increase with Weissenberg, indicating the presence of a disordered, turbulent-like mixing flow. The energy spectrum develops a power-law scaling range with an exponent close to the experimental and theoretical expectations.
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...
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.
Generalization of the electronic susceptibility for arbitrary molecular geometries
Scherrer, Arne; Dreßler, Christian; Ahlert, Paul; Sebastiani, Daniel
2016-04-01
We generalize the explicit representation of the electronic susceptibility χ[R](r, r') for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ[R](r, r') which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.
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.
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.
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
This paper presents an overview of the progress made in understanding plasma turbulence. It has relied heavily on numerical simulations to gain some intuition on the physical processes underlying nonlinear interaction and as a cross check for quantitative estimates derived from weak turbulence theory or DIA-based strong turbulence theory. The mathematical description of plasmas, especially those confined in a magnetic bottle, is far more complex than the Navier-Stokes fluid. Yet because of the dispersion of the plasma eigenmodes, the DIA perhaps has greater validity in a plasma than in a Navier-Stokes fluid. Recent developments in dynamical-systems theory have not yet been implemented in plasma turbulence at the level discussed in other studies for boundary-layer turbulence. This technique has promise for evaluating the behavior of large eddies, which may dominate plasma transport as a low-order system. In the collisionless, kinetic regime, where turbulence in x, v phase space has to be addressed, the new methods involving noneigenmode entities called clumps and holes, need further evolution to gain complete acceptability. For the future, a combination of analytical tools and numerical methods may afford the optimum route. Some examples of this are revireviewed
Quantitative photography of intermittency in surface wave turbulence
At high amplitudes of excitation surface waves on water distribute their energy according to a Kolmogorov type of turbulent power spectrum. We have used diffusing light photography to measure the power spectrum and to quantify the presence of large structures in the turbulent state
Quantitative photography of intermittency in surface wave turbulence
Wright, W.; Budakian, R.; Putterman, S.J. [Univ. of California, Los Angeles, CA (United States)
1997-12-31
At high amplitudes of excitation surface waves on water distribute their energy according to a Kolmogorov type of turbulent power spectrum. We have used diffusing light photography to measure the power spectrum and to quantify the presence of large structures in the turbulent state.
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.
Large scale numerical simulation for superfluid turbulence
Large scale numerical simulation of quantum turbulence is performed by using 3-D time-dependent Gross-Pitaevskii equation. The energy spectrum obeying Kolmogorov law and large scale self-similar structure of quantum vortex tangle are found in a fully developed dumped turbulent state. We confirm that inertial range of the energy spectrum becomes large as the system size of the simulation becomes large that is consistent with the result of the normal fluid turbulence. On the other hand, bottleneck effect near coherent length prevents the inertial range from extending to smaller scale. (author)
Simulation of atmospheric turbulence layers with phase screens by JAVA
Zhang, Xiaofang; Chen, Wenqin; Yu, Xin; Yan, Jixiang
2008-03-01
In multiconjugate Adaptive Optics (MCAO), the phase screens are used to simulate atmospheric turbulence layers to study the optimal turbulence delamination and the determination of layer boundary position. In this paper, the method of power spectrum inversion and sub-harmonic compensation were used to simulate atmospheric turbulence layers and results can be shown by grey map. The simulation results showed that, with the increase of turbulence layers, the RMS of adaptive system decreased, but the amplitude diminished. So the atmospheric turbulence can be split into 2-3 layers and be modeled by phase screens. Otherwise, a small simulation atmospheric turbulence delamination system was realized by JAVA.
Influence of atmospheric turbulence on OAM-based FSO system with use of realistic link model
Li, Ming; Yu, Zhongyuan; Cvijetic, Milorad
2016-04-01
We study the influence of atmospheric turbulence on OAM-based free-space optical (FSO) communication by using the Pump turbulence spectrum model which accurately characterizes the realistic FSO link. A comprehensive comparison is made between the Pump and Kolmogorov spectrum models with respect to the turbulence impact. The calculated results show that obtained turbulence-induced crosstalk is lower, which means that a higher channel capacity is projected when the realistic Pump spectrum is used instead of the Kolmogorov spectrum. We believe that our results prove that performance of practical OAM-based FSO is better than one predicted by using the original Kolmogorov turbulence model.
In situ measurements of wind and current speed and relationship between output power and turbulence
Duran Medina, Olmo; Schmitt, François G.; Sentchev, Alexei; Calif, Rudy
2015-04-01
In a context of energy transition, wind and tidal energy are sources of clean energy with the potential of partially satisfying the growing demand. The main problem of this type of energy, and other types of renewable energy remains the discontinuity of the electric power produced in different scales, inducing large fluctuations also called intermittency. This intermittency of wind and tidal energy is inherent to the turbulent nature of wind and marine currents. We consider this intermittent power production in strong relation with the turbulent intermittency of the resource. The turbulence theory is multifractal energy cascades models, a classic in physics of turbulence. From earlier studies in atmospheric sciences, we learn that wind speed and the aggregate power output are intermittent and multifractal over a wide range of scales [Calif and Schmitt 2014]. We want to extend this study to a marine current turbine and compare the scaling properties for those renewable energy sources. We consider here coupling between simultaneous velocity time series and output power from a wind turbine and a marine current turbine. Wind turbine data were obtained from Denmark and marine current data from Western Scheldt, Belgium where a prototype of a vertical and horizontal marine current turbines are tested. After an estimation of their Fourier density power spectra, we study their scaling properties in Kolmogorov's theory and the framework of fully developed turbulence. Hence, we employ a Hilbert-based methodology, namely arbitrary-order Hilbert spectral analysis [Calif et al. 2013a, 2013b] to characterize the intermittent property of the wind and marine current velocity in order to characterize the intermittent nature of the fluid. This method is used in order to obtain the spectrum and the corresponding power law for non-linear and non-stationary time series. The goal is to study the non-linear transfer characteristics in a multi-scale and multi-intensity framework.
A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions
Afsar, Mohammed Z.; Leib, Stewart J.; Bozak, Richard F.
2016-01-01
This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal
Tchen, C. M.
1986-01-01
Theoretical and numerical works in atmospheric turbulence have used the Navier-Stokes fluid equations exclusively for describing large-scale motions. Controversy over the existence of an average temperature gradient for the very large eddies in the atmosphere suggested that a new theoretical basis for describing large-scale turbulence was necessary. A new soliton formalism as a fluid analogue that generalizes the Schrodinger equation and the Zakharov equations has been developed. This formalism, processing all the nonlinearities including those from modulation provided by the density fluctuations and from convection due to the emission of finite sound waves by velocity fluctuations, treats large-scale turbulence as coalescing and colliding solitons. The new soliton system describes large-scale instabilities more explicitly than the Navier-Stokes system because it has a nonlinearity of the gradient type, while the Navier-Stokes has a nonlinearity of the non-gradient type. The forced Schrodinger equation for strong fluctuations describes the micro-hydrodynamical state of soliton turbulence and is valid for large-scale turbulence in fluids and plasmas where internal waves can interact with velocity fluctuations.
Controlling arbitrary humidity without convection.
Wasnik, Priyanka S; N'guessan, Hartmann E; Tadmor, Rafael
2015-10-01
In this paper we show a way that allows for the first time to induce arbitrary humidity of desired value for systems without convective flow. To enable this novelty we utilize a semi-closed environment in which evaporation is not completely suppressed. In this case, the evaporation rate is determined both by the outer (open) humidity and by the inner (semi-closed) geometry including the size/shape of the evaporating medium and the size/shape of the semi-closure. We show how such systems can be used to induce desired humidity conditions. We consider water droplet placed on a solid surface and study its evaporation when it is surrounded by other drops, hereon "satellite" drops and covered by a semi-closed hemisphere. The main drop's evaporation rate is proportional to its height, in agreement with theory. Surprisingly, however, the influence of the satellite drops on the main drop's evaporation suppression is not proportional to the sum of heights of the satellite drops. Instead, it shows proportionality close to the satellite drops' total surface area. The resultant humidity conditions in the semi-closed system can be effectively and accurately induced using different satellite drops combinations. PMID:26072445
This paper is an introduction course in modelling turbulent thermohydraulics, aimed at computational fluid dynamics users. No specific knowledge other than the Navier Stokes equations is required beforehand. Chapter I (which those who are not beginners can skip) provides basic ideas on turbulence physics and is taken up in a textbook prepared by the teaching team of the ENPC (Benque, Viollet). Chapter II describes turbulent viscosity type modelling and the 2k-ε two equations model. It provides details of the channel flow case and the boundary conditions. Chapter III describes the 'standard' (Rij-ε) Reynolds tensions transport model and introduces more recent models called 'feasible'. A second paper deals with heat transfer and the effects of gravity, and returns to the Reynolds stress transport model. (author)
General optical scintillation in turbulent atmosphere
Ruizhong Rao
2008-01-01
A general expression of the scintillation index is proposed for optical wave propagating in turbulent atmosphere under arbitrary fluctuation conditions. The expression depends on extreme behaviors of the scintillation indices under both weak and strong fluctuations. The maximum scintillation index in the onset region and the corresponding Rytov index can be evaluated from the general expression. Plane and spherical waves in the cases of zero and non-zero turbulence inner scale are given as examples for illustration of the general behaviors of scintillation indices.
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
Mixing in manipulated turbulence
Kuczaj, A K; Geurts, Bernard J.; Kuczaj, Arkadiusz K.
2006-01-01
A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst substrates in process-engineering. The flow-consequences of such complicated objects are incorporated by adding explicit multiscale forcing to the Navier-Stokes equations. The forcing represents the simultaneous agitation of a wide spectrum of length-scales when flow passes through the complex object. It is found that a considerable modulation of the traditional energy cascading can be introduced with a specific forcing strategy. In spectral space, forcing yields strongly localized deviations from the common Kolmogorov scaling law, directly associated with the explicitly forced scales. In addition, the accumulated effect of forcing induces a significant non-local alteration of the kinetic energy including the spectrum for the large scales. Consequently, a manipulation of turbu...
Calculating fusion neutron energy spectra from arbitrary reactant distributions
Eriksson, J.; Conroy, S.; Andersson Sundén, E.; Hellesen, C.
2016-02-01
The Directional Relativistic Spectrum Simulator (DRESS) code can perform Monte-Carlo calculations of reaction product spectra from arbitrary reactant distributions, using fully relativistic kinematics. The code is set up to calculate energy spectra from neutrons and alpha particles produced in the D(d, n)3He and T(d, n)4He fusion reactions, but any two-body reaction can be simulated by including the corresponding cross section. The code has been thoroughly tested. The kinematics calculations have been benchmarked against the kinematics module of the ROOT Data Analysis Framework. Calculated neutron energy spectra have been validated against tabulated fusion reactivities and against an exact analytical expression for the thermonuclear fusion neutron spectrum, with good agreement. The DRESS code will be used as the core of a detailed synthetic diagnostic framework for neutron measurements at the JET and MAST tokamaks.
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
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.
On turbulence in dilatant dispersions
Baumert, Helmut Z.; Wessling, Bernhard
2016-07-01
This paper presents a new theory on the behaviour of shear-thickening (dilatant) fluids under turbulent conditions. The structure of a dilatant colloidal fluid in turbulent motion may be characterized by (at least) four characteristic length scales: (i) the ‘statistically largest’ turbulent scale, {λ }0, labeling the begin of the inertial part of the wavenumber spectrum; (ii) the energy-containing scale, { L }; (iii) Kolmogorov’s micro-scale, {λ }{ K }, related with the size of the smallest vortices existing for a given kinematic viscosity and forcing; (iv) the inner (‘colloidal’) micro-scale, {λ }i, typically representing a major stable material property of the colloidal fluid. In particular, for small ratios r={λ }i/{λ }{ K }∼ { O }(1), various interactions between colloidal structures and smallest turbulent eddies can be expected. In the present paper we discuss particularly that for ρ ={λ }0/{λ }{ K }\\to { O }(1) turbulence (in the narrow, inertial sense) is strangled and chaotic but less mixing fluid motions remain. We start from a new stochastic, micro-mechanical turbulence theory without empirical parameters valid for inviscid fluids as seen in publications by Baumert in 2013 and 2015. It predicts e.g. von Karman’s constant correctly as 1/\\sqrt{2 π }=0.399. In its generalized version for non-zero viscosity and shear-thickening behavior presented in this contribution, it predicts two solution branches for the steady state: The first characterizes a family of states with swift (inertial) turbulent mixing and small {λ }{ K }, potentially approaching {λ }i. The second branch characterizes a state family with ρ \\to { O }(1) and thus strangled turbulence, ρ ≈ { O }(1). Stability properties and a potential dynamic commuting between the two solution branches had to be left for future research.
S-duality in N = 4 supersymmetric gauge theories with arbitrary gauge group
The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in the Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle θ. This extended S-duality conjecture includes the case when the unbroken gauge group in non-Abelian and a definite prediction for the spectrum of dyons results. (author)
Arbitrary orbital angular momentum of photons
Pan, Yue; Ren, Zhi-Cheng; Wang, Xi-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrary OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the azimuthally varying polarized vector field. The arbitrary OAM has the same characteristics as the well-defined integer OAM: intrinsic OAM, uniform local OAM and intensity ring, and propagation stability. The arbitrary OAM has unique natures: it is allowed to be flexibly tailored and the radius of the focusing ring can have various choices for a desired OAM, which are of great significance to the benefit of surprising applications of the arbitrary OAM.
THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES
Wen Li; Jian-xin Chen
2006-01-01
In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.
The Sugawara generators at arbitrary level
Gebert, R.; Koepsell, K.; Nicolai, H.
1996-01-01
We construct an explicit representation of the Sugawara generators for arbitrary level in terms of the homogeneous Heisenberg subalgebra, which generalizes the well-known expression at level 1. This is achieved by employing a physical vertex operator realization of the affine algebra at arbitrary level, in contrast to the Frenkel--Kac--Segal construction which uses unphysical oscillators and is restricted to level 1. At higher level, the new operators are transcendental functions of DDF ``osc...
Quantum polar codes for arbitrary channels
Wilde, Mark M.; Renes, Joseph M.
2012-01-01
We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from a given, arbitrary quantum channel. We first demonstrate the coding scheme for arbitrary quantum channels with qubit inputs, and we show that quantum data can be reliably decoded by O(N) rounds of coherent quantum successive cancellation, followed by N controlled-NOT gates (where N is the number of channel uses). We a...
Arbitrary Dimensional Schwarzschild-FRW Black Holes
Gao, Chang Jun
2004-01-01
The metric of arbitrary dimensional Schwarzschild black hole in the background of Friedman-Robertson-Walker universe is presented in the cosmic coordinates system. In particular, the arbitrary dimensional Schwarzschild-de Sitter metric is rewritten in the Schwarzschild coordinates system and basing on which the even more generalized higher dimensional Schwarzschild-de Sitter metric with another extra dimensions is found. The generalized solution shows that the cosmological constant may roots ...
Aspects of wave turbulence in preheating
In this work we have studied the nonlinear preheating dynamics of several inflationary models. It is well established that after a linear stage of preheating characterized by the parametric resonance, the nonlinear dynamics becomes relevant driving the system towards turbulence. Wave turbulence is the appropriated description of this phase since the matter contents are fields instead of usual fluids. Turbulence develops due to the nonlinear interations of waves, here represented by the small inhomogeneities of the scalar fields. We present relevant aspects of wave turbulence such as the Kolmogorov-Zakharov spectrum in frequency and wave number that indicates the energy transfer through scales. From the power spectrum of the matter energy density we were able to estimate the temperature of the thermalized system
Nielsen, Mogens Peter; Shui, Wan; Johansson, Jens
2011-01-01
In this report a new turbulence model is presented.In contrast to the bulk of modern work, the model is a classical continuum model with a relatively simple constitutive equation. The constitutive equation is, as usual in continuum mechanics, entirely empirical. It has the usual Newton or Stokes...... term with stresses depending linearly on the strain rates. This term takes into account the transfer of linear momentum from one part of the fluid to another. Besides there is another term, which takes into account the transfer of angular momentum. Thus the model implies a new definition of turbulence....... The model is in a virgin state, but a number of numerical tests have been carried out with good results. It is published to encourage other researchers to study the model in order to find its merits and possible limitations....
Bulk Comptonization by turbulence in accretion discs
Kaufman, J.; Blaes, O. M.
2016-06-01
Radiation pressure dominated accretion discs around compact objects may have turbulent velocities that greatly exceed the electron thermal velocities within the disc. Bulk Comptonization by the turbulence may therefore dominate over thermal Comptonization in determining the emergent spectrum. Bulk Comptonization by divergenceless turbulence is due to radiation viscous dissipation only. It can be treated as thermal Comptonization by solving the Kompaneets equation with an equivalent `wave' temperature, which is a weighted sum over the power present at each scale in the turbulent cascade. Bulk Comptonization by turbulence with non-zero divergence is due to both pressure work and radiation viscous dissipation. Pressure work has negligible effect on photon spectra in the limit of optically thin turbulence, and in this limit radiation viscous dissipation alone can be treated as thermal Comptonization with a temperature equivalent to the full turbulent power. In the limit of extremely optically thick turbulence, radiation viscous dissipation is suppressed, and the evolution of local photon spectra can be understood in terms of compression and expansion of the strongly coupled photon and gas fluids. We discuss the consequences of these effects for self-consistently resolving and interpreting turbulent Comptonization in spectral calculations in radiation magnetohydrodynamic simulations of high luminosity accretion flows.
Arbitrary laser beam propagation in free space
Arpali, Çağlar; Baykal, Yahya; Nakiboğlu, Cem
2009-08-01
The propagation of arbitrary laser beams in free space is examined. For this purpose, starting with an incident field of arbitrary field distribution, the intensity at the receiver plane is formulated via Huygens Fresnel diffraction integral. Arbitrary source field profile is produced by decomposing the source into incremental areas (pixels). The received field through the propagation in free space is found by superposing the contributions from all source incremental areas. The proposed method enables us to evaluate the received intensity originating from any type of source field. Using the arbitrary beam excitation, intensity of various laser beams such as cos-Gaussian, cosh-Gaussian, general type beams are checked to be consistent with the already existing results in literature, and the received intensity distributions are obtained for some original arbitrary beam field profiles. Our received intensity formulation for the arbitrary source field profiles presented in this paper can find application in optics communication links, reflection from rough surfaces, optical cryptography and optical imaging systems.
Bec, Jeremie; Khanin, Konstantin
2007-01-01
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 mod...
Kühnen, Jakob; Hof, Björn
2015-11-01
We show that a simple modification of the velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarises. The annihilation of turbulence is achieved by a steady manipulation of the streamwise velocity component alone, greatly reducing control efforts. Several different control techniques are presented: one with a local modification of the flow profile by means of a stationary obstacle, one employing a nozzle injecting fluid through a small gap at the pipe wall and one with a moving wall, where a part of the pipe is shifted in the streamwise direction. All control techniques act on the flow such that the streamwise velocity profile becomes more flat and turbulence gradually grows faint and disappears. In a smooth straight pipe the flow remains laminar downstream of the control. Hence a reduction in skin friction by a factor of 8 and more can be accomplished. Stereoscopic PIV-measurements and movies of the development of the flow during relaminarisation are presented.
Recent developments in plasma turbulence and turbulent transport
Terry, P.W. [Univ. of Wisconsin, Madison, WI (United States)
1997-09-22
This report contains viewgraphs of recent developments in plasma turbulence and turbulent transport. Localized nonlinear structures occur under a variety of circumstances in turbulent, magnetically confined plasmas, arising in both kinetic and fluid descriptions, i.e., in either wave-particle or three-wave coupling interactions. These structures are non wavelike. They cannot be incorporated in the collective wave response, but interact with collective modes through their shielding by the plasma dielectric. These structures are predicted to modify turbulence-driven transport in a way that in consistent with, or in some cases are confirmed by recent experimental observations. In kinetic theory, non wavelike structures are localized perturbations of phase space density. There are two types of structures. Holes are self-trapped, while clumps have a self-potential that is too weak to resist deformation and mixing by ambient potential fluctuations. Clumps remain correlated in turbulence if their spatial extent is smaller than the correlation length of the scattering fields. In magnetic turbulence, clumps travel along stochastic magnetic fields, shielded by the plasma dielectric. A drag on the clump macro-particle is exerted by the shielding, inducing emission into the collective response. The emission in turn damps back on the particle distribution via Landau dampling. The exchange of energy between clumps and particles, as mediated by the collective mode, imposes constraints on transport. For a turbulent spectrum whose mean wavenumber along the equilibrium magnetic field is nonzero, the electron thermal flux is proportional to the ion thermal velocity. Conventional predictions (which account only for collective modes) are larger by the square root of the ion to electron mass ratio. Recent measurements are consistent with the small flux. In fluid plasma,s localized coherent structures can occur as intense vortices.
Two-dimensional electron magnetohydrodynamic turbulence
A novel type of turbulence, which arises in 2D electron magnetohydrodynamics, is studied by numerical simulation. Energy dissipation rates are found to be independent of the dissipation coefficients. The energy spectrum Ek follows the basic Kolmogorov-type predictions, k-5/3 for kde > 1 and k-7/3 for kde e = electron inertial length) and is hence independent of the linear wave properties. Results are compared with other 2D turbulent systems. (author)
Compressible Turbulence: The Cascade and its Locality
Aluie, Hussein
2011-01-01
We prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation co-spectrum, we show that ...
Full text: Excitation of Geodesic Acoustic Modes (GAMs) by both energetic particles (EPs) and drift wave (DW) turbulences taking into account plasma nonuniformities are investigated in this work. The global radial mode structures of EP induced GAM (EGAM) are systematically studied and their properties are found to depend on the nonuniformities of both the GAM continuous spectrum and EP radial profile. For a radially broad EP drive, the eigenmode equation valid for arbitrary EP drift orbit width is derived, and then solved using a Fourier transformation technique. The excited EGAM is shown to strongly couple to the GAM continuous spectrum; resulting in a finite drive threshold in EP density. The cross-scale couplings between micro-, meso- and macro-scales, discussed in this work, are mediated by the EP dynamics and have many interesting similarities with complex behaviors, expected in burning plasmas of fusion interest. The excitation of GAM by DW turbulence accounting for various kinetic dispersiveness and nonuniformities is also investigated, with the paradigm of three-wave resonant parametric decay instability. Considering the scale length of linear DW eigenmode envelope is much smaller than that of particle diamagnetic drift frequency L*, in the linear growth phase, the parametric instability is convective for typical tokamak parameters, when the finite group velocities of GAM and DW sideband are taken into account. This is a case of less practical interest. However, if we look at longer time scales, and finite L* effects are taken into account, the convectively amplified GAM-DW wave-packet pair is reflected at the DW linear turning points, resulting in a quasi-exponentially growing absolute instability. DW turbulence spreading with the excitation of GAM is also investigated, with emphasis on quantitative understanding of the dispersiveness associated with kinetic GAM. (author)
Turbulence: mechanics and structure of anomalous scaling
S. N. Gordienko
2001-01-01
Full Text Available As the finite correlation time of a force driving turbulence is taken into account, a new, dimensionless parameter occurs in the theory of turbulence. This new parameter is responsible for two different mechanisms of formation of anomalous spectra. The first mechanism is related to the change of a governing parameter, which defines the spectrum of turbulent fluctuation. The second mechanism is associated with spontaneous formation of characteristic scales that differ parametrically from the scale of the external force. The last mechanism can explain the intermittent structure of turbulent flows. The appropriate discrete set of the possible characteristic scales and anomalous spectra has been calculated. The results give a new insight into the concept of universality: there is a set of universal power laws, although occurrence in the spectrum segments described by one or another power law from this set depends on the dimensionless parameter mentioned above. It is noted that for the broad class of geophysical flows, the new dimensionless parameter is connected with the so-called degree of turbulence, which guarantees that the smallness of this parameter, as the degree of turbulence is usually small enough. That explains the important role of the Kolmogorov spectrum in geophysical applications.
Phytoplankton's motion in turbulent ocean
Fouxon, Itzhak; Leshansky, Alexander
2015-07-01
We study the influence of turbulence on upward motion of phytoplankton. Interaction with the flow is described by the Pedley-Kessler model considering spherical microorganisms. We find a range of parameters when the upward drift is only weakly perturbed or when turbulence completely randomizes the drift direction. When the perturbation is small, the drift is either determined by the local vorticity or is Gaussian. We find a range of parameters where the phytoplankton interaction with the flow can be described consistently as diffusion of orientation in effective potential. By solving the corresponding Fokker-Planck equation we find exponential steady-state distribution of phytoplankton's propulsion orientation. We further identify the range of parameters where phytoplankton's drift velocity with respect to the flow is determined uniquely by its position. In this case, one can describe phytoplankton's motion by a smooth flow and phytoplankton concentrates on fractal. We find fractal dimensions and demonstrate that phytoplankton forms vertical stripes in space with a nonisotropic pair-correlation function of concentration increased in the vertical direction. The probability density function of the distance between two particles obeys power law with the negative exponent given by the ratio of integrals of the turbulent energy spectrum. We find the regime of strong clustering where the exponent is of order one so that turbulence increases the rate of collisions by a large factor. The predictions hold for Navier-Stokes turbulence and stand for testing.
Phytoplankton's motion in turbulent ocean.
Fouxon, Itzhak; Leshansky, Alexander
2015-07-01
We study the influence of turbulence on upward motion of phytoplankton. Interaction with the flow is described by the Pedley-Kessler model considering spherical microorganisms. We find a range of parameters when the upward drift is only weakly perturbed or when turbulence completely randomizes the drift direction. When the perturbation is small, the drift is either determined by the local vorticity or is Gaussian. We find a range of parameters where the phytoplankton interaction with the flow can be described consistently as diffusion of orientation in effective potential. By solving the corresponding Fokker-Planck equation we find exponential steady-state distribution of phytoplankton's propulsion orientation. We further identify the range of parameters where phytoplankton's drift velocity with respect to the flow is determined uniquely by its position. In this case, one can describe phytoplankton's motion by a smooth flow and phytoplankton concentrates on fractal. We find fractal dimensions and demonstrate that phytoplankton forms vertical stripes in space with a nonisotropic pair-correlation function of concentration increased in the vertical direction. The probability density function of the distance between two particles obeys power law with the negative exponent given by the ratio of integrals of the turbulent energy spectrum. We find the regime of strong clustering where the exponent is of order one so that turbulence increases the rate of collisions by a large factor. The predictions hold for Navier-Stokes turbulence and stand for testing. PMID:26274279
National Oceanic and Atmospheric Administration, Department of Commerce — Forecast turbulence hazards identified by the Graphical Turbulence Guidance algorithm. The Graphical Turbulence Guidance product depicts mid-level and upper-level...
Plasma diagnostics in TFTR using emission of cyclotron radiation at arbitrary frequencies
Emission of cyclotron radiation at arbitrary wave frequency for diagnostic purposes is discussed. It is shown that the radiation spectrum at arbitrary frequencies is more informative than the first few harmonics and it is suited for diagnosis of superthermal electrons without any open-quotes ad hocclose quotes value of the wall reflection coefficient. Thermal radiation from TFTR is investigated and it is shown that the bulk and the tail of the electron momentum distribution during strong neutral beam injection is a Maxwellian with a single temperature in all ranges of electron energies
Magnetohydrodynamic Turbulence
Montgomery, David C.
2004-01-01
Magnetohydrodynamic (MHD) turbulence theory is modeled on neutral fluid (Navier-Stokes) turbulence theory, but with some important differences. There have been essentially no repeatable laboratory MHD experiments wherein the boundary conditions could be controlled or varied and a full set of diagnostics implemented. The equations of MHD are convincingly derivable only in the limit of small ratio of collision mean-free-paths to macroscopic length scales, an inequality that often goes the other way for magnetofluids of interest. Finally, accurate information on the MHD transport coefficients-and thus, the Reynolds-like numbers that order magnetofluid behavior-is largely lacking; indeed, the algebraic expressions used for such ingredients as the viscous stress tensor are often little more than wishful borrowing from fluid mechanics. The one accurate thing that has been done extensively and well is to solve the (strongly nonlinear) MHD equations numerically, usually in the presence of rectangular periodic boundary conditions, and then hope for the best when drawing inferences from the computations for those astrophysical and geophysical MHD systems for which some indisputably turbulent detailed data are available, such as the solar wind or solar prominences. This has led to what is perhaps the first field of physics for which computer simulations are regarded as more central to validating conclusions than is any kind of measurement. Things have evolved in this way due to a mixture of the inevitable and the bureaucratic, but that is the way it is, and those of us who want to work on the subject have to live with it. It is the only game in town, and theories that have promised more-often on the basis of some alleged ``instability''-have turned out to be illusory.
Perturbation Theory for Arbitrary Coupling Strength ?
Mahapatra, B P
2016-01-01
We demonstrate Borel summability for arbitrary coupling strength in a new formulation of perturbation theory (designated here as "Mean Field Perturbation Theory (MFPT)") by applying it to one dimensional anharmonic-interactions, which includes the case of the quartic and sextic anharmonic oscillators(AHO) and the quartic double-well-oscillator (QDWO).It is well known that the perturbation-series is not Borel-summable for the QDWO in the standard formulation of perturbation theory(SFPT). In contrast, MFPT leads to a Borel-summable perturbation series and accurate values for the energy-spectra for arbitrary (physical) value of the coupling strength in each case as stated above. The general nature and the simplicity of the formulation underlying MFPT leads us to conjecture that this scheme may be applicable to arbitrary interactions in quantum theory.
Study of resistive pressure-gradient-driven turbulence
Previous studies have shown the resistive pressure-gradient-driven turbulence (RPGDT) is a likely cause of observed turbulent fluctuations and anomalous transport in magnetically confined plasmas. More recent study of RPGDT found a true saturation criterion and predicted significantly larger pressure diffusivity over simple mixing-length estimate. In this study, we investigate wavenumber spectrum for more detailed characteristics of this driven turbulence and consider an electromagnetic model with electron temperature evolution to study the effect of magnetic fluctuations on thermal transport
Synthetic turbulence methods for leading edge noise predictions
Gea-Aguilera, Fernando; Xin ZHANG; Chen, Xiaoxian; Gill, James R.; Node-Langlois, Thomas
2015-01-01
An advanced digital filter method to generate synthetic turbulence is presented for efficient two- and three-dimensional leading edge noise predictions. The technique, which is based on the Random Particle-Mesh method, produces a turbulent inflow that matches a target isotropic energy spectrum. The discretized equations for the synthetic eddies, and the input parameters needed to recover the desired turbulence statistics, are presented. Moreover, a simple and fast implementatio...
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...
Experiments in turbulent pipe flow
Torbergsen, Lars Even
1998-12-31
This thesis reports experimental results for the mean velocity and turbulence statistics in two straight pipe sections for bulk Reynolds numbers in the range 22000 to 75000. The flow was found consistent with a fully developed state. Detailed turbulence spectra were obtained for low and moderate turbulent Reynolds number. For the pipe centre line location at R{sub {lambda}} = 112, a narrow range in the streamwise power spectrum applied to the -5/3 inertial subrange. However this range was influenced both by turbulence production and viscous dissipation, and therefore did not reflect a true inertial range. The result indicates how the intermediate range between the production and dissipative scales can be misinterpreted as an inertial range for low and moderate R{sub {lambda}}. To examine the universal behaviour of the inertial range, the inertial scaling of the streamwise power spectrum is compared to the inertial scaling of the second order longitudinal velocity structure function, which relate directly by a Fourier transform. Increasing agreement between the Kolmogorov constant C{sub K} and the second order structure function scaling constant C{sub 2} was observed with increasing R{sub {lambda}}. The result indicates that a true inertial range requires several decades of separation between the energy containing and dissipative scales. A method for examining spectral anisotropy is reported and applied to turbulence spectra in fully developed pipe flow. It is found that the spectral redistribution from the streamwise to the two lateral spectra goes primarily to the circumferential component. Experimental results are reported for an axisymmetric contraction of a fully developed pipe flow. 67 refs., 75 figs., 9 tabs.
Mixing in Magnetized Turbulent Medium
Sur, Sharanya; Scannapieco, Evan
2014-01-01
Turbulent motions are essential to the mixing of entrained fluids and are also capable of amplifying weak initial magnetic fields by small-scale dynamo action. Here we perform a systematic study of turbulent mixing in magnetized media, using three-dimensional magnetohydrodynamic simulations that include a scalar concentration field. We focus on how mixing depends on the magnetic Prandtl number, Pm, from 1 to 4 and the Mach number, M}, from 0.3 to 2.4. For all subsonic flows, we find that the velocity power spectrum has a k^-5/3 slope in the early, kinematic phase, but steepens due to magnetic back reactions as the field saturates. The scalar power spectrum, on the other hand, flattens compared to k^-5/3 at late times, consistent with the Obukohov-Corrsin picture of mixing as a cascade process. At higher Mach numbers, the velocity power spectrum also steepens due to the presence of shocks, and the scalar power spectrum again flattens accordingly. Scalar structures are more intermittent than velocity structures...
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.
Spectral measures with arbitrary Hausdorff dimensions
Dai, Xin-Rong; Sun, Qiyu
2014-01-01
In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.
Vacuum Birefringence Caused by Arbitrary Spin Particles
Kruglov, S. I.
2007-01-01
We study the propagation of a linearly polarized laser beam in the external transverse magnetic field taking into consideration the vacuum polarization by arbitrary spin particles. Induced ellipticity of the beam are evaluated using the effective Lagrangian. With the help of the PVLAS experimental data, we obtain bounds on masses of charged higher spin particles contributed to ellipticity.
Kraus representation for arbitrary open qubit system
Tong, D M; Kwek, L C; Oh, C H; Chen, Jing-Ling
2003-01-01
We show that the time evolution of an arbitrary open qubit system can always be described in terms of the Kraus representation irrespective of the presence of initial correlations between the open system and its environment. A general scheme on how to construct the Kraus operators for an open qubit system is proposed, which can be generalized to open higher dimensional quantum systems.
Dual local and non-local cascades in 3D turbulent Beltrami flows
Herbert, E; Daviaud, F; Dubrulle, B.; Nazarenko, S.; A. Naso
2012-01-01
We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both local and non-local case. Comparison with a high Reynolds number turbulent von Karman flow is provided and discussed.
Consequences of Symmetries on the Analysis and Construction of Turbulence Models
Dina Razafindralandy
2006-05-01
Full Text Available Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ..., symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.
Stochastic ion heating by lower hybrid turbulence
The motion of an ion in a spectrum of lower hybrid waves propagating across a constant magnetic field is examined. In particular, numerical simulation is used to determine the extent to which a turbulent spectrum of these electrostatic waves may accelerate thermal ions (T < 1 eV). The significance of stochastic web development in this heating process is also discussed. 20 refs., 31 figs
A theoretical description of inhomogeneous turbulence
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). In this LDRD, we have developed a highly compact and descriptive formalism that allows us to broach the theoretically formidable morass of inhomogeneous turbulence. Our formalism has two novel aspects: (a) an adaptation of helicity basis functions to represent an arbitrary incompressible channel flow and (b) the invocation of a hypothesis of random phase. A result of this compact formalism is that the mathematical description of inhomogeneous turbulence looks much like that of homogeneous turbulence--at the moment, the most rigorously explored terrain in turbulence research. As a result, we can explore the effect of boundaries on such important quantities as the gradients of mean flow, mean pressure, triple-velocity correlations and pressure velocity correlations, all of which vanish under the conventional, but artificial, assumption that the turbulence is statistically spatially uniform. Under suitable conditions, we have predicted that a mean flow gradient can develop even when none is initially present
Introduction to quantum turbulence
Barenghi, Carlo F.; Skrbek, Ladislav; Sreenivasan, Katepalli R.
2014-01-01
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose–Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our ai...
Spinor structure and matter spectrum
Varlamov, V V
2016-01-01
Classification of relativistic wave equations is given on the ground of interlocking representations of the Lorentz group. A system of interlocking representations is associated with a system of eigenvector subspaces of the energy operator. Such a correspondence allows one to define matter spectrum, where the each level of this spectrum presents a some state of elementary particle. An elementary particle is understood as a superposition of state vectors in nonseparable Hilbert space. Classification of indecomposable systems of relativistic wave equations is produced for bosonic and fermionic fields on an equal footing (including Dirac and Maxwell equations), since all these fields are equivalent levels of matter spectrum, which differ from each other by the value of mass and spin. It is shown that a spectrum of the energy operator, corresponding to a given matter level, is non-degenerate for the fields of type $(l,0)\\oplus(0,l)$, where $l$ is a spin value, whereas for arbitrary spin chains we have degenerate ...
Strong Turbulence in Low-beta Plasmas
Tchen, C. M.; Pécseli, Hans; Larsen, Søren Ejling
1980-01-01
An investigation of the spectral structure of turbulence in a plasma confined by a strong homogeneous magnetic field was made by means of a fluid description. The turbulent spectrum is divided into subranges. Mean gradients of velocity and density excite turbulent motions, and govern the production...... subrange. The spectra of velocity and potential fluctuations interact in the coupling subrange, and the energy is transferred along the spectrum in the inertia subrange. Applying the method of cascade decomposition, the spectral laws k-3, k-3, k-2 are obtained for the velocity fluctuations, and k-3, k-5, k......-3/2 for the potential fluctuations in the production, coupling and inertia subranges, respectively. The coefficient of Bohm diffusion is reproduced, and its role in electrostatic coupling is derived. Comparison is made with measured power laws reported in the literature, from Q-devices, hot...
Photon Bubble Turbulence in Cold Atomic Gases
Rodrigues, João D; Ferreira, António V; Terças, Hugo; Kaiser, Robin; Mendonça, José T
2016-01-01
Turbulent radiation flow is ubiquitous in many physical systems where light-matter interaction becomes relevant. Photon bubbling, in particular, has been identified as the main source of turbulent radiation transport in many astrophysical objects, such as stars and accretion disks. This mechanism takes place when radiation trapping in optically dense media becomes unstable, leading to the energy dissipation from the larger to the smaller bubbles. Here, we report on the observation of photon bubble turbulence in cold atomic gases in the presence of multiple scattering of light. The instability is theoretically explained by a fluid description for the atom density coupled to a diffusive transport equation for the photons, which is known to be accurate in the multiple scattering regime investigated here. We determine the power spectrum of the atom density fluctuations, which displays an unusual $\\sim k^{-4}$ scaling, and entails a complex underlying turbulent dynamics resulting from the formation of dynamical bu...
D'Angelo, N.; Pécseli, Hans; Petersen, P. I.
1974-01-01
Spectral measurements are reported of plasma turbulence in the Cs plasma of a Q device, modified to a magnetic cusp geometry. The excitation mechanism for the fluctuations appears to be the centrifugal instability discussed by Chen. A transition from an f−5 to an f−3 power spectrum is observed as...
Signal modeling of turbulence-distorted imagery
Young, S. Susan; Driggers, Ronald G.; Krapels, Keith; Espinola, Richard L.; Reynolds, Joseph P.; Cha, Jae
2009-05-01
Understanding turbulence effects on wave propagation and imaging systems has been an active research area for more than 50 years. Conventional atmospheric optics methods use statistical models to analyze image degradation effects that are caused by turbulence. In this paper, we intend to understand atmospheric turbulence effects using a deterministic signal processing and imaging theory point of view and modeling. The model simulates the formed imagery by a lens by tracing the optical rays from the target through a band of turbulence. We examine the nature of the turbulence-degraded image, and identify its characteristics as the parameters of the band of turbulence, e.g., its width, angle, and index of refraction, are varied. Image degradation effects due to turbulence, such as image blurring and image dancing, are revealed by this signal modeling. We show that in fact these phenomena can be related not only to phase errors in the frequency domain of the image but also a 2D modulation effect in the image spectrum. Results with simulated and realistic data are provided.
Non-intrinsic ambipolar diffusion in turbulence theory
Ambipolar flow in a turbulent plasma is investigated by combining a WKB treatment of the waves with a turbulent collision operator resulting from either quasi-linear theory or certain renormalized turbulence theories. If the wave momentum has a flow from outgoing waves, then particle diffusion is not intrinsically ambipolar, and the time variation of the electric-potential profile is determined by the turbulent spectrum. However, in most cases of practical interest, as in the drift-wave problem, this effect is small; and, in steady state, equal rates of stochastic diffusion are predicted for electrons and ions
The $Re$-number dependence of the longitudinal dispersion in a turbulent channel flow
Hawkins, Christopher; Krotkiewski, Marcin; Jamtveit, Bjørn
2016-01-01
In Taylor's theory, the longitudinal dispersion in turbulent pipe flows approaches, on long timescales, a diffusive behavior with a constant diffusivity $K_L$, that depends \\emph{empirically} on the Reynolds number $Re$. We show that the dependence on $Re$ can be determined from the turbulent energy spectrum. By using the intimate connection between the friction factor and longitudinal dispersion in wall-bounded turbulence, we predict different asymptotic scaling laws of $K_L(Re)$ depending on the different turbulent cascades in two-dimensional turbulence. We also explore numerically the $K_L(Re)$ dependence in turbulent channel flows with smooth and rough walls using a lattice Boltzmann method.
Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Huang, Qingqing
2016-08-01
Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics. PMID:27505641
Quantum Fidelity for Arbitrary Gaussian States
Banchi, Leonardo; Braunstein, Samuel L.; Pirandola, Stefano
2015-12-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information, and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Quantum fidelity for arbitrary Gaussian states
Banchi, Leonardo; Pirandola, Stefano
2015-01-01
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mode or two-mode analyses, and paves the way to solve general problems in quantum metrology and quantum hypothesis testing with arbitrary multimode Gaussian resources.
Potential flow about arbitrary biplane wing sections
Garrick, I E
1937-01-01
A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.
On Arbitrary Phases in Quantum Amplitude Amplification
Hoyer, P
2000-01-01
We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\\tan(\\phi/2)=\\tan(\\phi/2)(1-2a)$, where $\\phi$ and $\\phi$ are the phases used and where $a$ is the success probability of the given algorithm. Thus the choice of phases depends nontrivially and nonlinearly on the success probability. Utilizing this condition, we give methods for constructing quantum algorithms that succeed with certainty and for implementing arbitrary rotations. We also conclude that phase errors of order up to $\\frac{1}{\\sqrt{a}}$ can be tolerated in amplitude amplification.
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...
Strong field ionization in arbitrary laser polarizations
Protopapas, M.; Lappas, D. G.; Knight, P. L.
1997-01-01
We present a new method for investigating the nonperturbative quantum mechanical interaction of light with atoms in two dimensions, without a basis expansion. This enables us to investigate intense laser-atom interactions with light of arbitrary polarization without approximation, within the model restrictions. Results are presented for the dependence of ionization and high harmonic generation on ellipticity seen in recent experiments. Strong evidence of stabilization in circular polarization...
Arbitrary orbital angular momentum of photons
Pan, Yue; Gao, Xu-Zhen; Ren, Zhi-Cheng; Wang, Xi-Lin; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2015-01-01
Orbital angular momentum (OAM) of photons, as a new fundamental degree of freedom, has excited a great diversity of interest, because of a variety of emerging applications. Arbitrarily tunable OAM has gained much attention, but its creation remains still a tremendous challenge. We demonstrate the realization of well-controlled arbitrary OAM in both theory and experiment. We present the concept of general OAM, which extends the OAM carried by the scalar vortex field to the OAM carried by the a...
Acoustic Casimir Pressure for Arbitrary Media
Barcenas, J.; Reyes, L.; Esquivel-Sirvent, R.
2004-01-01
In this paper we derive a general expression for the acoustic Casimir pressure between two parallel slabs made of arbitrary materials and whose acoustic reflection coefficients are not equal. The formalism is based on the calculation of the local density of modes using a Green's function approach. The results for the Casimir acoustic pressure are generalized to a sphere/plate configuration using the proximity theorem
Large eddy simulation of stably stratified turbulence
无
2010-01-01
Stable stratification turbulence, as a common phenomenon in atmospheric and oceanic flows, is an important mechanism for numerical prediction of such flows. In this paper the large eddy simulation is utilized for investigating stable stratification turbulence numerically. The paper is expected to provide correct statistical results in agreement with those measured in the atmosphere or ocean. The fully developed turbulence is obtained in the stable stratification fluid by large eddy simulation with different initial velocity field and characteristic parameters, i.e. Reynolds number Re and Froude number Fr. The evolution of turbulent kinetic energy, characteristic length scales and parameters is analyzed for investigating the development of turbulence in stable stratification fluid. The three-dimensional energy spectra, horizontal and vertical energy spectrum, are compared between numerical simulation and real observation in the atmosphere and ocean in order to test the reliability of the numerical simulation. The results of numerical cases show that the large eddy simulation is capable of predicting the properties of stable stratification turbulence in consistence with real measurements at less computational cost. It has been found in this paper that the turbulence can be developed under different initial velocity conditions and the internal wave energy is dominant in the developed stable stratification turbulence. It is also found that the characteristic parameters must satisfy certain conditions in order to have correct statistical property of stable stratification turbulence in the atmosphere and ocean. The Reynolds number and Froude number are unnecessarily equal to those in atmosphere or ocean, but the Reynolds number must be large enough, say, greater than 10 2 , and Froude number must be less than 0.1. The most important parameter is ReFr 2 which must be greater than 10.
Probing Turbulence in the Coma Galaxy Cluster
Schücker, P; Miniati, F; Böhringer, H; Briel, U G
2004-01-01
Spatially-resolved gas pressure maps of the Coma galaxy cluster are obtained from a mosaic of XMM-Newton observations in the scale range between a resolution of 20 kpc and an extent of 2.8 Mpc. A Fourier analysis of the data reveals the presence of a scale-invariant pressure fluctuation spectrum in the range between 40 and 90 kpc and is found to be well described by a projected Kolmogorov/Oboukhov-type turbulence spectrum. Deprojection and integration of the spectrum yields the lower limit of $\\sim 10$ percent of the total intracluster medium pressure in turbulent form. The results also provide observational constraints on the viscosity of the gas.
Probing turbulence in the Coma galaxy cluster
Schuecker, P.; Finoguenov, A.; Miniati, F.; Böhringer, H.; Briel, U. G.
2004-11-01
Spatially-resolved gas pressure maps of the Coma galaxy cluster are obtained from a mosaic of XMM-Newton observations in the scale range between a resolution of 20 kpc and an extent of 2.8 Mpc. A Fourier analysis of the data reveals the presence of a scale-invariant pressure fluctuation spectrum in the range between 40 and 90 kpc and is found to be well described by a projected Kolmogorov/Oboukhov-type turbulence spectrum. Deprojection and integration of the spectrum yields the lower limit of ˜ 10 percent of the total intracluster medium pressure in turbulent form. The results also provide observational constraints on the viscosity of the gas. Based on observations with XMM-Newton, an ESA Science Mission with instruments and contributions directly funded by ESA Member States and the USA (NASA).
Multiboson Correlation Interferometry with arbitrary single-photon pure states
Tamma, Vincenzo; Laibacher, Simon
2014-01-01
We provide a compact full description of multiboson correlation measurements of arbitrary order N in passive linear interferometers with arbitrary input single-photon pure states. This allows us to physically analyze the novel problem of multiboson correlation sampling at the output of random linear interferometers. Our results also describe general multiboson correlation landscapes for an arbitrary number of input single photons and arbitrary interferometers. In particular, we use two differ...
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...
Lessons from hydrodynamic turbulence
Turbulent flows, with their irregular behavior, confound any single attempts to understand them. But physicists have succeeded in identifying some universal properties of turbulence and relating them to broken symmetries. (author)
Scintillation index of optical wave propagating in turbulent atmosphere
Rao Rui-Zhong
2009-01-01
A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluc- tuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index axe evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Frcsnel size.
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
Statistical theory of turbulent incompressible multimaterial flow
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 κ-ε 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 κ, and the rate of fluctuational energy dissipation ε, for each material. Hence a set of κ and ε equations must be solved, together with mean mass and momentum conservation equations, for each material. Both κ 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 pipe
Power spectra of outflow-driven turbulence
Moraghan, Anthony; Yoon, Suk-Jin
2015-01-01
We investigate the power spectra of outflow-driven turbulence through high-resolution three-dimensional isothermal numerical simulations where the turbulence is driven locally in real-space by a simple spherical outflow model. The resulting turbulent flow saturates at an average Mach number of ~2.5 and is analysed through density and velocity power spectra, including an investigation of the evolution of the solenoidal and compressional components. We obtain a shallow density power spectrum with a slope of ~-1.2 attributed to the presence of a network of localised dense filamentary structures formed by strong shock interactions. The total velocity power spectrum slope is found to be ~-2.0, representative of Burgers shock dominated turbulence model. The density weighted velocity power spectrum slope is measured as ~-1.6, slightly less than the expected Kolmogorov scaling value (slope of -5/3) found in previous works. The discrepancy may be caused by the nature of our real space driving model and we suggest ther...
Distinguishing ichthyogenic turbulence from geophysical turbulence
Pujiana, Kandaga; Moum, James N.; Smyth, William D.; Warner, Sally J.
2015-05-01
Measurements of currents and turbulence beneath a geostationary ship in the equatorial Indian Ocean during a period of weak surface forcing revealed unexpectedly strong turbulence beneath the surface mixed layer. Coincident with the turbulence was a marked reduction of the current speeds registered by shipboard Doppler current profilers, and an increase in their variability. At a mooring 1 km away, measurements of turbulence and currents showed no such anomalies. Correlation with the shipboard echo sounder measurements indicate that these nighttime anomalies were associated with fish aggregations beneath the ship. The fish created turbulence by swimming against the strong zonal current in order to remain beneath the ship, and their presence affected the Doppler speed measurements. The principal characteristics of the resultant ichthyogenic turbulence are (i) low wave number roll-off of shear spectra in the inertial subrange relative to geophysical turbulence, (ii) Thorpe overturning scales that are small compared with the Ozmidov scale, and (iii) low mixing efficiency. These factors extend previous findings by Gregg and Horne (2009) to a very different biophysical regime and support the general conclusion that the biological contribution to mixing the ocean via turbulence is negligible.
Brand, Arno J.; Peinke, Joachim; Mann, Jakob
2011-01-01
The nature of turbulent flow towards, near and behind a wind turbine, the effect of turbulence on the electricity production and the mechanical loading of individual and clustered wind turbines, and some future issues are discussed.......The nature of turbulent flow towards, near and behind a wind turbine, the effect of turbulence on the electricity production and the mechanical loading of individual and clustered wind turbines, and some future issues are discussed....
Gupta, Kumar S.; Sen, Siddhartha
2009-01-01
We demonstrate the possibility of a turbulent flow of electrons in graphene in the hydrodynamic region, by calculating the corresponding turbulent probability density function. This is used to calculate the contribution of the turbulent flow to the conductivity within a quantum Boltzmann approach. The dependence of the conductivity on the system parameters arising from the turbulent flow is very different from that due to scattering.
Statistical features of freely decaying two-dimensional hydrodynamic turbulence
Kudryavtsev, A N; Sereshchenko, E V
2013-01-01
Statistical characteristics of freely decaying two-dimensional hydrodynamic turbulence at high Reynolds numbers are numerically studied. In particular, numerical experiments (with resolution up to $8192\\times 8192$) provide a Kraichnan-type turbulence spectrum $E_k\\sim k^{-3}$. By means of spatial filtration, it is found that the main contribution to the spectrum comes from the sharp vorticity gradients in the form of quasi-shocks. Such quasi-singularities are responsible for a strong angular dependence of the spectrum owing to well-localized (in terms of the angle) jets with minor and/or large overlapping. In each jet, the spectrum decreases as $k^{-3}$. The behavior of the third-order structure function accurately agrees with Kraichnan direct cascade concept corresponding to a constant enstrophy flux. It is shown that the power law exponents $\\zeta_n$ for higher structure functions grow more slowly than the linear dependence of $n$, which testifies to turbulence intermittency.
Peterson, M A
1997-01-01
The possibility is considered that turbulence is described by differential equations for which uniqueness fails maximally, at least in some limit. The inviscid Burgers equation, in the context of Onsager's suggestion that turbulence should be described by a negative absolute temperature, is such a limit. In this picture, the onset of turbulence coincides with the proliferation of singularities which characterizes the failure of uniqueness.
Distributed chaos and inertial ranges in turbulence
Bershadskii, A
2016-01-01
It is shown that appearance of inertial range of scales, adjacent to distributed chaos range, results in adiabatic invariance of an energy correlation integral for isotropic homogeneous turbulence and for buoyancy driven turbulence (with stable or unstable stratification, including Rayleigh-Taylor mixing zone). Power spectrum of velocity field for distributed chaos dominated by this adiabatic invariant has a stretched exponential form $\\propto \\exp(-k/k_{\\beta})^{3/5}$. Results of recent direct numerical simulations have been used in order to support these conclusions.
Gaussian quadrature formulae for arbitrary positive measures.
Fernandes, Andrew D; Atchley, William R
2006-01-01
We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student's t, inverse-gamma, beta, and Fisher's F) we present exact formulae for computing the respective quadrature scheme. PMID:19455218
Gaussian Quadrature Formulae for Arbitrary Positive Measures
William R. Atchley
2006-01-01
Full Text Available We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known density measures (the normal, gamma, log-normal, Student’s t, inversegamma, beta, and Fisher’s F we present exact formulae for computing the respective quadrature scheme.
Sampling to estimate arbitrary subset sums
Duffield, Nick; Lund, Carsten; Thorup, Mikkel
2005-01-01
Starting with a set of weighted items, we want to create a generic sample of a certain size that we can later use to estimate the total weight of arbitrary subsets. For this purpose, we propose priority sampling which tested on Internet data performed better than previous methods by orders of magnitude. Priority sampling is simple to define and implement: we consider a steam of items i=0,...,n-1 with weights w_i. For each item i, we generate a random number r_i in (0,1) and create a priority ...
Circuits with arbitrary gates for random operators
Jukna, S.; Schnitger, G.
2010-01-01
We consider boolean circuits computing n-operators f:{0,1}^n --> {0,1}^n. As gates we allow arbitrary boolean functions; neither fanin nor fanout of gates is restricted. An operator is linear if it computes n linear forms, that is, computes a matrix-vector product y=Ax over GF(2). We prove the existence of n-operators requiring about n^2 wires in any circuit, and linear n-operators requiring about n^2/\\log n wires in depth-2 circuits, if either all output gates or all gates on the middle laye...
Path integrals for arbitrary canonical transformations
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author)
The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach
The motion of a simple pendulum of arbitrary amplitude is usually treated by approximate methods. By using generalized hypergeometric functions, it is however possible to solve the problem exactly. In this paper, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. A new and exact expression for the time of swinging of a simple pendulum from the vertical position to an arbitrary angular position θ is given by equation (3.10). The time period of such a pendulum is also exactly expressible in terms of hypergeometric functions. The exact expressions thus obtained are used to plot the graphs that compare the exact time period T(θ0) with the time period T(0) (based on simple harmonic approximation). We also compare the relative difference between T(0) and T(θ0) found from the exact equation of motion with the usual perturbation theory estimate. The treatment is intended for graduate students, who have acquired some familiarity with the hypergeometric functions. This approach may also be profitably used by specialists who encounter during their investigations nonlinear differential equations similar in form to the pendulum equation. Such nonlinear differential equations could arise in diverse fields, such as acoustic vibrations, oscillations in small molecules, turbulence and electronic filters, among others.
Radio Halo Formation through Magneto-turbulent Particle Acceleration in Clusters of Galaxies
Ohno, Hiroshi; Takizawa, Motokazu; Shibata, Shinpei
2002-01-01
We developed a magneto-turbulent model for the cosmic ray (CR) electrons seen in the radio halo clusters of galaxies. Steady state momentum distribution functions of the CR electrons are calculated for given spectra of the turbulent Alfven waves. The radio spectrum produced by the obtained CR electron distribution is compared to the observed radio spectrum of the Coma radio halo. We find that the observed radio spectrum of the Coma cluster is well reproduced when the spectral index of the tur...
Turbulence in the Intergalactic Medium
Evoli, Carmelo
2011-01-01
We study supernova-driven galactic outflows as a mechanism for injecting turbulence in the intergalactic medium (IGM) far from galaxies. To this aim we follow the evolution of a 10^13 Msun galaxy along its merger tree, with carefully calibrated prescriptions for star formation and wind efficiencies. At z~3 the majority of the bubbles around galaxies are old (ages >1Gyr), i.e. they contain metals expelled by their progenitors at earlier times; their filling factor increases with time reaching about 10% at z<2. The energy deposited by these expanding shocks in the IGM is predominantly in kinetic form (mean energy density of 1 \\mu eV cm^-3, about 2-3 x the thermal one), which is rapidly converted in disordered motions by instabilities, finally resulting in a fully developed turbulent spectrum whose evolution is followed through a spectral transfer function approach. The derived mean IGM turbulent Doppler parameter, b_t, peaks at z~1 at about 1.5 km/s with maximum b_t = 25 km/s. The shape of the b_t distributi...
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...
PROPAGATION OF ADAPTIVELY CORRECTED LASER BEAMS THROUGH A TURBULENT ATMOSPHERE
Bissonnette, L
1980-01-01
This paper describes a mathematical model for solving the propagation problem of laser beams travelling in atmospheric turbulence and corrected by adaptive optics. The modeling of the adaptive optics is mathematically simple but sufficiently general to encompass the majority of the existing systems. The method allows the prediction of the average irradiance and the irradiance variance beam profiles for arbitrary scintillation levels. Typical solutions are presented for 3.8 and 10.6 µm laser b...
Universal statistics of density of inertial particles sedimenting in turbulence
Fouxon, Itzhak; Park, Yongnam; Harduf, Roei; Lee, Changhoon
2014-01-01
We solve the problem of spatial distribution of inertial particles that sediment in Navier-Stokes turbulence with small ratio $Fr$ of acceleration of fluid particles to acceleration of gravity $g$. The particles are driven by linear drag and have arbitrary inertia. We demonstrate that independently of the particles' size or density the particles distribute over fractal set with log-normal statistics determined completely by the Kaplan-Yorke dimension $D_{KY}$. When inertia is not small $D_{KY...
Mitra, Dhrubaditya; Rogachevskii, Igor
2016-01-01
We show, by direct numerical simulations, that heavy inertial particles (with Stokes number ${\\rm St}$) in inhomogeneously forced statistically stationary turbulent flows cluster at the minima of turbulent kinetic energy. We further show that two turbulent transport processes, turbophoresis and turbulent diffusion together determine the spatial distribution of the particles. The ratio of the corresponding transport coefficient -- the turbulent Soret coefficient -- increases with ${\\rm St}$ for small ${\\rm St}$, reaches a maxima for ${\\rm St}\\approx 10$ and decreases as $\\sim {\\rm St}^{-0.33}$ for large ${\\rm St}$.
Introduction to quantum turbulence.
Barenghi, Carlo F; Skrbek, Ladislav; Sreenivasan, Katepalli R
2014-03-25
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics. PMID:24704870
Klumperink, Eric A.M.; Shrestha, Rameswor; Mensink, Eisse; Arkesteijn, Vincent J.; Nauta, Bram
2007-01-01
Dynamic access of unused spectrum via a cognitive radio asks for flexible radio circuits that can work at an arbitrary radio frequency. This article reviews techniques to realize radios without resorting to frequency selective dedicated filters. In particular, a recently proposed polyphase multipath technique canceling harmonics and sidebands is discussed. Using this technique, a wideband and flexible power upconverter with a clean output spectrum has been realized on a CMOS chip, aiming at f...
Multidimensional Potential Burgers Turbulence
Boritchev, Alexandre
2016-03-01
We consider the multidimensional generalised stochastic Burgers equation in the space-periodic setting: partial {u}/partial t+(nabla f({u}) \\cdot nabla) {u}-ν Δ {u}= nabla η, quad t ≥ 0, {x} in{T}^d=({R}/ {Z})^d, under the assumption that u is a gradient. Here f is strongly convex and satisfies a growth condition, ν is small and positive, while η is a random forcing term, smooth in space and white in time. For solutions u of this equation, we study Sobolev norms of u averaged in time and in ensemble: each of these norms behaves as a given negative power of ν. These results yield sharp upper and lower bounds for natural analogues of quantities characterising the hydrodynamical turbulence, namely the averages of the increments and of the energy spectrum. These quantities behave as a power of the norm of the relevant parameter, which is respectively the separation ℓ in the physical space and the wavenumber k in the Fourier space. Our bounds do not depend on the initial condition and hold uniformly in {ν}. We generalise the results obtained for the one-dimensional case in [10], confirming the physical predictions in [4, 30]. Note that the form of the estimates does not depend on the dimension: the powers of {ν, |{{k}}|, ℓ} are the same in the one- and the multi-dimensional setting.
Xu, G. S.; Wan, B. N.; Wang, H. Q.;
2016-01-01
number spectrum of turbulence, as evidenced here, for the first time, by the direct observation of a turbulence radial wave number spectral shift and turbulence structure tilting prior to the L-H transition at tokamak edge by direct probing. This new mechanism does not require a pretransition overshoot...
Avila, Marc; Roland, Nicolas; Hof, Bjoern
2013-01-01
Turbulence is ubiquitous in nature and although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. The nonlinear nature and the large number of spatial and temporal degrees of freedom turn this into one of the most challenging problems in mathematics and the physical sciences alike. We here report the discovery of unstable localised solutions for pipe flow that share key spatial characteristics of turbulence in the intermittent regime. While their temporal dynamics are very simple, much of the spatial complexity found in low Reynolds number turbulence is already encoded in them. We furthermore demonstrate how turbulent transients arise from one such solution branch. Our observations shed light on the origin of turbulence and link the localised structures commonly observed in turbulent flows to invariant solutions of the Navier-Stokes equations.
New trends in turbulence; Turbulence: nouveaux aspects
Lesieur, M. [Institut National Polytechnique, LEGI/INPG, Institut de Mecanique, UMR 101, 38 - Grenoble (France); Yaglom, A. [Institut of Atmospheric Physics, Russian Academy of Sciences, Moscow (Russian Federation)]|[MIT, Dept. of Aeronautics and Astronautics, Cambridge, MA (United States); David, F. [CEA Saclay, SPhT, 91 - Gif-sur-Yvette (France)
2001-07-01
According to a Russian scientist, the flow of fluids actually met both in nature and engineering practice are turbulent in the overwhelmingly majority of cases. This document that reviews all the progress made recently in the understanding of turbulence, is made up of 10 courses. Course 1 ''a century of turbulence'' deals with the linear and non-linear points of views. In course 2 ''measures of anisotropy and the universal properties of turbulence'' the author gives a very complete account of fully developed turbulence experimental data both in the laboratory and in the atmosphere. Course 3 ''large-eddy simulations of turbulence (LES)'', LES are powerful tools to simulate the coherent vortices formation and evolution in a deterministic way. In Course 4 ''statistical turbulence modelling for the computation of physically complex flows'' the author describes methods used for predicting statistical industrial flows, where the geometry is right now too complex to allow the use of LES. In course 5 ''computational aero-acoustics'' an informative review of computational aero-acoustics with many applications to aircraft noise, is made. In course 6 ''the topology of turbulence'' the author presents the basis of topological fluid dynamics and stresses the importance of helicity in neutral and in magnetohydrodynamics (MHD) flows. In course 7 ''burgulence'' the authors deal with finite-time singularities, but mostly on the basis of Burger equations in one or several dimensions with the formation of multiple shocks. In course 8 ''2-dimensional turbulence'' the author presents numerous examples of 2D turbulence in the laboratory (rotating or MHD flows, plasmas), in the ocean and in the planetary atmosphere. Course 9 ''analysing and computing turbulent flows using wavelets'' is a useful presentation of
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. PMID:24329368
Gauthier, Serge; Keane, Christopher J.; Niemela, Joseph J.; Abarzhi, Snezhana I.
2013-07-01
companion paper Rooker et al provide a very interesting study on the generation and detection of 'whistler waves' induced space plasma turbulence at Gakona (Alaska). Physics of atmosphere. Five papers are devoted to the physics of atmosphere. Byalko presents the first experimental observation of a new hydrodynamic phenomenon, the underwater tornado. Herring and Kimura provide a review on recent results on homogeneous stably stratified turbulence. Pouquet et al use a high-resolution direct numerical simulation of rotating helical turbulence to obtain new numerical results on the inverse energy cascade in rotating flows. Tailleux discusses energy conversion and dissipation in depth in mixing flows. Zagumennyi and Chashechkin study the structure of convective flows driven by density variations in a stratified fluid by means of experiments and numerical simulations. Geophysics and Earth science. Three papers are dedicated to geophysics and Earth science. Jinadasa et al investigate small-scale and lateral intermittency of oceanic microstructure in the pycnocline. Shrira and Townsend review on a plausible mechanism of deep-ocean mixing caused by near-inertial waves in the abyssal ocean. Using numerical simulations, Imazio and Mininni study how helicity affects the spectrum of a passive scalar in rotating turbulent flows. Combustion. Two papers deal with flows with chemical reactions. Meshram used the Lewis-Kraichnan space-time version of Hopf's functional formalism to investigate turbulence with chemical reaction. Watanabe et al carry out experiments on a turbulent plane liquid jet with a second-order chemical reaction. Theoretical aspects of non-equilibrium dynamics. Six papers are devoted to fundamental aspects of non-equilibrium dynamics. Chen et al present state-of-the-art work on exact and direct derivation of macroscopic theoretical description for a flow at arbitrary Knudsen number from the Boltzmann-Bhatnagar-Gross-Krook kinetic theory with constant relaxation time
Rank-Ordered Multifractal Analysis of Probability Distributions in Fluid Turbulence
Wu, Cheng-Chin; Chang, Tien
2015-11-01
Rank-Ordered Multifractal Analysis (ROMA) was introduced by Chang and Wu (2008) to describe the multifractal characteristic of intermittent events. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has successfully been applied to MHD turbulence simulations and turbulence data observed in various space plasmas. In this paper, the technique is applied to the probability distributions in the inertial range of the turbulent fluid flow, as given in the vast Johns Hopkins University (JHU) turbulence database. In addition, a refined method of finding the continuous ROMA spectrum and the scaled probability distribution function (PDF) simultaneously is introduced.
Spin filter for arbitrary spins by substrate engineering
Pal, Biplab; Römer, Rudolf A.; Chakrabarti, Arunava
2016-08-01
We design spin filters for particles with potentially arbitrary spin S≤ft(=1/2,1,3/2,\\ldots \\right) using a one-dimensional periodic chain of magnetic atoms as a quantum device. Describing the system within a tight-binding formalism we present an analytical method to unravel the analogy between a one-dimensional magnetic chain and a multi-strand ladder network. This analogy is crucial, and is subsequently exploited to engineer gaps in the energy spectrum by an appropriate choice of the magnetic substrate. We obtain an exact correlation between the magnitude of the spin of the incoming beam of particles and the magnetic moment of the substrate atoms in the chain desired for opening up of a spectral gap. Results of spin polarized transport, calculated within a transfer matrix formalism, are presented for particles having half-integer as well as higher spin states. We find that the chain can be made to act as a quantum device which opens a transmission window only for selected spin components over certain ranges of the Fermi energy, blocking them in the remaining part of the spectrum. The results appear to be robust even when the choice of the substrate atoms deviates substantially from the ideal situation, as verified by extending the ideas to the case of a ‘spin spiral’. Interestingly, the spin spiral geometry, apart from exhibiting the filtering effect, is also seen to act as a device flipping spins—an effect that can be monitored by an interplay of the system size and the period of the spiral. Our scheme is applicable to ultracold quantum gases, and might inspire future experiments in this direction.
Buoyancy driven turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, laboratory experiments and atmospheric measurements, that buoyancy driven turbulence exhibits a broad diversity of the types of distributed chaos with its stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$. The distributed chaos with $\\beta = 1/3$ (determined by the helicity correlation integral) is the most common feature of the stably stratified turbulence (due to the strong helical waves presence). These waves mostly dominate spectral properties of the vertical component of velocity field, while the horizontal component is dominated by the diffusive processes both for the weak and strong stable stratification ($\\beta =2/3$). For the last case influence of the low boundary can overcome the wave effects and result in $\\beta =1/2$ for the vertical component of the velocity field (the spontaneous breaking of the space translational symmetry - homogeneity). For the unstably stratified turbulence in the Rayleigh-Taylor mixing zone the di...
Zonal Flows and Turbulence in Fluids and Plasmas
Parker, Jeffrey B
2015-01-01
In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal flows. Starting from the Hasegawa--Mima equation, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking `zonostrophic instability'. Zonostrophic instability can be understood in a very general way as the instability of some turbulent background spectrum to a zonally symmetric coherent mode. As a special case, the background spectrum can consist of only a single mode. We find that in this case the dispersion relation of zonostrophic instability from the CE2 formalism reduces exactly to that of the 4-mode truncation of generalized modulational instability. We then show that zonal flow...
Lidar sounding of the optical parameter of atmospheric turbulence
Gurvich, A. S.; Fortus, M. I.
2016-03-01
The operation of a lidar intended for clear air turbulence (CAT) positioning on the basis of the backscatter enhancement (BSE) effect is analyzed using a turbulence model with a power-law spectrum. Systematic distortions occurring due to a need to regularize the lidar positioning problem solution are estimated. It is shown that the effect of molecular viscosity of air on the positioning result can be neglected if the wave parameter, which characterizes the diffraction manifestation, is higher than 3. This corresponds to sounding ranges of more than 1 km for optical or UV lidars. The analysis results show that the BSE lidar positioning accuracy weakly depends on the exponent in the turbulence spectrum in regions of severe turbulence. The results can justify a physical experiment for the design of an aircraft system for the lidar detection of CAT regions ahead of the flight course.
Triad interactions in multi-scale ITG/TEM/ETG turbulence
Maeyama, Shinya; Watanabe, Tomohiko; Idomura, Yasuhiro; Nakata, Motoki; Ishizawa, Akihiro; Nunami, Masanori
2015-11-01
Most of turbulent transport studies assume scale separation between electron- and ion-scale turbulence. However, latest massively parallel simulations based on gyrokinetics reveal that multi-scale interactions between electron- and ion-scale turbulence can influence turbulent transport [S. Maeyama, Phys. Rev. Lett. 114, 255002 (2015)]. The physical mechanism is investigated by applying triad transfer analysis. It is revealed that short-wave-length ITG turbulent eddies stabilize electron-scale streamers. Additionally, it is found that electron-scale turbulence has a damping effect on zonal flows. As a result, turbulent transport spectrum obtained from the multi-scale turbulence simulation differs from the sum of ones obtained from single-scale simulations. We will discuss gyrokinetic triad transfer analysis and the applicability of its fluid approximation, and explain the physical mechanism of multi-scale interactions by means of triad transfer analysis.
Discrete Equilibrium Sampling with Arbitrary Nonequilibrium Processes
Hamze, Firas
2015-01-01
We present a novel framework for performing statistical sampling, expectation estimation, and partition function approximation using \\emph{arbitrary} heuristic stochastic processes defined over discrete state spaces. Using a highly parallel construction we call the \\emph{sequential constraining process}, we are able to simultaneously generate states with the heuristic process and accurately estimate their probabilities, even when they are far too small to be realistically inferred by direct counting. After showing that both theoretically correct importance sampling and Markov chain Monte Carlo are possible using the sequential constraining process, we integrate it into a methodology called \\emph{state space sampling}, extending the ideas of state space search from computer science to the sampling context. The methodology comprises a dynamic data structure that constructs a robust Bayesian model of the statistics generated by the heuristic process subject to an accuracy constraint, the posterior Kullback-Leibl...
ABJM Wilson loops in arbitrary representations
Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Honda, Masazumi [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.
ABJM Wilson loops in arbitrary representations
We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.
Metamaterial Electromagnetic Superabsorber with Arbitrary Geometries
Jingjing Yang
2010-06-01
Full Text Available The electromagnetic superabsorber that has larger absorption cross section than its real size may be a novel photothermal device with improved solar energy conversion rates. Based on a transformation optical approach, the material parameters for a two-dimensional (2D metamaterial-assisted electromagnetic superabsorber with arbitrary geometries are derived and validated by numerical simulation. We find that for the given geometry size, the absorption cross section of the superabsorber using nonlinear transformation is larger than that using linear transformation. These transformations can also be specialized to the designing the N-sided regular polygonal superabsorber just by changing the contour equation. All theoretical and numerical results validate the material parameters for the 2D electromagnetic superabsorber we have developed.
ABJM Wilson Loops in Arbitrary Representations
Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi
2013-01-01
We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.
Toward the Theory of Turbulence in Magnetized Plasmas
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 kllel)). 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
Superfluid (quantum) turbulence and distributed chaos
Bershadskii, A
2016-01-01
Properties of distributed chaos in superfluid (quantum) turbulence have been studied using the data of recent direct numerical simulations (HVBK two-fluid model for He II, and a moving grid in the frames of Gross-Pitaevskii model of the Bose-Einstein condensates at low temperatures). It is found that for the viscous (normal) component of the velocity field in He II the viscosity dominates the distributed chaos with the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ and $\\beta = 2/3$. For the superfluid component the distributed chaos is dominated by the vorticity correlation integral with $\\beta =1/2$ (the soft spontaneous breaking of the space translational symmetry - homogeneity). For very low temperature the distributed chaos is tuned to the large-scale coherent motions: the viscous (normal) component is tuned to the fundamental mode, whereas the superfluid component is subharmonically tuned. For the Gross-Pitaevskii superfluid turbulence incompressible part of the energy spectrum (containing ...
Compressible turbulent mixing: Effects of Schmidt number
Ni, Qionglin
2015-01-01
We investigated the effects of Schmidt number on passive scalar transport in forced compressible turbulence. In the inertial-convective range the scalar spectrum followed the k^{-5/3} power law. For Sc >> 1, there appeared a k^{-1} power law in the viscous-convective range, while for Sc > 1, the scalar field rolled up and got mixed sufficiently. However, for Sc > 1 and Sc > 1 and Sc << 1 flows decayed faster than the theoretical prediction of k^{-2/3} for incompressible flows. Finally, the comparison with incompressible results showed that the scalar in compressible turbulence with Sc=1 lacked a conspicuous bump structure in its spectrum, but was more intermittent in the dissipative range.
The shell model approach to the rotating turbulence
Reshetnyak, M
2003-01-01
Applications of the shell model of turbulence to the case of rapidly rotating bodies are considered. Starting from the classical GOY model we introduce the Coriolis force and obtain a $\\sim k^{-2}$ spectrum for 3D hydrodynamical turbulence for the free decay regime as well for the regime with external forcing. Additional modifications of the GOY model providing a realistic form of the helicity are proposed.
Double layer formed by beam driven ion-acoustic turbulence
Small amplitudes steady-state ion-acoustic double layers are observed to form in a plasma transversed by a beam of cold electrons. The importance of turbulence in maintaining the double layer is demonstrated. The measured wave spectrum is in approximate agreement with models deriveted from renornalized turbulence theory. The general features of the double layer are compared with results from particle simulation studies. (author)
We study a nonlinear equation which is equivalent to an equation of generalization of the Leith model of turbulence and to the equation of the model of nonlinear diffusion in an inhomogeneous media without absorption. Using this equation, all submodels admitting continuous Lie transformation groups, acting on the set of solutions of the equations of these submodels are obtained. For obtained submodels, all invariant submodels are found. All essentially distinct invariant solutions describing these invariant submodels are found explicitly, or their finding is reduced to solving nonlinear integral equations. The integral equations defining these solutions reveal new possibilities for analytical and numerical studies. The presence of arbitrary constants in these equations allows one to apply them to the study of different boundary value problems. We have proved the existence and uniqueness of the solution for some boundary value problems. We have investigated the following boundary value problems: (1) a distribution of front-density turbulent kinetic energy in a framework of the generalizion of the Leith model of wave turbulence for which either the spectrum and its wavenumber derivative or the spectrum and its time derivative are given at the initial moment of time at a fixed wavenumber; (2) a nonlinear diffusion process in an inhomogeneous media without absorption, for which either the concentration and its gradient or the concentration and its rate of change are given at the initial moment of time at a fixed point. Under certain additional conditions we have established the existence and uniqueness of the solutions to boundary value problems describing these processes. (paper)
Wave turbulent diffusion due to the Doppler shift
Balk, A. M.
2006-08-01
Turbulent diffusion of a passive tracer caused by a random wavefield is believed to be quadratic with respect to the energy spectrum ɛk of the velocity field (i.e. proportional to epsi4, where epsi is the order of the wave amplitudes). So, the wave turbulent diffusion (say, on the ocean surface or in the air) is often believed to be dominated by the turbulent diffusion due to the incompressible flow. In this paper, we show that the wave turbulent diffusion can be associated with the Doppler shift and find that the wave turbulent diffusion can be more significant than previously thought. This mechanism works if the velocity field is compressible and statistically anisotropic, with the result that the wave system has a significant Stokes drift. The contribution of this mechanism has a lower order in epsi. We confirm our results with numerical simulations. To derive these results, we develop the statistical near-identity transformation.
An Arbitrary Benchmark CAPM: One Additional Frontier Portfolio is Sufficient
Ekern, Steinar
2008-01-01
The benchmark CAPM linearly relates the expected returns on an arbitrary asset, an arbitrary benchmark portfolio, and an arbitrary MV frontier portfolio. The benchmark is not required to be on the frontier and may be non-perfectly correlated with the frontier portfolio. The benchmark CAPM extends and generalizes previous CAPM formulations, including the zero beta, two correlated frontier portfolios, riskless augmented frontier, and inefficient portfolio versions. The covariance between the of...
Interdisciplinary aspects of turbulence
Kupka, Friedrich
2008-01-01
What do combustion engines, fusion reactors, weather forecast, ocean flows, our sun, and stellar explosions in outer space have in common? Of course, the physics and the length and time scales are vastly different in all cases, but it is also well known that in all of them, on some relevant length scales, the material flows that govern the dynamical and/or secular evolution of the systems are chaotic and often unpredictable: they are said to be turbulent. The interdisciplinary aspects of turbulence are brought together in this volume containing chapters written by experts from very different fields, including geophysics, astrophysics, and engineering. It covers several subjects on which considerable progress was made during the last decades, from questions concerning the very nature of turbulence to some practical applications. These subjects include: a basic introduction into turbulence, statistical mechanics and nonlinear dynamics, turbulent convection in stars, atmospheric turbulence in the context of nume...
Kerstein, A.R. [Sandia National Lab., Livermore, CA (United States)
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
Turbulence generation by waves
Kaftori, D.; Nan, X.S.; Banerjee, S. [Univ. of California, Santa Barbara, CA (United States)
1995-12-31
The interaction between two-dimensional mechanically generated waves, and a turbulent stream was investigated experimentally in a horizontal channel, using a 3-D LDA synchronized with a surface position measuring device and a micro-bubble tracers flow visualization with high speed video. Results show that although the wave induced orbital motion reached all the way to the wall, the characteristics of the turbulence wall structures and the turbulence intensity close to the wall were not altered. Nor was the streaky nature of the wall layer. On the other hand, the mean velocity profile became more uniform and the mean friction velocity was increased. Close to the free surface, the turbulence intensity was substantially increased as well. Even in predominantly laminar flows, the introduction of 2-D waves causes three dimensional turbulence. The turbulence enhancement is found to be proportional to the wave strength.
Finite element method application for turbulent and transitional flow
Sváček Petr
2016-01-01
Full Text Available This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil. Particularly, the problem of the turbulent flow around the airfoil with elastic support is considered. The main attention is paid to the numerical approximation of the flow problem using the finite element approximations. The laminar - turbulence transition of the flow on the surface airfoil is considered. The chois of the transition model is discussed. The transition model based on the two equation k−ω turbulence model is used. The structure motion is described with the aid of two degrees of freedom. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. Numerical results are shown.
Feedback Control of Turbulent Shear Flows by Genetic Programming
Duriez, Thomas; von Krbek, Kai; Bonnet, Jean-Paul; Cordier, Laurent; Noack, Bernd R; Segond, Marc; Abel, Markus; Gautier, Nicolas; Aider, Jean-Luc; Raibaudo, Cedric; Cuvier, Christophe; Stanislas, Michel; Debien, Antoine; Mazellier, Nicolas; Kourta, Azeddine; Brunton, Steven L
2015-01-01
Turbulent shear flows have triggered fundamental research in nonlinear dynamics, like transition scenarios, pattern formation and dynamical modeling. In particular, the control of nonlinear dynamics is subject of research since decades. In this publication, actuated turbulent shear flows serve as test-bed for a nonlinear feedback control strategy which can optimize an arbitrary cost function in an automatic self-learning manner. This is facilitated by genetic programming providing an analytically treatable control law. Unlike control based on PID laws or neural networks, no structure of the control law needs to be specified in advance. The strategy is first applied to low-dimensional dynamical systems featuring aspects of turbulence and for which linear control methods fail. This includes stabilizing an unstable fixed point of a nonlinearly coupled oscillator model and maximizing mixing, i.e.\\ the Lyapunov exponent, for forced Lorenz equations. For the first time, we demonstrate the applicability of genetic p...
Langevin approach to generate synthetic turbulence
Martí, A C; Sagues, F; Careta, A
1997-01-01
We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.
Depression of nonlinearity in decaying isotropic turbulence
Simulations of decaying isotropic Navier--Stokes turbulence exhibit depression of the normalized mean-square nonlinear term to 57% of the value for a Gaussianly distributed velocity field with the same instantaneous velocity spectrum. Similar depression is found for dynamical models with random coupling coefficients (modified Betchov models). This suggests that the depression is dynamically generic rather than specifically driven by alignment of velocity and vorticity
Geometrical critical phenomena on a random surface of arbitrary genus
The statistical mechanics of self-avoiding walks (SAW) or of the O(n)-loop model on a two-dimensional random surface are shown to be exactly solvable. The partition functions of SAW and surface configurations (possibly in the presence of vacuum loops) are calculated by planar diagram enumeration techniques. Two critical regimes are found: a dense phase where the infinite walks and loops fill the infinite surface, the non-filled part staying finite, and a dilute phase where the infinite surface singularity on the one hand, and walk and loop singularities on the other, merge together. The configuration critical exponents of self-avoiding networks of any fixed topology G, on a surface with arbitrary genus H, are calculated as universal functions of G and H. For self-avoiding walks, the exponents are built from an infinite set of basic conformal dimensions associated with central charges c = -2 (dense phase) and c = 0 (dilute phase). The conformal spectrum ΔL, L ≥ 1 associated with L-leg star polymers is calculated exactly, for c = -2 and c = 0. This is generalized to the set of L-line 'watermelon' exponents ΔL of the O(n) model on a random surface. The divergences of the partition functions of self-avoiding networks on the random surface, possibly in the presence of vacuum loops, are shown to satisfy a factorization theorem over the vertices of the network. This provides a proof, in the presence of a fluctuating metric, of a result conjectured earlier in the standard plane. From this, the value of the string susceptibility γstr(H,c) is extracted for a random surface of arbitrary genus H, bearing a field theory of central charge c, or equivalently, embedded in d=c dimensions. Lastly, by enumerating spanning trees on a random lattice, we solve the similar problem of hamiltonian walks on the (fluctuating) Manhattan covering lattice. We also obtain new results for dilute trees on a random surface. (orig./HSI)
Scour monitoring via turbulent open channel flow
Scour is the leading cause of bridge failure in the United States. It can result in the loss of lives and costs millions to repair the damage. A novel method is proposed for monitoring scour that exploits the turbulence in natural channels. The method utilizes the dynamic pressure associated with the turbulent velocity fluctuations in the flow to excite a flexible plate. A semi-empirical model is developed to describe the interaction of turbulent open channel flow with the plate. The model describes the variation of turbulent velocity fluctuations across the flow depth in an open channel resulting in a method for determining the average dynamic pressure on the flexible plate. The dynamic response of the plate is then modeled by superimposing the response of multiple modes of the disk to the random, turbulent dynamic pressure spectrum. The model is verified considering the pressure integration across the plate surface to ensure converged solutions. Due to the uncertainties in the material properties of the plate, the experimentally determined natural frequencies and vibration measurements are used to calibrate the model. The calibrated model predictions are then compared against an independent dataset for validation. In addition to describing the physical operation of the device, the semi-empirical model is also employed to optimize the field device. Measurements made using the field device also confirmed the model results, even in a non-design, misaligned flow condition. (paper)
Imbalanced relativistic force-free magnetohydrodynamic turbulence
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), Alfvénic 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∝(ϵ+/ϵ−)n with n > 2). These results are consistent with those obtained for imbalanced non-relativistic Alfvénic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.
Phase-space structure in plasma turbulence
Plasma turbulence driven by the ion temperature gradient (ITG) is theoretically studied with high-resolution Eulerian kinetic simulations. A spectral analysis of the velocity distribution function in the slab ITG turbulence clarifies how the entropy variable associated with the fine scale structure of the distribution function is produced by the turbulent heat transport in the presence of the temperature gradient, transferred from macro- to micro-scales in the velocity space through phase-mixing processes, and dissipated by collisions. The entropy spectral function is analytically derived and confirmed by the simulation result. It is shown that the entropy spectrum obeys a power law in the range that is free from instability sources and collisional dissipation. The Eulerian gyrokinetic simulation of the toroidal ITG turbulence yields the ion thermal diffusivity in the steady turbulent state, in which the balance between the entropy production by the ion thermal transport and the collisional dissipation is verified. A formula for a long time behavior of the zonal flow potential in helical systems is analytically derived, by which collisionless zonal flow dynamics in tokamaks and helical plasmas are compared. A good agreement between the formula and the gyrokinetic simulation results is obtained. (authors)
The residual energy in freely decaying magnetohydrodynamic turbulence
Within the framework of the eddy-damped quasi-normal Markovian approximation for incompressible isotropic magnetohydrodynamic (MHD) turbulence a prediction for the inertial range scaling of the residual energy spectrum, ERk= vertical bar Ekkinetic - Emagnetick vertical bar ∼ k-7/3, is obtained. This scaling, while in contradiction to earlier theoretical results, is shown to be in agreement with high-resolution direct numerical simulations of nonhelical decaying MHD turbulence. The underlying phenomenology states a dynamic quasi-equilibrium of the small-scale turbulent dynamo and the Alfven effect
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.
Jejjala, Vishnu; Minic, Djordje; Ng, Y. Jack; Tze, Chia-Hsiung
We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.
Jejjala, Vishnu; Minic, Djordje(Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA); Ng, Y. Jack; Tze, Chia-Hsiung
2009-01-01
We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.
Triggering filamentation using turbulence
Eeltink, D; Marchiando, N; Hermelin, S; Gateau, J; Brunetti, M; Wolf, J P; Kasparian, J
2016-01-01
We study the triggering of single filaments due to turbulence in the beam path for a laser of power below the filamenting threshold. Turbulence can act as a switch between the beam not filamenting and producing single filaments. This 'positive' effect of turbulence on the filament probability, combined with our observation of off-axis filaments suggests the underlying mechanism is modulation instability caused by transverse perturbations. We hereby experimentally explore the interaction of modulation instability and turbulence, commonly associated with multiple-filaments, in the single-filament regime.
Fossil turbulence and fossil turbulence waves can be dangerous
Gibson, Carl H.
2012-01-01
Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any other forces that tend to damp the eddies out. By this definition, turbulence always cascades from small scales where vorticity is created to larger scales where turbulence fossilizes. Fossil turbulence is any perturbation in a hydrophysical field produced by turbulence that persists after the fluid is no longer turbulent at the scale of the perturbation. Fossil turbu...