Nonlinear Landau damping and Alfven wave dissipation
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Nonlinear Landau damping of Alfven waves.
Hollweg, J. V.
1971-01-01
Demonstration that large-amplitude linearly or elliptically polarized Alfven waves propagating parallel to the average magnetic field can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfven wave. The damping rate can be large even in a cold plasma (beta much less than 1, but not zero), and the mechanism proposed may be the dominant one in many plasmas of astrophysical interest.
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two...
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
Alfven waves in the solar atmosphere. III - Nonlinear waves on open flux tubes
Hollweg, J. V.; Jackson, S.; Galloway, D.
1982-01-01
Consideration is given the nonlinear propagation of Alfven waves on solar magnetic flux tubes, where the tubes are taken to be vertical, axisymmetric and initially untwisted and the Alfven waves are time-dependent axisymmetric twists. The propagation of the waves into the chromosphere and corona is investigated through the numerical solution of a set of nonlinear, time-dependent equations coupling the Alfven waves into motions that are parallel to the initial magnetic field. It is concluded that Alfven waves can steepen into fast shocks in the chromosphere, pass through the transition region to produce high-velocity pulses, and then enter the corona, which they heat. The transition region pulses have amplitudes of about 60 km/sec, and durations of a few tens of seconds. In addition, the Alfven waves exhibit a tendency to drive upward flows, with many of the properties of spicules.
Nonlinear Alfv\\'en wave dynamics at a 2D magnetic null point: ponderomotive force
Thurgood, J O
2013-01-01
Context : In the linear, {\\beta}=0 MHD regime, the transient properties of MHD waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfv\\'en waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfv\\'en speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfv\\'en waves about a 2D magnetic null point in nonlinear, {\\beta}= 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfv\\'en waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfv\\'en wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. t...
Sabeen, A.; Masood, W.; Qureshi, M. N. S.; Shah, H. A.
2017-07-01
In this paper, linear and nonlinear coupling of kinetic Alfven and acoustic waves has been studied in a dusty plasma in the presence of trapping and self-gravitation effects. In this regard, we have derived the linear dispersion relations for positively and negatively coupled dust kinetic Alfven-acoustic waves. Stability analysis of the coupled dust kinetic Alfven-acoustic wave has also been presented. The formation of solitary structures has been investigated following the Sagdeev potential approach by using the two-potential theory. Numerical results show that the solitary structures can be obtained only for sub-Alfvenic regimes in the scenario of space plasmas.
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation.
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P; Murawski, K; Musielak, Z E
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfven waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfven waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfven waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfven waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfven waves show that they can contribute only to the plasma dynamics and heating of t...
Pulse-driven nonlinear Alfv\\'en waves and their role in the spectral line broadening
Chmielewski, P; Murawski, K; Musielak, Z E
2012-01-01
We study the impulsively generated non-linear Alfv\\'en waves in the solar atmosphere, and describe their most likely role in the observed non-thermal broadening of some spectral lines in solar coronal holes. We solve numerically the time-dependent magnetohydrodynamic equations to find temporal signatures of large-amplitude Alfv\\'en waves in the model atmosphere of open and expanding magnetic field configuration, with a realistic temperature distribution. We calculate the temporally and spatially averaged, instantaneous transversal velocity of non-linear Alfv\\'en waves at different heights of the model atmosphere, and estimate its contribution to the unresolved non-thermal motions caused by the waves. We find that the pulse-driven nonlinear Alfv\\'en waves with the amplitude $A_{\\rm v}$=50 km s$^{-1}$ are the most likely candidates for the non-thermal broadening of Si VIII $\\lambda$1445.75 \\AA\\ line profiles in the polar coronal hole as reported by Banerjee et al. (1998). We also demonstrate that the Alfv\\'en w...
Role of Convective Cells in Nonlinear Interaction of Kinetic Alfven Waves
Luk, Onnie
The convective cells are observed in the auroral ionosphere and they could play an important role in the nonlinear interaction of Alfven waves and disrupt the kinetic Alfven wave (KAW) turbulence. Zonal fields, which are analogous to convective cells, are generated by microturbulence and regulate microturbulence inside toroidally confined plasmas. It is important to understand the role of convective cells in the nonlinear interaction of KAW leading to perpendicular cascade of spectral energy. A nonlinear gyrokinetic particle simulation has been developed to study the perpendicular spectral cascade of kinetic Alfven wave. However, convective cells were excluded in the study. In this thesis project, we have modified the formulation to implement the convective cells to study their role in the nonlinear interactions of KAW. This thesis contains detail description of the code formulation and convergence tests performed, and the simulation results on the role of convective cells in the nonlinear interactions of KAW. In the single KAW pump wave simulations, we observed the pump wave energy cascades to waves with shorter wavelengths, with three of them as dominant daughter waves. Convective cells are among those dominant daughter waves and they enhance the rate of energy transfer from pump to daughter waves. When zonal fields are present, the growth rates of the dominant daughter waves are doubled. The convective cell (zonal flow) of the zonal fields is shown to play a major role in the nonlinear wave interaction, while the linear zonal vector potential has little effects. The growth rates of the daughter waves linearly depends on the pump wave amplitude and the square of perpendicular wavenumber. On the other hand, the growth rates do not depend on the parallel wavenumber in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The nonlinear wave interactions with various perpendicular wavenumbers are also studied in this work. When
Study of Nonlinear Interaction and Turbulence of Alfven Waves in LAPD Experiments
Energy Technology Data Exchange (ETDEWEB)
Boldyrev, Stanislav; Perez, Jean Carlos
2013-11-29
The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracy the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectral properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the
Nonlinear reflection process of linearly-polarized, broadband Alfv\\'en waves in the fast solar wind
Shoda, Munehito
2016-01-01
Using one-dimensional numerical simulations, we study the elementary process of Alfv\\'{e}n wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfv\\'{e}n wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave-wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfv\\'{e}n wave. In this study we consider a linearly polarized Alfv\\'en wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wave with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfv\\...
Analysis of Magnetic Fields in Inertial Alfven Wave Collisions
Drake, Dereth J; Shanken, Brian C; Howes, Gregory G; Skiff, Frederick; Kletzing, Craig A; Carter, Troy A; Dorfman, Seth
2014-01-01
Turbulence in astrophysical and space plasmas is dominated by the nonlinear interaction of counterpropagating Alfven waves. Most Alfven wave turbulence theories have been based on ideal plasma models, such as incompressible MHD, for Alfven waves at large scales. However, in the inertial Alfven wave regime (vA > vthe), relevant to magnetospheric plasmas, how the turbulent nonlinear interactions are modified by the dispersive nature of the waves remains to be explored. Here we present the first laboratory evidence of the nonlinear interaction in the inertial regime. A comparison is made with the theory for MHD Alfven waves.
Alfven Wave Tomography for Cold MHD Plasmas
Energy Technology Data Exchange (ETDEWEB)
I.Y. Dodin; N.J. Fisch
2001-09-07
Alfven waves propagation in slightly nonuniform cold plasmas is studied by means of ideal magnetohydrodynamics (MHD) nonlinear equations. The evolution of the MHD spectrum is shown to be governed by a matrix linear differential equation with constant coefficients determined by the spectrum of quasi-static plasma density perturbations. The Alfven waves are shown not to affect the plasma density inhomogeneities, as they scatter off of them. The application of the MHD spectrum evolution equation to the inverse scattering problem allows tomographic measurements of the plasma density profile by scanning the plasma volume with Alfven radiation.
Kinetic Alfven wave turbulence in space plasmas
Energy Technology Data Exchange (ETDEWEB)
Sharma, R.P. [Plasma Simulation Laboratory, Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, New Delhi (India); Kumar, Sachin, E-mail: dynamicalfven@gmail.co [Plasma Simulation Laboratory, Centre for Energy Studies, Indian Institute of Technology, Delhi-110016, New Delhi (India)
2010-07-26
This work presents the derivation of nonlinear coupled equations for the evolution of solar wind turbulence. These equations are governing the coupled dynamics of kinetic Alfven wave and ion acoustic wave. Numerical simulation of these equations is also presented. The ponderomotive nonlinearity is incorporated in the wave dynamics. Filamentation of kinetic Alfven wave and the turbulent spectra are presented in intermediate-{beta} plasmas at heliocentric distances (0.3 AU{<=}r<1.0 AU). The growing filaments and steeper turbulent spectra (of power law k{sup -S}, 5/3{<=}S{<=}3) can be responsible for plasma heating and particle acceleration in solar wind.
James Clerk Maxwell Prize for Plasma Physics Talk: On Nonlinear Physics of Shear Alfv'en Waves
Chen, Liu
2012-10-01
Shear Alfv'en Waves (SAW) are electromagnetic oscillations prevalent in laboratory and nature magnetized plasmas. Due to its anisotropic propagation property, it is well known that the linear wave propagation and dispersiveness of SAW are fundamentally affected by plasma nonuniformities and magnetic field geometries; for example, the existence of continuous spectrum, spectral gaps, and discrete eigenmodes in toroidal plasmas. This talk will discuss the crucial roles that nonuniformity and geometry could also play in the physics of nonlinear SAW interactions. More specifically, the focus will be on the Alfv'enic state and its breaking up by finite compressibility, non-ideal kinetic effects, and geometry. In the case of compressibility, finite ion-Larmor-radius effects are shown to qualitatively and quantitatively modify the three-wave parametric decays via the ion-sound perturbations. In the case of geometry, the spontaneous excitation of zonal structures by toroidal Alfv'en eigenmodes is investigated; demonstrating that, for realistic tokamak geometries, zonal current dominates over zonal flow. [4pt] Present address: Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou, China.
Medina-Tanco, G. A.; Opher, R.
1990-11-01
RESUMEN. Se presentan resultados numericos para un modelo hidrodinamico de cuatro componentes (plasma de fondo, particulas energeticas, ondas de Alfven autogeneradas y campo magnetico) para choques oblicuos. ABSTRACT. Numerical results of a four component hydrodynamic model (background plasma, energetic particles, self-generated Alfven waves and magnetic field) for oblique shocks are presented. Keq wo't : COSMIC RAY-GENERAL - PLASMAS - SHOCK WAVES
Alfven Wave-Driven Supernova Explosion
Suzuki, T K; Yamada, S
2007-01-01
We investigate the role of Alfven waves in the core-collapse supernova (SN) explosion. We assume that Alfven waves are generated by convections inside a proto-neutron star (PNS) and emitted from its surface. Then these waves propagate outwards and dissipate via nonlinear processes and heat up matter around a stalled prompt shock. To quantitatively assess the importance of this process for revival of the stalled shock, we perform 1D time-dependent hydrodynamical simulations, taking into account the heating via the dissipation of Alfven waves. We show that the shock revival occurs if the surface field strength is larger than ~2x10^{15}G and if the amplitude of velocity fluctuation at the PNS surface is larger than ~ 20% of the local sound speed. Interestingly, the Alfven wave mechanism is self-regulating in the sense that the explosion energy is not very sensitive to the surface field strength and initial amplitude of Alfven waves as long as they are larger than the threshold values given above. It should be em...
Impulsively Generated Linear and Non-linear Alfven Waves in the Coronal Funnels
Chmielewski, P.; Srivastava, A. K.; Murawski, K.; Musielak, Z. E.
2014-01-01
We present simulation results of the impulsively generated linear and non-linear Alfvén waves in the weakly curved coronal magnetic flux-tubes (coronal funnels) and discuss their implications for the coronal heating and solar wind acceleration. We solve numerically the time-dependent magnetohydrodynamic equations to find the temporal signatures of the small and large-amplitude Alfvén waves in the model atmosphere of open and expanding magnetic field configuration with a realistic temperature distribution. We compute the maximum transversal velocity of both linear and non-linear Alfvén waves at different heights of the model atmosphere, and study their response in the solar corona during the time of their propagation. We infer that the pulse-driven non-linear Alfvén waves may carry sufficient wave energy fluxes to heat the coronal funnels and also to power the solar wind that originates in these funnels. Our study of linear Alfvén waves shows that they can contribute only to the plasma dynamics and heating of the funnel-like magnetic flux-tubes associated with the polar coronal holes.
Matsumoto, Takuma
2010-01-01
We have performed MHD simulations of Alfven wave propagation along an open flux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photospheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy flux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave generator. This difference can be explained by the Alfven wave resonance between the photosphere and the transition region. After performing Fourier analysis on our numerical results, we have found that the region between the photosphere and the transition region becomes an Alfven wave resonant cavity. We have confirmed that there are at least three resonant frequencies, 1, 3 and 5 mHz, in our numerical model. Alfven wave resonance is one of the most effective mechanisms to explai...
Interchange Reconnection Alfven Wave Generation
Lynch, B J; Li, Y
2014-01-01
Given recent observational results of interchange reconnection processes in the solar corona and the theoretical development of the S-Web model for the slow solar wind, we present further analysis of the 3D MHD simulation of interchange reconnection by Edmondson et al. (Astrophys. J. 707, 1427, 2009). Specifically, we analyze the consequences of the dynamic streamer belt jump that corresponds to flux opening by interchange reconnection. Information about the magnetic field restructuring by interchange reconnection is carried throughout the system by Alfven waves propagating away from the reconnection region, distributing the shear and twist imparted by the driving flows, including shedding the injected stress-energy and accumulated magnetic helicity along newly-open field lines. We quantify the properties of the reconnection-generated wave activity in the simulation. There is a localized high frequency component associated with the current sheet/reconnection site and an extended low frequency component associ...
Quantum effects on compressional Alfven waves in compensated semiconductors
Energy Technology Data Exchange (ETDEWEB)
Amin, M. R. [Department of Electronics and Communications Engineering, East West University, Aftabnagar, Dhaka 1212 (Bangladesh)
2015-03-15
Amplitude modulation of a compressional Alfven wave in compensated electron-hole semiconductor plasmas is considered in the quantum magnetohydrodynamic regime in this paper. The important ingredients of this study are the inclusion of the particle degeneracy pressure, exchange-correlation potential, and the quantum diffraction effects via the Bohm potential in the momentum balance equations of the charge carriers. A modified nonlinear Schrödinger equation is derived for the evolution of the slowly varying amplitude of the compressional Alfven wave by employing the standard reductive perturbation technique. Typical values of the parameters for GaAs, GaSb, and GaN semiconductors are considered in analyzing the linear and nonlinear dispersions of the compressional Alfven wave. Detailed analysis of the modulation instability in the long-wavelength regime is presented. For typical parameter ranges of the semiconductor plasmas and at the long-wavelength regime, it is found that the wave is modulationally unstable above a certain critical wavenumber. Effects of the exchange-correlation potential and the Bohm potential in the wave dynamics are also studied. It is found that the effect of the Bohm potential may be neglected in comparison with the effect of the exchange-correlation potential in the linear and nonlinear dispersions of the compressional Alfven wave.
Kuridze, D
2007-01-01
Nonlinear coupling between 3-minute oscillations and Alfven waves in the solar lower atmosphere is studied. 3-minute oscillations are considered as acoustic waves trapped in a chromospheric cavity and oscillating along transversally inhomogeneous vertical magnetic field. It is shown that under the action of the oscillations the temporal dynamics of Alfven waves is governed by Mathieu equation. Consequently, the harmonics of Alfven waves with twice period and wavelength of 3-minute oscillations grow exponentially in time near the layer where the sound and Alfven speeds equal. Thus the 3-minute oscillations are resonantly absorbed by pure Alfven waves near this resonant layer. The resonant Alfven waves may penetrate into the solar corona taking energy from the chromosphere. Therefore the layer c_s=v_A may play a role of energy channel for otherwise trapped acoustic oscillations.
Drake, D J; Howes, G G; Kletzing, C A; Skiff, F; Carter, T A; Auerbach, D W
2013-01-01
Turbulence is a phenomenon found throughout space and astrophysical plasmas. It plays an important role in solar coronal heating, acceleration of the solar wind, and heating of the interstellar medium. Turbulence in these regimes is dominated by Alfven waves. Most turbulence theories have been established using ideal plasma models, such as incompressible MHD. However, there has been no experimental evidence to support the use of such models for weakly to moderately collisional plasmas which are relevant to various space and astrophysical plasma environments. We present the first experiment to measure the nonlinear interaction between two counterpropagating Alfven waves, which is the building block for astrophysical turbulence theories. We present here four distinct tests that demonstrate conclusively that we have indeed measured the daughter Alfven wave generated nonlinearly by a collision between counterpropagating Alfven waves.
Riemann solvers and Alfven waves in black hole magnetospheres
Punsly, Brian; Balsara, Dinshaw; Kim, Jinho; Garain, Sudip
2016-09-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. Thus, it is important for numerical simulations of black hole magnetospheres to minimize the dissipation of Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, numerical dissipation can affect how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. In order to help minimize dissipation of Alfven waves in relativistic numerical simulations we have formulated a one-dimensional Riemann solver, called HLLI, which incorporates the Alfven discontinuity and the contact discontinuity. We have also formulated a multidimensional Riemann solver, called MuSIC, that enables low dissipation propagation of Alfven waves in multiple dimensions. The importance of higher order schemes in lowering the numerical dissipation of Alfven waves is also catalogued.
Torsional Alfven waves in stratified and expanding magnetic flux tubes
2011-01-01
The effects of both density stratification and magnetic field expansion on torsional Alfven waves in magnetic flux tubes are studied. The frequencies, the period ratio P1/P2 of the fundamental and its first-overtone, and eigenfunctions of torsional Alfven modes are obtained. Our numerical results show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional Alfven waves.
Adiabatic trapping in coupled kinetic Alfven-acoustic waves
Energy Technology Data Exchange (ETDEWEB)
Shah, H. A.; Ali, Z. [Department of Physics, G.C. University, 54000 Lahore (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Theoretical Plasma Physics Division, P. O. Nilore, Islamabad (Pakistan)
2013-03-15
In the present work, we have discussed the effects of adiabatic trapping of electrons on obliquely propagating Alfven waves in a low {beta} plasma. Using the two potential theory and employing the Sagdeev potential approach, we have investigated the existence of arbitrary amplitude coupled kinetic Alfven-acoustic solitary waves in both the sub and super Alfvenic cases. The results obtained have been analyzed and presented graphically and can be applied to regions of space where the low {beta} assumption holds true.
Global Alfven Waves in Solar Physics: Coronal Heating
de Azevedo, C. A.; de Assis, A. S.
1990-11-01
RESUMEN. Se ha demostrado que Ia onda discreta de Alfven puede generar por lo memos un 20% de la energia coronal requerida con densidad de flujo de lO- erg 5 . Las ondas discretas de Alfven son una nueva clase `de ondas de Alfven las cuales pueden describirse por el modelo con que incluye un i6n finito, con frecuencia ciclotr6nica ( /uci # 0) y los efectos del equilibrio de plasma mostrados por Appert, Vaclavik and Villar 1984. ABSTRACT. It has been shown that the Discrete Alfven wave can power at least 20% of the required coronal energy flux density iO- Discrete Alfven waves are a new class of Alfven waves wich can be described by the model with the inclusion of finite ion cyclotron frequency (w/wci 0) and the equilibrium plasma current effects as shown by Appert, Vaclavik and Villar 1984. o,t :, HYDROMAGNETICS - SUN-CORONA
Alfven wave in higher dimensional space time
Panigrahi, D; Chatterjee, S
2009-01-01
Following the wellknown spacetime decomposition technique as applied to (d+1) dimensions we write down the equations of magnetohydrodynamics (MHD) in a spatially at generalised FRW universe. Assuming an equation of state for the background cosmic fluid we find solutions in turn for acous- tic waves and also for Alfven waves in a warm (cold) magnetised plasma. Interestingly the different plasma modes closely resemble the at space coun- terparts except that here the field variables all redshift with their time due to the expansion of the background. It is observed that in the ultrarelativistic limit the field parameters all scale as the free photon. The situation changes in the prerelativistic limit where the frequencies change in a bizarre fashion depending on initial conditions. It is observed that for a fixed magnetic field in a particular medium the Alfven wave velocity decreases with the number of dimensions, being the maximum in the usual 4D. Further for a fixed dimension the velocity attenuation is more ...
Nonlinear interplay of Alfven instabilities and energetic particles in tokamaks
Biancalani, A; Cole, M; Di Troia, C; Lauber, Ph; Mishchenko, A; Scott, B; Zonca, F
2016-01-01
The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of the frequency, growth rate and radial structure of the TAE, depending on the evolution of the EP distribution in phase space. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. This nonlinear evolution is found to be correctly reproduced by means of a quasilinear model, namely a model where the linear effects of the nonlinearly modified EP distri...
Damping of visco-resistive Alfven waves in solar spicules
Directory of Open Access Journals (Sweden)
Z Fazel
2014-12-01
Full Text Available Interaction of Alfven waves with plasma inhomogeneity generates phase mixing which can cause the dissipation of Alfven waves. We investigated the dissipation of standing Alfven waves due to phase mixing at the presence of steady flow and sheared magnetic field in solar spicules. Moreover, the transition region between chromosphere and corona was considered. Our numerical simulation showed that the phase mixing and dissipation rate of Alfven waves are enhanced relative to viscosity and resistivity gradients. Comparison of the results of our models with and without these gradients illustrated a significant difference between them. In other words, with these assumptions, Alfven waves may transfer the photospheric energy to the corona during timescales corresponding to the observed lifetimes of spicules. It should be noted that the results of our numerical simulation were in good agreement with observational scaling law obtained by Kuridze et al. [1
Observation of an Alfv\\'en Wave Parametric Instability in a Laboratory Plasma
Dorfman, S
2016-01-01
A shear Alfv\\'en wave parametric instability is observed for the first time in the laboratory. When a single finite $\\omega/\\Omega_i$ kinetic Alfv\\'en wave (KAW) is launched in the Large Plasma Device above a threshold amplitude, three daughter modes are produced. These daughter modes have frequencies and parallel wave numbers that are consistent with copropagating KAW sidebands and a low frequency nonresonant mode. The observed process is parametric in nature, with the frequency of the daughter modes varying as a function of pump wave amplitude. The daughter modes are spatially localized on a gradient of the pump wave magnetic field amplitude in the plane perpendicular to the background field, suggesting that perpendicular nonlinear forces (and therefore $k_{\\perp}$ of the pump wave) play an important role in the instability process. Despite this, modulational instability theory with $k_{\\perp}=0$ has several features in common with the observed nonresonant mode and Alfv\\'en wave sidebands.
Numerical Simulation of Solitary Kinetic Alfven Waves
Institute of Scientific and Technical Information of China (English)
DING Jian; LI Yi; WANG Shui
2008-01-01
Using the two-fluid model in the case of α1 (α=β/2Q, β is the ratio of thermal pressure to magnetic pressure, and Q=m,e/m,I), we numerically investigate the interactions between two solitary kinetic Alfven waves (SKAWs) and between an SKAW and a density discontinuity. The results show that the two SKAWs would remain in their original shapes and propagate at their initiating speeds, which indicates that SKAWs behave just like standard solitons. The simulation also shows that SKAWs will reflect and refract when crossing a discontinuity and propagating into a higher density region. The transmission wave is an SKAW with increasing density, and the reverberation is a disturbance with lower amplitude.
Alfven Wave Solar Model: Part 1, Coronal Heating
van der Holst, Bart; Meng, Xing; Jin, Meng; Manchester, Ward B; Toth, Gabor; Gombosi, Tamas I
2013-01-01
We present the new Alfven Wave Solar Model (AWSoM), a global model from the upper chromosphere to the corona and the heliosphere. The coronal heating and solar wind acceleration are addressed with low-frequency Alfven wave turbulence. The injection of Alfven wave energy at the inner boundary is such that the Poynting flux is proportional to the magnetic field strength. The three-dimensional magnetic field topology is simulated using data from photospheric magnetic field measurements. This model does not impose open-closed magnetic field boundaries; those develop self-consistently. The physics includes: (1) The model employs three different temperatures, namely the isotropic electron temperature and the parallel and perpendicular ion temperatures. The firehose, mirror, and ion-cyclotron instabilities due to the developing ion temperature anisotropy are accounted for. (2) The Alfven waves are partially reflected by the Alfven speed gradient and the vorticity along the field lines. The resulting counter-propagat...
HLL Riemann Solvers and Alfven Waves in Black Hole Magnetospheres
Punsly, Brian; Kim, Jinho; Garain, Sudip
2016-01-01
In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. However, numerical simulations of black hole magnetospheres are often based on 1-D HLL Riemann solvers that readily dissipate Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, it is unclear how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. The HLL Riemann solver is also notorious for producing large recurring...
Effects of compressional magnetic perturbation on kinetic Alfven waves
Dong, Ge; Bhattacharjee, Amitava; Lin, Zhihong
2016-10-01
Kinetic Alfven waves play a very important role in the dynamics of fusion as well as space and astrophysical plasmas. The compressional magnetic perturbation δB|| can play important role in kinetic Alfven waves (KAW) and various instabilities at large plasma β. It could affect the nonlinear behavior of these modes significantly even at small β. In this study, we have implemented δB|| in gyrokinetic toroidal code (GTC). The perpendicular Ampere's law is solved as a force balance equation. Double gyroaveraging is incorporated in the code to treat the finite Larmor radius effects related to δB|| terms. KAW is studied in slab geometry as a benchmark case. A scan in β for the KAW dispersion relation shows that as β approaches 1 (>0.3), the effects of δB|| becomes important. Connections are made with other existing studies of KAWs in the fusion and space plasma literature. This new capability of including δB|| in GTC could be applied to nonlinear simulations of modes such as kinetic ballooning and tearing modes. This research is supported by DOE Contract No. DE-AC02-09CH11466.
On reflection of Alfven waves in the solar wind
Krogulec, M.; Musielak, Z. E.; Suess, S. T.; Moore, R. L.; Nerney, S. F.
1993-01-01
We have revisited the problem of propagation of toroidal and linear Alfven waves formulated by Heinemann and Olbert (1980) to compare WKB and non-WKB waves and their effects on the solar wind. They considered two solar wind models and showed that reflection is important for Alfven waves with periods of the order of one day and longer, and that non-WKB Alfven waves are no more effective in accelerating the solar wind than WKB waves. There are several recently published papers which seem to indicate that Alfven waves with periods of the order of several minutes should be treated as non-WKB waves and that these non-WKB waves exert a stronger acceleration force than WKB waves. The purpose of this paper is to study the origin of these discrepancies by performing parametric studies of the behavior of the waves under a variety of different conditions. In addition, we want to investigate two problems that have not been addressed by Heinemann and Olbert, namely, calculate the efficiency of Alfven wave reflection by using the reflection coefficient and identify the region of strongest wave reflection in different wind models. To achieve these goals, we investigated the influence of temperature, electron density distribution, wind velocity and magnetic field strength on the waves. The obtained results clearly demonstrate that Alfven wave reflection is strongly model dependent and that the strongest reflection can be expected in models with the base temperatures higher than 10(exp 6) K and with the base densities lower than 7 x 10(exp 7) cm(exp -3). In these models as well as in the models with lower temperatures and higher densities, Alfven waves with periods as short as several minutes have negligible reflection so that they can be treated as WKB waves; however, for Alfven waves with periods of the order of one hour or longer reflection is significant, requiring a non-WKB treatment. We also show that non-WKB, linear Alfven waves are always less effective in accelerating the
Small amplitude Kinetic Alfven waves in a superthermal electron-positron-ion plasma
Adnan, Muhammad; Mahmood, Sahahzad; Qamar, Anisa; Tribeche, Mouloud
2016-11-01
We are investigating the propagating properties of coupled Kinetic Alfven-acoustic waves in a low beta plasma having superthermal electrons and positrons. Using the standard reductive perturbation method, a nonlinear Korteweg-de Vries (KdV) type equation is derived which describes the evolution of Kinetic Alfven waves. It is found that nonlinearity and Larmor radius effects can compromise and give rise to solitary structures. The parametric role of superthermality and positron content on the characteristics of solitary wave structures is also investigated. It is found that only sub-Alfvenic and compressive solitons are supported in the present model. The present study may find applications in a low β electron-positron-ion plasma having superthermal electrons and positrons.
A laboratory search for plasma erosion by Alfven waves
Vincena, S.; Gekelman, W.; Pribyl, P.
2007-12-01
Obliquely propagating shear Alfven waves with transverse wavelengths on the order of the electron inertial length or even the ion gyro-radius are commonly observed in the earth's low-altitude auroral zones. These regions are also replete with observations of electron beams and transversely heated ions. A kinetic treatment of shear Alfven wave-particle interaction reveals how these waves can be responsible for some of the observed particle acceleration. The auroral plasma environment is further enriched by the presence of field-aligned depletions in plasma density, and it has been suggested* that the Alfven waves may, in fact, be the cause of the erosion of ionospheric density. In this laboratory experiment, shear waves will be launched using a variety of proven antennas, and also allowed to grow spontaneously as Drift-Alfven modes in seeded density depletions**. Detailed measurements of the wave magnetic fields in the perpendicular density gradient regions will be presented which demonstrate the generation of short perpendicular wave scales due to the perpendicular gradient in parallel wave phase speed. Miniature in-situ particle diagnostics will also be used to look for electron and ion acceleration. The waves will also be launched into an increasing region of background magnetic field in an attempt to model the ratios of Alfven speed to electron thermal speed, and density gradient scale length to electron inertial length appropriate to the earth's auroral zone. Preliminary results will be presented on the efficacy of shear Alfven waves to self-generate plasma density depletions, or deepen ambient density inhomogeneities. The experiments are conducted at UCLA's Basic Plasma Science Facility in the Large Plasma Device. *Chaston, et al., "Ionospheric erosion by Alfven Waves," JGR, V 111, A03206, 2006. **Penano, et al., "Drift-Alfven fluctuations associated with a narrow pressure striation," Phys. Plasmas, V 7, Issue 1, pp. 144-157 (2000).
Emission of radiation induced by pervading Alfven waves
Energy Technology Data Exchange (ETDEWEB)
Zhao, G. Q. [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Wu, C. S. [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing (China); Institute of Space Science, National Central University, Zhongli, Taiwan (China)
2013-03-15
It is shown that under certain conditions, propagating Alfven waves can energize electrons so that consequently a new cyclotron maser instability is born. The necessary condition is that the plasma frequency is lower than electron gyrofrequency. This condition implies high Alfven speed, which can pitch-angle scatter electrons effectively and therefore the electrons are able to acquire free energy which are needed for the instability.
ALFVEN WAVES IN A PARTIALLY IONIZED TWO-FLUID PLASMA
Energy Technology Data Exchange (ETDEWEB)
Soler, R.; Ballester, J. L.; Terradas, J. [Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Carbonell, M., E-mail: roberto.soler@uib.es, E-mail: joseluis.ballester@uib.es, E-mail: jaume.terradas@uib.es, E-mail: marc.carbonell@uib.es [Departament de Matematiques i Informatica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2013-04-20
Alfven waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfven waves is affected by the interaction between ionized and neutral species. Here we study Alfven waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible, we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cutoff values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mode approach and solve the initial-value problem in order to study the time-dependent evolution of the wave perturbations in the two fluids. An application to Alfven waves in the low solar atmospheric plasma is performed and the implication of partial ionization for the energy flux is discussed.
The role of torsional Alfven waves in coronal heating
Antolin, P
2009-01-01
In the context of coronal heating, among the zoo of MHD waves that exist in the solar atmosphere, Alfven waves receive special attention. Indeed, these waves constitute an attractive heating agent due to their ability to carry over the many different layers of the solar atmosphere sufficient energy to heat and maintain a corona. However, due to their incompressible nature these waves need a mechanism such as mode conversion (leading to shock heating), phase mixing, resonant absorption or turbulent cascade in order to heat the plasma. New observations with polarimetric, spectroscopic and imaging instruments such as those on board of the japanese satellite Hinode, or the SST or CoMP, are bringing strong evidence for the existence of energetic Alfven waves in the solar corona. In order to assess the role of Alfven waves in coronal heating, in this work we model a magnetic flux tube being subject to Alfven wave heating through the mode conversion mechanism. Using a 1.5-dimensional MHD code we carry out a paramete...
Reflection and dissipation of Alfv\\'en waves in interstellar clouds
Pinto, C; Galli, D; Velli, M
2012-01-01
Context: Supersonic nonthermal motions in molecular clouds are often interpreted as long-lived magnetohydrodynamic (MHD) waves. The propagation and amplitude of these waves is affected by local physical characteristics, most importantly the gas density and the ionization fraction. Aims: We study the propagation, reflection and dissipation of Alfv\\'en waves in molecular clouds deriving the behavior of observable quantities such as the amplitudes of velocity fluctuations and the rate of energy dissipation. Methods: We formulated the problem in terms of Els\\"asser variables for transverse MHD waves propagating in a one-dimensional inhomogeneous medium, including the dissipation due to collisions between ions and neutrals and to a nonlinear turbulent cascade treated in a phenomenological way. We considered both steady-state and time-dependent situations and solved the equations of the problem numerically with an iterative method and a Lax-Wendroff scheme, respectively. Results: Alfv\\'en waves incident on overdens...
Swirling astrophysical flows - efficient amplifiers of Alfven waves
Rogava, A D; Bodo, G; Massaglia, S; Rogava, Andria D.; Mahajan, Swadesh M.; Bodo, Gianluigi; Massaglia, Silvano
2003-01-01
We show that a helical shear flow of a magnetized plasma may serve as an efficient amplifier of Alfven waves. We find that even when the flow is purely ejectional (i.e., when no rotation is present) Alfven waves are amplified through the transient, shear-induced, algebraic amplification process. Series of transient amplifications, taking place sequentially along the flow, may result in a cascade amplification of these waves. However, when a flow is swirling or helical (i.e., some rotation is imposed on the plasma motion), Alfven waves become subject to new, much more powerful shear instabilities. In this case, depending on the type of differential rotation, both usual and parametric instabilities may appear. We claim that these phenomena may lead to the generation of large amplitude Alfven waves and the mechanism may account for the appearance of such waves in the solar atmosphere, in accretion-ejecion flows and in accretion columns. These processes may also serve as an important initial (linear and nonmodal)...
The Modulation of Ionospheric Alfven Resonator on Heating HF Waves and the Doppler Effect
Institute of Scientific and Technical Information of China (English)
NiBin-bin; ZhaoZheng-yu; XieShu-guo
2003-01-01
The propagation of HF waves in IAR can produce many nonlinear effects, including the modulation effect of IAR on HF waves and the Doppler effect. To start with the dependence of the ionospheric electron temperature varia-tions on the Alfven resonant field, We discuss the mechanism of the modulation effect and lucubrate possible reasons for the Doppler effect. The results show that the Alfven resonant field can have an observable modulation effect on HF waves while its mechanism is quite different from that of Schumann resonant field on HF waves. The depth of modulation of IAR on HF waves has a quasi-quadratic relation with the Alfven field, which directly inspires the formation of cross-spectrum between ULF waves and HF waves and results in spectral peaks at some gyro-frequencies of IAR. With respect to the Doppler effect during the propagation of HF waves in IAR, it is mainly caused by the motion of the high-speed flyer and the drifting electrons and the frequency shift from the phase vari-ation of the reflected waves can be neglected when the frequency of HF incident wave is high enough.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Heating and Acceleration of the Fast Solar Wind by Alfv\\'{e}n Wave Turbulence
van Ballegooijen, A A
2016-01-01
We present numerical simulations of reduced magnetohydrodynamic (RMHD) turbulence in a magnetic flux tube at the center of a polar coronal hole. The model for the background atmosphere is a solution of the momentum equation, and includes the effects of wave pressure on the solar wind outflow. Alfv\\'{e}n waves are launched at the coronal base, and reflect at various heights due to variations in Alfv\\'{e}n speed and outflow velocity. The turbulence is driven by nonlinear interactions between the counter-propagating Alfv\\'{e}n waves. Results are presented for two models of the background atmosphere. In the first model the plasma density and Alfv\\'{e}n speed vary smoothly with height, resulting in minimal wave reflections and low energy dissipation rates. We find that the dissipation rate is insufficient to maintain the temperature of the background atmosphere. The standard phenomenological formula for the dissipation rate significantly overestimates the rate derived from our RMHD simulations, and a revised formu...
Direct excitation of resonant torsional Alfven waves by footpoint motions
Ruderman, M. S.; Berghmans, D.; Goossens, M.; Poedts, S.
1997-01-01
The present paper studies the heating of coronal loops by linear resonant Alfven waves that are excited by the motions of the photospheric footpoints of the magnetic field lines. The analysis is restricted to torsionally polarised footpoint motions in an axially symmetric system so that only
Non-linear modulation of short wavelength compressional Alfven eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E. D.; Gorelenkov, N. N.; Podesta, M.; Gerhardt, S. P.; Bell, R. E.; Diallo, A.; LeBlanc, B. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Bortolon, A. [University of California, Irvine, California 92697 (United States); Crocker, N. A. [University of California, Los Angeles, California 90095 (United States); Levinton, F. M.; Yuh, H. [Nova Photonics, Princeton, New Jersey 08543 (United States)
2013-04-15
Most Alfvenic activity in the frequency range between toroidal Alfven eigenmodes and roughly one half of the ion cyclotron frequency on National Spherical Torus eXperiment [Ono et al., Nucl. Fusion 40, 557 (2000)], that is, approximately 0.3 MHz up to Almost-Equal-To 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n = 1 kink-like mode. In this paper, we present measurements of the spectrum of these high frequency CAE (hfCAE) and their mode structure. We compare those measurements to a simple model of CAE and present a predator-prey type model of the curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Parametric instabilities of large amplitude Alfven waves with obliquely propagating sidebands
Vinas, A. F.; Goldstein, M. L.
1992-01-01
This paper presents a brief report on properties of the parametric decay and modulational, filamentation, and magnetoacoustic instabilities of a large amplitude, circularly polarized Alfven wave. We allow the daughter and sideband waves to propagate at an arbitrary angle to the background magnetic field so that the electrostatic and electromagnetic characteristics of these waves are coupled. We investigate the dependance of these instabilities on dispersion, plasma/beta, pump wave amplitude, and propagation angle. Analytical and numerical results are compared with numerical simulations to investigate the full nonlinear evolution of these instabilities.
Alfven waves in a partially ionized two-fluid plasma
Soler, R; Ballester, J L; Terradas, J
2013-01-01
Alfv\\'en waves are a particular class of magnetohydrodynamic waves relevant in many astrophysical and laboratory plasmas. In partially ionized plasmas the dynamics of Alfv\\'en waves is affected by the interaction between ionized and neutral species. Here we study Alfv\\'en waves in a partially ionized plasma from the theoretical point of view using the two-fluid description. We consider that the plasma is composed of an ion-electron fluid and a neutral fluid, which interact by means of particle collisions. To keep our investigation as general as possible we take the neutral-ion collision frequency and the ionization degree as free parameters. First, we perform a normal mode analysis. We find the modification due to neutral-ion collisions of the wave frequencies and study the temporal and spatial attenuation of the waves. In addition, we discuss the presence of cut-off values of the wavelength that constrain the existence of oscillatory standing waves in weakly ionized plasmas. Later, we go beyond the normal mo...
Arbitrary amplitude kinetic Alfven solitary waves in two temperature electron superthermal plasma
Singh, Manpreet; Singh Saini, Nareshpal; Ghai, Yashika
2016-07-01
Through various satellite missions it is observed that superthermal velocity distribution for particles is more appropriate for describing space and astrophysical plasmas. So it is appropriate to use superthermal distribution, which in the limiting case when spectral index κ is very large ( i.e. κ→∞), shifts to Maxwellian distribution. Two temperature electron plasmas have been observed in auroral regions by FAST satellite mission, and also by GEOTAIL and POLAR satellite in the magnetosphere. Kinetic Alfven waves arise when finite Larmor radius effect modifies the dispersion relation or characteristic perpendicular wavelength is comparable to electron inertial length. We have studied the kinetic Alfven waves (KAWs) in a plasma comprising of positively charged ions, superthermal hot electrons and Maxwellian distributed cold electrons. Sagdeev pseudo-potential has been employed to derive an energy balance equation. The critical Mach number has been determined from the expression of Sagdeev pseudo-potential to see the existence of solitary structures. It is observed that sub-Alfvenic compressive solitons and super-Alfvenic rarefactive solitons exist in this plasma model. It is also observed that various parameters such as superthermality of hot electrons, relative concentration of cold and hot electron species, Mach number, plasma beta, ion to cold electron temperature ratio and ion to hot electron temperature ratio have significant effect on the amplitude and width of the KAWs. Findings of this investigation may be useful to understand the dynamics of coherent non-linear structures (i.e. KAWs) in space and astrophysical plasmas.
Simulation of the interaction between Alfven waves and fast particles
Energy Technology Data Exchange (ETDEWEB)
Feher, Tamas Bela
2014-02-18
There is a wide variety of Alfven waves in tokamak and stellarator plasmas. While most of them are damped, some of the global eigenmodes can be driven unstable when they interact with energetic particles. By coupling the MHD code CKA with the gyrokinetic code EUTERPE, a hybrid kinetic-MHD model is created to describe this wave-particle interaction in stellarator geometry. In this thesis, the CKA-EUTERPE code package is presented. This numerical tool can be used for linear perturbative stability analysis of Alfven waves in the presence of energetic particles. The equations for the hybrid model are based on the gyrokinetic equations. The fast particles are described with linearized gyrokinetic equations. The reduced MHD equations are derived by taking velocity moments of the gyrokinetic equations. An equation for describing the Alfven waves is derived by combining the reduced MHD equations. The Alfven wave equation can retain kinetic corrections. Considering the energy transfer between the particles and the waves, the stability of the waves can be calculated. Numerically, the Alfven waves are calculated using the CKA code. The equations are solved as an eigenvalue problem to determine the frequency spectrum and the mode structure of the waves. The results of the MHD model are in good agreement with other sophisticated MHD codes. CKA results are shown for a JET and a W7-AS example. The linear version of the EUTERPE code is used to study the motion of energetic particles in the wavefield with fixed spatial structure, and harmonic oscillations in time. In EUTERPE, the gyrokinetic equations are discretized with a PIC scheme using the delta-f method, and both full orbit width and finite Larmor radius effects are included. The code is modified to be able to use the wavefield calculated externally by CKA. Different slowing-down distribution functions are also implemented. The work done by the electric field on the particles is measured to calculate the energy transfer
Garcia-Munoz, M.; Hicks, N.; van Voornveld, R.; Classen, I.G.J.; Bilato, R.; Bobkov, V.; Bruedgam, M.; Fahrbach, H. U.; Igochine, V.; Jaemsae, S.; Maraschek, M.; Sassenberg, K.
2010-01-01
We present here the first phase-space characterization of convective and diffusive energetic particle losses induced by shear Alfven waves in a magnetically confined fusion plasma. While single toroidal Alfven eigenmodes (TAE) and Alfven cascades (AC) eject resonant fast ions in a convective process
Kinetic Alfv\\'en waves generation by large-scale phase-mixing
Vasconez, C L; Valentini, F; Servidio, S; Matthaeus, W H; Malara, F
2015-01-01
One view of the solar-wind turbulence is that the observed highly anisotropic fluctuations at spatial scales near the proton inertial length $d_p$ may be considered as Kinetic Alfv\\'en waves (KAWs). In the present paper, we show how phase-mixing of large-scale parallel propagating Alfv\\'en waves is an efficient mechanism for the production of KAWs at wavelengths close to $d_p$ and at large propagation angle with respect to the magnetic field. Magnetohydrodynamic (MHD), Hall-Magnetohydrodynamic (HMHD), and hybrid Vlasov-Maxwell (HVM) simulations modeling the propagation of Alfv\\'en waves in inhomogeneous plasmas are performed. In linear regime, the role of dispersive effects is singled out by comparing MHD and HMHD results. Fluctuations produced by phase-mixing are identified as KAWs through a comparison of polarization of magnetic fluctuations and wave group velocity with analytical linear predictions. In the nonlinear regime, comparison of HMHD and HVM simulations allows to point out the role of kinetic effe...
Torsional Alfven Waves in Solar Magnetic Flux Tubes of Axial Symmetry
Murawski, K; Musielak, Z E; Srivastava, A K; Kraskiewicz, J
2015-01-01
Aims: Propagation and energy transfer of torsional Alfv\\'en waves in solar magnetic flux tubes of axial symmetry is studied. Methods: An analytical model of a solar magnetic flux tube of axial symmetry is developed by specifying a magnetic flux and deriving general analytical formulae for the equilibrium mass density and a gas pressure. The main advantage of this model is that it can be easily adopted to any axisymmetric magnetic structure. The model is used to simulate numerically the propagation of nonlinear Alfv\\'en waves in such 2D flux tubes of axial symmetry embedded in the solar atmosphere. The waves are excited by a localized pulse in the azimuthal component of velocity and launched at the top of the solar photosphere, and they propagate through the solar chromosphere, transition region, and into the solar corona. Results: The results of our numerical simulations reveal a complex scenario of twisted magnetic field lines and flows associated with torsional Alfv\\'en waves as well as energy transfer to t...
Stimulated emission of fast Alfv\\'en waves within magnetically confined fusion plasmas
Cook, J W S; Chapman, S C
2016-01-01
A fast Alfv\\'en wave with finite amplitude is shown to grow by a stimulated emission process that we propose for exploitation in toroidal magnetically confined fusion plasmas. Stimulated emission occurs while the wave propagates inward through the outer mid-plane plasma, where a population inversion of the energy distribution of fusion-born ions is observed to arise naturally. Fully nonlinear first principles simulations, which self-consistently evolve particles and fields under the Maxwell-Lorentz system, demonstrate this novel "alpha-particle channelling" scenario for the first time.
Kinetic Alfv\\'{e}n solitary and rogue waves in superthermal plasmas
Bains, A; Xia, L -D
2014-01-01
We investigate the small but finite amplitude solitary Kinetic Alfv\\'{e}n waves (KAWs) in low $\\beta$ plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter $\\kappa$, plasma $\\beta$ and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfv\\'enic, compressive solitons are supported. We then extend the study to examine kinetic Alfv\\'en rogue waves by deriving a nonlinear Schr\\"{o}dinger equation from {the KdV} equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermal...
Upper-hybrid wave driven Alfvenic turbulence in magnetized dusty plasmas
Misra, A P
2010-01-01
The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations [J.Plasma Phys. 73, 3 (2006)] that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs is solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also shown to appear in the states of spatiotemporal coherence, temporal as well as spatiotemporal chaos due to collision and fusion among the patterns in stochastic motion. Furthermore, these spatiotemporal features are demonstrated by the analysis of wavelet power spectra. It is found that a redistribution of wave energy takes place to higher harmonic modes with small wavelengths which, in turn, ...
Characteristics of Short-wavelength Oblique Alfven and Slow waves
Zhao, J S; Yu, M Y; Lu, J Y; Wu, D J
2014-01-01
Linear properties of kinetic Alfv\\'en waves (KAWs) and kinetic slow waves (KSWs) are studied in the framework of two-fluid magnetohydrodynamics. We obtain the wave dispersion relations that are valid in a wide range of the wave frequency {\\omega} and plasma-to-magnetic pressure ratio {\\beta}. The KAW frequency can reach and exceed the ion cyclotron frequency at ion kinetic scales, whereas the KSW frequency remains sub-cyclotron. At {\\beta}\\sim1, the plasma and magnetic pressure perturbations of both modes are in anti-phase, so that there is nearly no total pressure perturbations. However, these modes exhibit several different properties. At high {\\beta}, the electric field polarization of KAW and KSW is opposite at the ion gyroradius scale, where KAWs are polarized in sense of electron gyration (right-hand polarized) and KSWs are left-hand polarized. The magnetic helicity {\\sigma}\\sim1 for KAWs and {\\sigma}\\sim-1 for KSWs, and the ion Alfv\\'en ratio R_{Ai}\\ll 1 for KAWs and R_{Ai}\\gg 1 for KSWs. We also found...
Clack, C T M; Douglas, M
2010-01-01
Resonant absorption of fast magnetoacoustic (FMA) waves in an inhomogeneous, weakly dissipative, one-dimensional planar, strongly anisotropic and dispersive plasma is investigated. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localised slow or Alfven waves present in the inhomogeneous layer and are partly reflected, dissipated and transmitted by this region. The presented research aims to find the coefficient of wave energy absorption under solar chromospheric and coronal conditions. Numerical results are analyzed to find the coefficient of wave energy absorption at both the slow and Alfven resonance positions. The mathematical derivations are based on the two simplifying assumptions that (i) nonlinearity is weak, and (ii) the thickness of the inhomogeneous layer is small in comparison to the wavelength of the wave, i.e. we empl...
Plasma acceleration by the interaction of parallel propagating Alfv\\'en waves
Mottez, Fabrice
2014-01-01
It is shown that two circularly polarised Alfv\\'en waves that propagate along the ambient magnetic field in an uniform plasma trigger non oscillating electromagnetic field components when they cross each other. The non-oscilliating field components can accelerate ions and electrons with great efficiency. This work is based on particle-in-cell (PIC) numerical simulations and on analytical non-linear computations. The analytical computations are done for two counter-propagating monochromatic waves. The simulations are done with monochromatic waves and with wave packets. The simulations show parallel electromagnetic fields consistent with the theory, and they show that the particle acceleration result in plasma cavities and, if the waves amplitudes are high enough, in ion beams. These acceleration processes could be relevant in space plasmas. For instance, they could be at work in the auroral zone and in the radiation belts of the Earth magnetosphere. In particular, they may explain the origin of the deep plasma...
Parametric decay of parallel and oblique Alfven waves in the expanding solar wind
Del Zanna, L; Landi, S; Verdini, A; Velli, M
2014-01-01
The long-term evolution of large-amplitude Alfven waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.
Phase Mixing of Alfv\\'en Waves Near a 2D Magnetic Null Point
McLaughlin, J A
2014-01-01
The propagation of linear Alfv\\'en wave pulses in an inhomogeneous plasma near a 2D coronal null point is investigated. When a uniform plasma density is considered, it is seen that an initially planar Alfv\\'en wavefront remains planar, despite the varying equilibrium Alfv\\'en speed, and that all the wave collects at the separatrices. Thus, in the non-ideal case, these Alfv\\'enic disturbances preferentially dissipate their energy at these locations. For a non-uniform equilibrium density, it is found that the Alfv\\'en wavefront is significantly distorted away from the initially planar geometry, inviting the possibility of dissipation due to phase mixing. Despite this however, we conclude that for the Alfv\\'en wave, current density accumulation and preferential heating still primarily occur at the separatrices, even when an extremely non-uniform density profile is considered.
Behavior of Torsional Alfven Waves and Field Line Resonance on Rotating Magnetars
Kojima, T O Y
2005-01-01
Torsional Alfven waves are likely excited with bursts in rotating magnetars. These waves are probably propagated through corotating atmospheres toward a vacuum exterior. We have studied the physical effects of the azimuthal wave number and the characteristic height of the plasma medium on wave transmission. In this work, explicit calculations were carried out based on the three-layered cylindrical model. We found that the coupling strength between the internal shear and the external Alfven modes is drastically enhanced, when resonance occurs in the corotating plasma cavity. The spatial structure of the electromagnetic fields in the resonance cavity is also investigated when Alfven waves exhibit resonance.
Alfv\\'en Wave Driven High Frequency Waves in the Solar Atmosphere: Implications for Ion Heating
Kaghashvili, Edisher Kh
2014-01-01
This work is an extension of Kaghashvili [1999] where ion-cyclotron wave dissipation channel for Alfv\\'en waves was discussed. While our earlier study dealt with the mode coupling in the commonly discussed sense, here we study changes in the initial waveform due to interaction of the initial driver Alfv\\'en wave and the plasma inhomogeneity, which are implicitly present in the equations, but were not elaborated in Kaghashvili [1999]. Using a cold plasma approximation, we show how high frequency waves (higher than the initial driver Alfv\\'en wave frequency) are generated in the inhomogeneous solar plasma flow. The generation of the high frequency forward and backward propagating modified fast magnetosonic/whistler waves as well as the generation of the driven Alfv\\'en waves is discussed in the solar atmosphere. The generated high frequency waves have a shorter dissipation timescale, and they can also resonant interact with particles using both the normal cyclotron and anomalous cyclotron interaction channels. ...
Vlasov simulations of Kinetic Alfv\\'en Waves at proton kinetic scales
Vasconez, C L; Camporeale, E; Veltri, P
2014-01-01
Kinetic Alfv\\'en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length $d_p$ and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfv\\'en waves at proton kinetic scales, in typical conditions of the solar wind environment. In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to $d_p$ and proton plasma beta $\\bet...
Parametric instabilities of large-amplitude parallel propagating Alfven waves: 2-D PIC simulation
Nariyuki, Yasuhiro; Hada, Tohru
2008-01-01
We discuss the parametric instabilities of large-amplitude parallel propagating Alfven waves using the 2-D PIC simulation code. First, we confirmed the results in the past study [Sakai et al, 2005] that the electrons are heated due to the modified two stream instability and that the ions are heated by the parallel propagating ion acoustic waves. However, although the past study argued that such parallel propagating longitudinal waves are excited by transverse modulation of parent Alfven wave, we consider these waves are more likely to be generated by the usual, parallel decay instability. Further, we performed other simulation runs with different polarization of the parent Alfven waves or the different ion thermal velocity. Numerical results suggest that the electron heating by the modified two stream instability due to the large amplitude Alfven waves is unimportant with most parameter sets.
Tholerus, Emmi; Hellsten, Torbjörn
2016-01-01
FOXTAIL is a new hybrid magnetohydrodynamic-kinetic code used to describe interactions between energetic particles and Alfv\\'en eigenmodes in tokamaks with realistic geometries. The code simulates the nonlinear dynamics of the amplitudes of individual eigenmodes and of a set of discrete markers in five-dimensional phase space representing the energetic particle distribution. Action-angle coordinates of the equilibrium system are used for efficient tracing of energetic particles, and the particle acceleration by the wave fields of the eigenmodes is Fourier decomposed in the same angles. The eigenmodes are described using temporally constant eigenfunctions with dynamic complex amplitudes. Possible applications of the code are presented, e.g., making a quantitative validity evaluation of the one-dimensional bump-on-tail approximation of the system. Expected effects of the fulfillment of the Chirikov criterion in two-mode scenarios have also been verified.
Similon, Philippe L.; Sudan, R. N.
1989-01-01
The importance of field line geometry for shear Alfven wave dissipation in coronal arches is demonstrated. An eikonal formulation makes it possible to account for the complicated magnetic geometry typical in coronal loops. An interpretation of Alfven wave resonance is given in terms of gradient steepening, and dissipation efficiencies are studied for two configurations: the well-known slab model with a straight magnetic field, and a new model with stochastic field lines. It is shown that a large fraction of the Alfven wave energy flux can be effectively dissipated in the corona.
Solitary Kinetic Alfven Waves in a Low-β Dusty Plasma
Institute of Scientific and Technical Information of China (English)
CHEN Yin-Hua; LU Wei
2000-01-01
The nonlinear kinetic Alfven waves in a low-β(0<β<1)dusty plasma have been investigated with the fluid model of three-component plasma. The nonlinear equation governing the perturbation density of electrons in a form of the energy integral has been derived. In the approximation of small amplitude, the soliton solution for the perturbation density of electrons is found, and the characteristics of solitons in different range of plasma parameters is studied numerically. The results show that the density dip or hump can be formed in a dusty plasma for different ranges of parameters, the amplitude of density dip is enhanced and the amplitude of density hump is reduced with increasing dust grain content.
Matsumoto, Takuma
2011-01-01
We report the results of the first two-dimensional self-consistent simulations directly covering from the photosphere to the interplanetary space. We carefully set up grid points with spherical coordinate to treat Alfv\\'enic waves in the atmosphere with the huge density contrast, and successfully simulate hot coronal wind streaming out as a result of surface convective motion. Footpoint motion excites upwardly propagating Alfv\\'enic waves along an open magnetic flux tube. These waves, traveling in non-uniform medium, suffer reflection, nonlinear mode conversion to compressive modes, and turbulent cascade. Combination of these mechanisms, the Alfv\\'enic waves eventually dissipate to accelerate the solar wind. While the shock heating by the dissipation of the compressive wave plays a primary role in the coronal heating, both turbulent cascade and shock heating contribute to drive the solar wind.
Transfer of Energy, Potential, and Current by Alfv\\'en Waves in Solar Flares
Melrose, D B
2013-01-01
Alfv\\'en waves play three related roles in the impulsive phase of a solar flare: they transport energy from a generator region to an acceleration region; they map the cross-field potential (associated with the driven energy release) from the generator region onto the acceleration region; and within the acceleration region they damp by setting up a parallel electric field that accelerates electrons and transfers the wave energy to them. The Alfv\\'en waves may also be regarded as setting up new closed current loops, with field-aligned currents that close across field lines at boundaries. A model is developed for large-amplitude Alfv\\'en waves that shows how Alfv\\'en waves play these roles in solar flares. A picket-fence structure for the current flow is incorporated into the model to account for the "number problem" and the energy of the accelerated electrons.
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Alfven Waves in a Plasma Sheet Boundary Layer Associated with Near-Tail Magnetic Reconnection
Institute of Scientific and Technical Information of China (English)
YUAN Zhi-Gang; DENG Xiao-Hua; PANG Ye; LI Shi-You; WANG Jing-Fang
2007-01-01
We report observations from Geotail satellite showing that large Poynting fluxes associated with Alfven waves in the plasma sheet boundary layer(PSBL) occur in the vicinity of the near-tail reconnection region on 10 December 1996.During the period of large Poynting fluxex,Geotail also observed strong tailward plasma flws.These observations demonstrate the importance of near-tail reconnection process as the energy source of Alfven waves in the PSBL.Strong tailward(Earthward)plasma flows ought to be an important candidate in generating Alfven waves.Furthermore,the strong pertutbations not only of the magnetic field but also of the electric field observed in the PSBL indicate that the PSBL plays an important role in the generation and propagation of the energy flux associated with Alfven waves.
Heating of the Solar Corona by Alfven Waves: Self-Induced Opacity
Zahariev, N I
2011-01-01
There have been derived equations describing the static distributions of temperature and wind velocity at the transition region within the framework of the magnetohydrodynamics (MHD) of fully ionized hydrogen plasma . We have also calculated the width of the transition between the chromosphere and corona as a self-induced opacity of the high-frequency Alfven waves (AWs). The domain wall is a direct consequence of the self-consistent MHD treatment of AWs propagation. We predict considerable spectral density of the high-frequency AWs in the photosphere. The idea that Alfven waves might heat the solar corona belong to Alfven - we simply derived the corresponding MHD equations. The comparison of the solutions to those equations with the observational/measured data will be crucial for revealing the heating mechanism. The analysis of those solutions will explain how Alfven waves brick unto the corona and dissipate their energy there.
Numerical simulations of impulsively generated Alfv\\'en waves in solar magnetic arcades
Chmielewski, P; Musielak, Z E; Srivastava, A K
2014-01-01
We perform numerical simulations of impulsively generated Alfv\\'en waves in an isolated solar arcade, which is gravitationally stratified and magnetically confined. We study numerically the propagation of Alfv\\'en waves along such magnetic structure that extends from the lower chromosphere, where the waves are generated, to the solar corona, and analyze influence of the arcade size and width of the initial pulses on the wave propagation and reflection. Our model of the solar atmosphere is constructed by adopting the temperature distribution based on the semi-empirical VAL-C model and specifying the curved magnetic field lines that constitute the asymmetric magnetic arcade. The propagation and reflection of Alfv\\'en waves in this arcade is described by 2.5D magnetohydrodynamic equations that are numerically solved by the FLASH code. Our numerical simulations reveal that the Alfv\\'en wave amplitude decreases as a result of a partial reflection of Alfv\\'en waves in the solar transition region, and that the waves...
Alfv\\'enic Wave Heating of the Upper Chromosphere in Flares
Reep, Jeffrey W
2016-01-01
We have developed a numerical model of flare heating due to the dissipation of Alfv\\'enic waves propagating from the corona to the chromosphere. With this model, we present an investigation of the key parameters of these waves on the energy transport, heating, and subsequent dynamics. For sufficiently high frequencies and perpendicular wave numbers, the waves dissipate significantly in the upper chromosphere, strongly heating it to flare temperatures. This heating can then drive strong chromospheric evaporation, bringing hot and dense plasma to the corona. We therefore find three important conclusions: (1) Alfv\\'enic waves, propagating from the corona to the chromosphere, are capable of heating the upper chromosphere and the corona, (2) the atmospheric response to heating due to the dissipation of Alfv\\'enic waves can be strikingly similar to heating by an electron beam, and (3) this heating can produce explosive evaporation.
Disperson relation of finite amplitude Alfven wave in a relativistic electron- positron plasma
Hada, T; Muñoz, V; Hada, Tohru; Matsukiyo, Shuichi; Munoz, Victor
2004-01-01
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfv\\'en wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one electromagnetic wave, with a low frequency cutoff at $\\sqrt{1+2\\omega_p^2/\\Omega_p^2}$ (where $\\omega_p=(4\\pi n e^2/m)^{1/2}$ is the electron/positron plasma frequency), and an Alfv\\'en wave, with high frequency cutoff at the positron gyrofrequency $\\Omega_p$. There is only one forward propagating mode for a given frequency. However, due to relativistic effects, there is no low frequency cutoff for the electromagnetic branch, and there appears a critical wave number above which the Alfv\\'en wave ceases to exist. This critical wave number is given by $ck_c/\\Omega_p=a/\\eta$, where $a=\\omega_p^2/\\Omega_p^2$ and $\\eta$ is the ratio between the Alfv\\'en wave magnetic field amplitude and the background magnetic field. In this case, for each frequency in the Alfv\\'en branch, two additional...
Threaded-Field-Lines Model for the Low Solar Corona Powered by the Alfven Wave Turbulence
Sokolov, Igor V; Manchester, Ward B; Ozturk, Doga Can Su; Szente, Judit; Taktakishvili, Aleksandre; Tóth, Gabor; Jin, Meng; Gombosi, Tamas I
2016-01-01
We present an updated global model of the solar corona, including the transition region. We simulate the realistic tree-dimensional (3D) magnetic field using the data from the photospheric magnetic field measurements and assume the magnetohydrodynamic (MHD) Alfv\\'en wave turbulence and its non-linear dissipation to be the only source for heating the coronal plasma and driving the solar wind. In closed field regions the dissipation efficiency in a balanced turbulence is enhanced. In the coronal holes we account for a reflection of the outward propagating waves, which is accompanied by generation of weaker counter-propagating waves. The non-linear cascade rate degrades in strongly imbalanced turbulence, thus resulting in colder coronal holes. The distinctive feature of the presented model is the description of the low corona as almost-steady-state low-beta plasma motion and heat flux transfer along the magnetic field lines. We trace the magnetic field lines through each grid point of the lower boundary of the g...
Zaqarashvili, T V; Soler, R
2012-01-01
Ion-neutral collisions may lead to the damping of Alfven waves in chromospheric and prominence plasmas. Neutral helium atoms enhance the damping in certain temperature interval, where the ratio of neutral helium and neutral hydrogen atoms is increased. Therefore, the height-dependence of ionization degrees of hydrogen and helium may influence the damping rate of Alfven waves. We aim to study the effect of neutral helium in the damping of Alfven waves in stratified partially ionized plasma of the solar chromosphere. We consider a magnetic flux tube, which is expanded up to 1000 km height and then becomes vertical due to merging with neighboring tubes, and study the dynamics of linear torsional Alfven waves in the presence of neutral hydrogen and neutral helium atoms. We start with three-fluid description of plasma and consequently derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfven waves. Thin flux tube approximation allows to obtain the dispersion relation of the waves in the lower pa...
Exploring the Use of Alfven Waves in Magnetometer Calibration at Geosynchronous Orbit
Bentley, John; Sheppard, David; RIch, Frederick; Redmon, Robert; Loto'aniu, Paul; Chu, Donald
2016-01-01
An Alfven wave is a type magnetohydrodynamicwave that travels through a conducting fluid under the influence of a magnetic field. Researchers have successfully calculated offset vectors of magnetometers in interplanetary space by optimizing the offset to maximize certain Alfvenic properties of observed waves (Leinweber, Belcher). If suitable Alfven waves can be found in the magnetosphere at geosynchronous altitude then these techniques could be used to augment the overall calibration plan for magnetometers in this region such as on the GOES spacecraft, possibly increasing the time between regular maneuvers. Calibration maneuvers may be undesirable because they disrupt the activities of other instruments. Various algorithms to calculate an offset using Alfven waves were considered. A new variation of the Davis-Smith method was derived because it can be mathematically shown that the Davis-Smith method tolerates filtered data, which expands potential applications. The variant developed was designed to find only the offset in the plane normal to the main field because the overall direction of Earth's magnetic field rarely changes, and theory suggests the Alfvenic disturbances occur transverse to the main field. Other variations of the Davis-Smith method encounter problems with data containing waves that propagate in mostly the same direction. A searching algorithm was then designed to look for periods of time with potential Alfven waves in GOES 15 data based on parameters requiring that disturbances be normal to the main field and not change field magnitude. Final waves for calculation were hand-selected. These waves produced credible two-dimensional offset vectors when input to the Davis-Smith method. Multiple two-dimensional solutions in different planes can be combined to get a measurement of the complete offset. The resulting three dimensional offset did not show sufficient precision over several years to be used as a primary calibration method, but reflected
Quantum Treatment of Kinetic Alfv\\'en Waves instability in a dusty plasma: Magnetized ions
Rubab, N
2016-01-01
The dispersion relation of kinetic Alfv\\'en wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum correction significantly influence the dispersion relation and the growth rate of instability.
Energy Technology Data Exchange (ETDEWEB)
Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)
2001-02-01
In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.
Stability of Global Alfven Waves (Tae, Eae) in Jet Tritium Discharges
Kerner, W.; Borba, D.; Huysmans, G. T. A.; Porcelli, F.; Poedts, S.; Goedbloed, J. P.; Betti, R.
1994-01-01
The interaction of alpha-particles in JET tritium discharges with global Alfven waves via inverse Landau damping is analysed. It is found that alpha-particle driven eigenmodes were stable in the PTE1 and should also be stable in a future 50:50 deuterium-tritium mix discharge aiming at Q(DT) = 1,
Overdamped Alfven waves due to ion-neutral collisions in the solar chromosphere
Soler, R; Zaqarashvili, T V
2014-01-01
Alfvenic waves are ubiquitous in the solar atmosphere and their dissipation may play an important role in atmospheric heating. In the partially ionized solar chromosphere, collisions between ions and neutrals are an efficient dissipative mechanism for Alfven waves with frequencies near the ion-neutral collision frequency. The collision frequency is proportional to the ion-neutral collision cross section for momentum transfer. Here, we investigate Alfven wave damping as a function of height in a simplified chromospheric model and compare the results for two sets of collision cross sections, namely those of the classic hard-sphere model and those based on recent quantum-mechanical computations. We find important differences between the results for the two sets of cross sections. There is a critical interval of wavelengths for which impulsively excited Alfven waves are overdamped as a result of the strong ion-neutral dissipation. The critical wavelengths are in the range from 1 km to 50 km for the hard-sphere cr...
Prokopov, P. A.; Zakharov, Yu P.; Tishchenko, V. N.; Shaikhislamov, I. F.; Boyarintsev, E. L.; Melekhov, A. V.; Ponomarenko, A. G.; Posukh, V. G.; Terekhin, V. A.
2016-11-01
Generation of Alfven waves propagating along external magnetic field B0 and Collisionless Shock Waves propagating across B0 are studied in experiments with laser- produced plasma and magnetized background plasma. The collisionless interaction of interpenetrating plasma flows takes place through a so-called Magnetic Laminar Mechanism (MLM) or Larmor Coupling. At the edge of diamagnetic cavity LP-ions produce induction electric field Eφ which accelerates BP-ions while LP-ions rotate in opposite direction. The ions movement generates sheared azimuthal magnetic field Bφ which could launches torsional Alfven wave. In previous experiments at KI-1 large scale facility a generation of strong perturbations propagating across B0 with magnetosonic speed has been studied at a moderate value of interaction parameter δ∼0.3. In the present work we report on experiments at conditions of 5∼R2 and large Alfven-Mach number MA∼10 in which strong transverse perturbations traveling at a scale of ∼1 m in background plasma at a density of ∼3*1013 cm-3 is observed. At the same conditions but smaller MA ∼ 2 a generation, the structure and dynamic of Alfven wave with wavelength ∼0.5 m propagating along fields B0∼100÷500 G for a distance of ∼2.5 m is studied.
Energy Technology Data Exchange (ETDEWEB)
Carrion, P.M.; Hasegawa, A.; Patton, W.; Prakash, M.
1988-06-01
A set of linearized magnetohydrodynamic equations was reduced to the reflectivity equation for the compressional magnetic perturbations in the framework of the Radoski model. It is shown that the reflection coeficient is a function of the inhomogeneities of the magnetic field, and the inhomogeneities of the Alfven velocity. An interesting property of the reflectivity equation is that, near Alfven resonant magnetic-force lines, this equation reduces to the curvature-free Budden equation. Near Alfven resonances, the curvature does not play a significant role and Budden's asymptotics in time can be applied to the wave field near the magnetic-force lines where the Alfven dispersion relation holds.
Effects of electron drift on the collisionless damping of kinetic Alfv\\'en waves in the solar wind
Tong, Yuguang; Chen, Christopher H K; Salem, Chadi S; Verscharen, Daniel
2015-01-01
The collisionless dissipation of anisotropic Alfv\\'enic turbulence is a promising candidate to solve the solar wind heating problem. Extensive studies examined the kinetic properties of Alfv\\'en waves in simple Maxwellian or bi-Maxwellian plasmas. However, the observed electron velocity distribution functions in the solar wind are more complex. In this study, we analyze the properties of kinetic Alfv\\'en waves in a plasma with two drifting electron populations. We numerically solve the linearized Maxwell-Vlasov equations and find that the damping rate and the proton-electron energy partition for kinetic Alfv\\'en waves are significantly modified in such plasmas, compared to plasmas without electron drifts. We suggest that electron drift is an important factor to take into account when considering the dissipation of Alfv\\'enic turbulence in the solar wind or other $\\beta \\sim 1$ astrophysical plasmas.
Experimental evidence of Alfv\\'en wave propagation in a Gallium alloy
Alboussiere, Thierry; Debray, François; La Rizza, Patrick; Masson, Jean-Paul; Plunian, Franck; Ribeiro, Adolfo; Schmitt, Denys
2011-01-01
Experiments with a liquid metal alloy, galinstan, are reported and show clear evidence of Alfv\\'en wave propagation as well as resonance of Alfv\\'en modes. Galinstan is liquid at room temperature, and although its electrical conductivity is not as large as that of liquid sodium or NaK, it has still been possible to study Alfv\\'en waves, thanks to the use of intense magnetic fi elds, up to 13 teslas. The maximal values of Lundquist number, around 60, are similar to that of the reference experimental study by Jameson [1]. The generation mechanism for Alfv\\'en waves and their refl ection is studied carefully. Numerical simulations have been performed and have been able to reproduce the experimental results despite the fact that the simulated magnetic Prandtl number was much larger than that of galinstan. An originality of the present study is that a poloidal disturbance (magnetic and velocity fields) is generated, allowing us to track its propagation from outside the conducting domain, hence without interfering.
Cut-off wavenumber of Alfven waves in partially ionized plasmas of the solar atmosphere
Zaqarashvili, T V; Ballester, J L; Khodachenko, M L
2012-01-01
Alfven wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cut-off wavenumber, i.e. the Alfven waves with wavenumbers higher than the cut-off value are evanescent. The cut-off wavenumber appears in single-fluid magnetohydrodynamic (MHD) approximation but it is absent in a multi-fluid approach. Up to now, an explanation for the existence of the cut-off wavenumber is still missing. The aim of this paper is to point out the reason for the appearance of a cut-off wavenumber in single-fluid MHD. Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description is obtained. We solved the dispersion relation of linear Alfven waves at each step and sought the approximation responsible of the cut-off wavenumber appearance. We have found that neglecting inertial terms significantly reduces the real part of the Alfven frequency although it never becomes zero. T...
Alfven wave coupled with flow-driven fluid instability in interpenetrating plasmas
Vranjes, J
2015-01-01
The Alfven wave is analyzed in case of one quasineutral plasma propagating with some constant speed $v_0$ through another static quasineutral plasma. A dispersion equation is derived describing the Alfven wave coupled with the flow driven mode $\\omega= k v_0$ and solutions are discussed analytically and numerically. The usual solutions for two oppositely propagating Alfv\\'en waves are substantially modified due to the flowing plasma. More profound is modification of the solution propagating in the negative direction with respect to the magnetic field and the plasma flow. For a large enough flow speed (exceeding the Alfven speed in the static plasma), this negative solution may become non-propagating, with frequency equal to zero. In this case it represents a spatial variation of the electromagnetic field. For greater flow speed it becomes a forward mode, and it may merge with the positive one. This merging of the two modes represents the starting point for a flow-driven instability, with two complex-conjugate...
3D Alfven wave behaviour around proper and improper magnetic null points
Thurgood, J O
2013-01-01
Context: MHD waves and magnetic null points are both prevalent in many astrophysical plasmas, including the solar atmosphere. Interaction between waves and null points has been implicated as a possible mechanism for localised heating events. Aims: Here we investigate the transient behaviour of the Alfven wave about fully 3D proper and improper 3D magnetic null points. Previously, the behaviour of fast magnetoacoustic waves at null points in 3D, cold MHD was considered by Thurgood & McLaughlin (Astronomy & Astrophysics, 2012, 545, A9). Methods: We introduce an Alfven wave into the vicinity of both proper and improper null points by numerically solving the ideal, $\\beta=0$ MHD equations using the LARE3D code. A magnetic fieldline and flux-based coordinate system permits the isolation of resulting wave-modes and the analysis of their interaction. Results: We find that the Alfven wave propagates throughout the region and accumulates near the fan-plane, causing current build up. For different values of nul...
Small scales formation via Alfven wave propagation in compressible nonuniform media
Malara, F.; Primavera, L.; Veltri, P.
1995-01-01
In weakly dissipative media governed by the magnetohydrodynamics (MHD) equations, any efficient mechanism of energy dissipation requires the formation of small scales. The possibility to produce small scales has been studied by Malara et al. in the case of MHD disturbances propagating in an incompressible and inhomogeneous medium, for a strictly 2D geometry. We extend the work of Malara et al. to include both compressibility and the third component for vector quantities. Using numerical simulations we show that, when an Alfven wave propagates in a compressible nonuniform medium, the two dynamical effects responsible for the small scales formation in the incompressible case are still at work: energy pinching and phase-mixing. Moreover, the interaction between the initial Alfven wave and the inhomogeneity gives rise to the formation of compressible perturbations (fast and slow waves or a static entropy wave). Some of these compressive fluctuations are subject to the steepening of the wave front and become shock waves, which are extremely efficient in dissipating their energy, their dissipation being independent of the Reynolds number. A rough estimate of the typical times which the various dynamical processes take to produce small scales and then to dissipate the energy show that these times are consistent with those required to dissipate inside the solar corona the energy of Alfven waves of photospheric origin.
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Parametric instabilities of parallel propagating,circularly polarized Alfv\\'en waves in a uniform background plasma is studied, within a framework of one-dimensional Vlasov equation for ions and massless electron fluid, so that kinetic perturbations in the longitudinal direction (ion Landau damping) are included. The present formulation also includes the Hall effect. The obtained results agree well with relevant analysis in the past, suggesting that kinetic effects in the longitudinal direction play essential roles in the parametric instabilities of Alfven waves when the kinetic effects react "passively". Furthermore, existence of the kinetic parametric instabilities is confirmed for the regime with small wave number daughter waves. Growth rates of these instabilities are sensitive to ion temperature.
Chandran, Benjamin D G; Quataert, Eliot; Bale, Stuart D
2011-01-01
We develop a 1D solar-wind model that includes separate energy equations for the electrons and protons, proton temperature anisotropy, collisional and collisionless heat flux, and an analytical treatment of low-frequency, reflection-driven, Alfven-wave turbulence. To partition the turbulent heating between electron heating, parallel proton heating, and perpendicular proton heating, we employ results from the theories of linear wave damping and nonlinear stochastic heating. We account for mirror and oblique firehose instabilities by increasing the proton pitch-angle scattering rate when the proton temperature anisotropy exceeds the threshold for either instability. We numerically integrate the equations of the model forward in time until a steady state is reached, focusing on two fast-solar-wind-like solutions. These solutions are consistent with a number of observations, supporting the idea that Alfven-wave turbulence plays an important role in the origin of the solar wind.
A global 3-D MHD model of the solar wind with Alfven waves
Usmanov, A. V.
1995-01-01
A fully three-dimensional solar wind model that incorporates momentum and heat addition from Alfven waves is developed. The proposed model upgrades the previous one by considering self-consistently the total system consisting of Alfven waves propagating outward from the Sun and the mean polytropic solar wind flow. The simulation region extends from the coronal base (1 R(sub s) out to beyond 1 AU. The fully 3-D MHD equations written in spherical coordinates are solved in the frame of reference corotating with the Sun. At the inner boundary, the photospheric magnetic field observations are taken as boundary condition and wave energy influx is prescribed to be proportional to the magnetic field strength. The results of the model application for several time intervals are presented.
Effect of Alfven resonance on low-frequency fast wave current drive
Energy Technology Data Exchange (ETDEWEB)
Wang, C.Y.; Batchelor, D.B.; Carter, M.D.; Jaeger, E.F.; Stallings, D.C. [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States)
1995-07-01
The Alfven resonances may occur on the low- and high-field sides for a low-frequency fast wave current drive scenario proposed for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion {bold 31}, 1135 (1991)]. At the resonance on the low-field side, the fast wave may be mode converted into a short-wavelength slow wave, which can be absorbed by electrons at the plasma edge, before the fast wave propagates into the core area of the plasma. Such absorption may cause a significant parasitic power loss. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
Mithaiwala, Manish; Crabtree, Chris; Ganguli, Gurudas
2012-01-01
It is shown that the dispersion relation for whistler waves is identical for a high or low beta plasma. Furthermore in the high-beta solar wind plasma whistler waves meet the Landau resonance with electrons for velocities less than the thermal speed, and consequently the electric force is small compared to the mirror force. As whistlers propagate through the inhomogeneous solar wind, the perpendicular wave number increases through refraction, increasing the Landau damping rate. However, the whistlers can survive because the background kinetic Alfven wave turbulence creates a plateau by quasilinear diffusion in the solar wind electron distribution at small velocities. It is found that for whistler energy density of only ~10^-3 that of the kinetic Alfven waves, the quasilinear diffusion rate due to whistlers is comparable to KAW. Thus very small amplitude whistler turbulence can have a significant consequence on the evolution of the solar wind electron distribution function.
On the reflection of Alfv\\'en waves and its implication for Earth's core modeling
Schaeffer, Nathanaël; Cardin, Philippe; Marie, Drouard
2011-01-01
Alfv\\'en waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case Pm=1, there is no reflection on an insulating, no-slip boundary, and the wave energy is entirely dissipated in the boundary layer. We investigate the consequences of this remarkable behaviour for the numerical modeling of torsional Alfv\\'en waves (also known as torsional oscillations), which represent a special class of Alfv\\'en waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal modes.
Energy densities of Alfven waves between 0.7 and 1.6 AU. [in interplanetary medium
Belcher, J. W.; Burchsted, R.
1974-01-01
Plasma and field data from Mariner 4 and 5 between 0.7 and 1.6 AU are used to study the radial dependence of the levels of microscale fluctuation associated with interplanetary Alfven waves. The observed decrease of these levels with increasing distance from the sun is consistent with little or no local generation or damping of the ambient Alfven waves over this range of radial distance.
Inbound waves in the solar corona: a direct indicator of Alfv\\'en Surface location
DeForest, C E; McComas, D J
2014-01-01
The tenuous supersonic solar wind that streams from the top of the corona passes through a natural boundary -- the Alfv\\'en surface -- that marks the causal disconnection of individual packets of plasma and magnetic flux from the Sun itself. The Alfv\\'en surface is the locus where the radial motion of the accelerating solar wind passes the radial Alfv\\'en speed, and therefore any displacement of material cannot carry information back down into the corona. It is thus the natural outer boundary of the solar corona, and the inner boundary of interplanetary space. Using a new and unique motion analysis to separate inbound and outbound motions in synoptic visible-light image sequences from the COR2 coronagraph on board the STEREO-A spacecraft, we have identified inbound wave motion in the outer corona beyond 6 solar radii for the first time, and used it to determine that the Alfv\\'en surface is at least 12.5 solar radii from the Sun over the polar coronal holes and 17 solar radii in the streamer belt, well beyond ...
Generation of Alfvenic Waves and Turbulence in Magnetic Reconnection Jets
Hoshino, M.
2014-12-01
The magneto-hydro-dynamic (MHD) linear stability for the plasma sheet with a localized bulk plasma flow parallel to the neutral sheet is investigated. We find three different unstable modes propagating parallel to the anti-parallel magnetic field line, and we call them as "streaming tearing'', "streaming sausage'', and "streaming kink'' mode. The streaming tearing and sausage modes have the tearing mode-like structure with symmetric density fluctuation to the neutral sheet, and the streaming kink mode has the asymmetric fluctuation. The growth rate of the streaming tearing mode decreases with increasing the magnetic Reynolds number, while those of the streaming sausage and kink modes do not strongly depend on the Reynolds number. The wavelengths of these unstable modes are of the order of the thickness of plasma sheet, which behavior is almost same as the standard tearing mode with no bulk flow. Roughly speaking the growth rates of three modes become faster than the standard tearing mode. The situation of the plasma sheet with the bulk flow can be realized in the reconnection exhaust with the Alfvenic reconnection jet, and the unstable modes may be regarded as one of the generation processes of Alfvenic turbulence in the plasma sheet during magnetic reconnection.
Formation of quasiparallel Alfven solitons
Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.
1992-01-01
The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.
Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes
Goossens, Marcel; Ruderman, Michail S.; Hollweg, Joseph V.
1995-01-01
The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.
Alfv\\'en Wave Heating of the Solar Chromosphere: 1.5D models
Arber, T D; Shelyag, S
2015-01-01
Physical processes which may lead to solar chromospheric heating are analyzed using high-resolution 1.5D non-ideal MHD modelling. We demonstrate that it is possible to heat the chromospheric plasma by direct resistive dissipation of high-frequency Alfv\\'en waves through Pedersen resistivity. However this is unlikely to be sufficient to balance radiative and conductive losses unless unrealistic field strengths or photospheric velocities are used. The precise heating profile is determined by the input driving spectrum since in 1.5D there is no possibility of Alfv\\'en wave turbulence. The inclusion of the Hall term does not affect the heating rates. If plasma compressibility is taken into account, shocks are produced through the ponderomotive coupling of Alfv\\'en waves to slow modes and shock heating dominates the resistive dissipation. In 1.5D shock coalescence amplifies the effects of shocks and for compressible simulations with realistic driver spectra the heating rate exceeds that required to match radiative...
Spectroscopic Observations and Modelling of Impulsive Alfv\\'en Waves Along a Polar Coronal Jet
Jelínek, P; Murawski, K; Kayshap, P; Dwivedi, B N
2015-01-01
Using the Hinode/EIS 2$"$ spectroscopic observations, we study the intensity, velocity, and FWHM variations of the strongest Fe XII 195.12 \\AA\\ line along the jet to find the signature of Alfv\\'en waves. We simulate numerically the impulsively generated Alfv\\'en waves within the vertical Harris current-sheet, forming the jet plasma flows, and mimicking their observational signatures. Using the FLASH code and the atmospheric model with embedded weakly expanding magnetic field configuration within a vertical Harris current-sheet, we solve the two and half-dimensional (2.5-D) ideal magnetohydrodynamic (MHD) equations to study the evolution of Alfv\\'en waves and vertical flows forming the plasma jet. At a height of $\\sim 5~\\mathrm{Mm}$ from the base of the jet, the red-shifted velocity component of Fe XII 195.12 \\AA\\ line attains its maximum ($5~\\mathrm{km\\,s}^{-1}$) which converts into a blue-shifted one between the altitude of $5-10~\\mathrm{Mm}$. The spectral intensity continously increases up to $10~\\mathrm{Mm...
2D continuous spectrum of shear Alfven waves in the presence of a magnetic island
Biancalani, Alessandro; Pegoraro, Francesco; Zonca, Fulvio
2010-01-01
The radial structure of the continuous spectrum of shear Alfven modes is calculated in the presence of a magnetic island in tokamak plasmas. Modes with the same helicity of the magnetic island are considered in a slab model approximation. In this framework, with an appropriate rotation of the coordinates the problem reduces to 2 dimensions. Geometrical effects due to the shape of the flux surfaceâs cross section are retained to all orders. On the other hand, we keep only curvature effects responsible of the beta induced gap in the low-frequency part of the continuous spectrum. New continuum accumulation points are found at the O-point of the magnetic island. The beta-induced Alfven Eigenmodes (BAE) continuum accumulation point is found to be positioned at the separatrix flux surface. The most remarkable result is the nonlinear modification of the BAE continuum accumulation point frequency.
Shukla, P K
2012-01-01
It is shown that a three-dimensional (3D) modified-kinetic Alfv\\'en waves (m-KAWs) can propagate in the form of Alfv\\'enic tornadoes characterized by plasma density whirls or magnetic flux ropes carrying orbital angular momentum (OAM). By using the two fluid model, together with Amp\\`ere's law, we derive the wave equation for a 3D m-KAWs in a magnetoplasma with $m_e/m_i \\ll \\beta \\ll 1$, where $m_e$ $(m_i)$ is the electron (ion) mass, $\\beta =4 \\pi n_0 k_B (T_e + T_i)/B_0^2$, $n_0$ the unperturbed plasma number density, $k_B$ the Boltzmann constant, $T_e (T_e)$ the electron (ion) temperature, and $B_0$ the strength of the ambient magnetic field. The 3D m-KAW equation admits solutions in the form of a Laguerre-Gauss (LG) Alfv\\'enic vortex beam or Alfv\\'enic tornadoes with plasma density whirls that support the dynamics of Alfv\\'en magnetic flux ropes.
Resonant Alfven waves in partially ionized plasmas of the solar atmosphere
Soler, R; Goossens, M
2011-01-01
Context. Magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. In magnetic waveguides resonant absorption due to plasma inhomogeneity naturally transfers wave energy from large-scale motions to small-scale motions. In the cooler parts of the solar atmosphere as, e.g., the chromosphere, effects due to partial ionization may be relevant for wave dynamics and heating. Aims. We study resonant Alfven waves in partially ionized plasmas. Methods. We use the multifluid equations in the cold plasma approximation. We investigate propagating resonant MHD waves in partially ionized flux tubes. We use approximate analytical theory based on normal modes in the thin tube and thin boundary approximations along with numerical eigenvalue computations. Results. We find that the jumps of the wave perturbations across the resonant layer are the same as in fully ionized plasmas. The damping length due to resonant absorption is inversely proportional to the frequency, while that due to ion-neutral collisions is in...
The role of Alfv\\'en wave heating in solar prominences
Soler, Roberto; Oliver, Ramon; Ballester, Jose Luis
2016-01-01
Observations have shown that magnetohydrodynamic waves over a large frequency range are ubiquitous in solar prominences. The waves are probably driven by photospheric motions and may transport energy up to prominences suspended in the corona. Dissipation of wave energy can lead to heating of the cool prominence plasma, so contributing to the local energy balance within the prominence. Here we discuss the role of Alfv\\'en wave dissipation as a heating mechanism for the prominence plasma. We consider a slab-like quiescent prominence model with a transverse magnetic field embedded in the solar corona. The prominence medium is modelled as a partially ionized plasma composed of a charged ion-electron single fluid and two separate neutral fluids corresponding to neutral hydrogen and neutral helium. Friction between the three fluids acts as a dissipative mechanism for the waves. The heating caused by externally-driven Alfv\\'en waves incident on the prominence slab is analytically explored. We find that the dense pro...
Plastic damping of Alfv\\'en waves in magnetar flares and delayed afterglow emission
Li, Xinyu
2015-01-01
Magnetar flares generate Alfv\\'en waves bouncing in the closed magnetosphere with energy up to $\\sim 10^{46}$ erg. We show that on a 10-ms timescale the waves are transmitted into the star and form a compressed packet of high energy density. This packet strongly shears the stellar crust and initiates a plastic flow, heating the crust and melting it hundreds of meters below the surface. A fraction of the deposited plastic heat is eventually conducted to the stellar surface, contributing to the surface afterglow months to years after the flare. A large fraction of heat is lost to neutrino emission or conducted into the core of the neutron star.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Bierwage, Andreas; Spong, Donald A.
2009-05-01
Hybrid-MHD-Gyrokinetic Code (HMGC) [1] and the gyrofluid code TAEFL [2,3] are used for nonlinear simulation of Alfven Eigenmodes in Tokamak plasma. We compare results obtained in two cases: (I) a case designed for cross-code benchmark of TAE excitation; (II) a case based on a dedicated DIII-D shot #132707 where RSAE and TAE activity is observed. Differences between the numerical simulation results are discussed and future directions are outlined. [1] S. Briguglio, G. Vlad, F. Zonca and C. Kar, Phys. Plasmas 2 (1995) 3711. [2] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Fluids B4 (1992) 3316. [3] D.A. Spong, B.A. Carreras and C.L. Hedrick, Phys. Plasmas 1 (1994) 1503.
Experimental evidence of Alfven wave propagation in a Gallium alloy
2011-01-01
10p.; International audience; Experiments with a liquid metal alloy, galinstan, are reported and show clear evidence of Alfvén wave propagation as well as resonance of Alfvén modes. Galinstan is liquid at room temperature, and although its electrical conductivity is not as large as that of liquid sodium or NaK, it has still been possible to study Alfvén waves, thanks to the use of intense magnetic fi elds, up to 13 teslas. The maximal values of Lundquist number, around 60, are similar to that...
Nonlinear waves in the terrestrial quasi-parallel foreshock
Hnat, B; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-01-01
We study the applicability of the derivative nonlinear Schr\\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a pseudo-potential is elucidated and, in particular, the importance of canonical representation in the correct interpretation of solutions in this formulation is discussed. Numerical solutions of the DNLS equation are then compared directly with the wave forms observed by Cluster spacecraft. Non harmonic slow variations are filtered out by applying the empirical mode decomposition. We find large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency, followed in time by nearly harmonic low amplitude fluctuations. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfv\\'{e}n speed.
Burgulence and Alfv\\'en waves heating mechanism of solar corona
Mishonov, T M
2006-01-01
Heating of magnetized turbulent plasma is calculated in the framework of Burgers turbulence [A.M. Polyakov, Phys. Rev. E. 52, 6183, (1995)]. There is calculated the energy flux of Alfv\\'en waves along the magnetic field. The Alfven waves are considered as intermediary between the turbulent energy and the heat. The derived results are related to wave channel of the heating of solar corona. After incorporating dissipation of convective plasma waves instabilities [G.D. Chagelishvili, R.G. Chanishvili, T.S. Hristov, and J.G. Lominadze, Phys. Rev. E 47, 366 (1993)] and [A.D. Rogava, S.M. Mahajan, G. Bodo, and S. Marsaglia, Astronomy & Astrophysics, 399, 421-431 (2003)] the suggested model of heating can be applied to analysis of the missing viscosity of accretion discs and to reveal why the quasars are the most powerful sources of light in the universe. We suppose that applied Langevin-Burgers approach to turbulence can be helpful for other systems where we have intensive interaction between a stochastic turbu...
Shukla, P. K.
2012-01-01
It is shown that a three-dimensional (3D) modified-kinetic Alfv\\'en waves (m-KAWs) can propagate in the form of Alfv\\'enic tornadoes characterized by plasma density whirls or magnetic flux ropes carrying orbital angular momentum (OAM). By using the two fluid model, together with Amp\\`ere's law, we derive the wave equation for a 3D m-KAWs in a magnetoplasma with $m_e/m_i \\ll \\beta \\ll 1$, where $m_e$ $(m_i)$ is the electron (ion) mass, $\\beta =4 \\pi n_0 k_B (T_e + T_i)/B_0^2$, $n_0$ the unpert...
Studies of the Jet in BL Lacertae. II. Superluminal Alfv\\'en Waves
Cohen, M H; Arshakian, T G; Clausen-Brown, E; Homan, D C; Hovatta, T; Kovalev, Y Y; Lister, M L; Pushkarev, A B; Richards, J L; Savolainen, T
2014-01-01
Ridge lines on the pc-scale jet of the active galactic nucleus BL Lac display transverse patterns that move superluminally downstream. The patterns are not ballistic, but are analogous to waves on a whip. Their apparent speeds $\\beta_\\mathrm{app}$ (units of $c$) range from 4.2 to 13.5, corresponding to $\\beta_\\mathrm{wave}^\\mathrm{gal}= 0.981 - 0.998$ in the galaxy frame. We show that the magnetic field in the jet is well-ordered with a strong transverse component, and assume that it is helical and that the transverse patterns are longitudinal Alfv\\'en waves. The wave-induced transverse speed of the jet is non-relativistic ($\\beta_\\mathrm{tr}^\\mathrm{gal}\\sim 0.09$) and in agreement with our assumption of low-amplitude waves. In 2010 the wave activity subsided and the jet displayed a mild wiggle that had a complex oscillatory behavior. The waves are excited by changes in the position angle of the recollimation shock, in analogy to exciting a wave on a whip by shaking it. Simple models of the system are presen...
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Two-wave interaction in ideal magnetohydrodynamics
T. V. Zaqarashvili; Roberts, B.
2006-01-01
The weakly nonlinear interaction of sound and linearly polarised Alfv{\\'e}n waves propagating in the same direction along an applied magnetic field is studied. It is found that a sound wave is coupled to the Alfv{\\'e}n wave with double period and wavelength when the sound and Alfv{\\'e}n speeds are equal. The Alfv{\\'e}n wave drives the sound wave through the ponderomotive force, while the sound wave returns energy back to the Alfv{\\'e}n wave through the parametric (swing) influence. As a resul...
Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence
Galtier, S
2014-01-01
The role of magnetic helicity is investigated in kinetic Alfv\\'en wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0 {\\bf e_\\parallel}$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \\& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\\tilde n = -6$, where $n$ and $\\tilde n$ are the power law indices of the perpendicular (to ${\\bf b_0}$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\\tilde n = - 3.5$,...
Propagation of Alfv\\'enic Waves From Corona to Chromosphere and Consequences for Solar Flares
Russell, Alexander J B
2013-01-01
How do magnetohydrodynamic waves travel from the fully ionized corona, into and through the underlying partially ionized chromosphere, and what are the consequences for solar flares? To address these questions, we have developed a 2-fluid model (of plasma and neutrals) and used it to perform 1D simulations of Alfv\\'en waves in a solar atmosphere with realistic density and temperature structure. Studies of a range of solar features (faculae, plage, penumbra and umbra) show that energy transmission from corona to chromosphere can exceed 20% of incident energy for wave periods of one second or less. Damping of waves in the chromosphere depends strongly on wave frequency: waves with periods 10 seconds or longer pass through the chromosphere with relatively little damping, however, for periods of 1 second or less, a substantial fraction (37%-100%) of wave energy entering the chromosphere is damped by ion-neutral friction in the mid and upper chromosphere, with electron resistivity playing some role in the lower ch...
Roles of Fast-Cyclotron and Alfven-Cyclotron Waves for the Multi-Ion Solar Wind
Xiong, Ming
2012-01-01
Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave-particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfven waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. We assume that (1) low-frequency Alfven and fast waves have the same spectral shape and the same amplitude of power spectral density; (2) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade; (3) kinetic wave-particle interaction powers the solar wind. The existence of alpha particles in a dominant proton/electron plasma can trigger linear mode conversion between oblique fast-whistler and hybrid alpha-proton cyclotron waves. The fast-cyclotron waves undergo both alpha and proton cyclotron resonances. The alpha cyclotron resonance in fast-cyclotron waves is much stronger than that in Alfven-cyclotron waves. ...
Focusing of Alfvenic wave power in the context of gamma-ray burst emissivity
Fatuzzo, Marco; Melia, Fulvio
1993-01-01
Highly dynamic magnetospheric perturbations in neutron star environments can naturally account for the features observed in gamma-ray burst spectra. The source distribution, however, appears to be extragalactic. Although noncatastrophic isotropic emission mechanisms may be ruled out on energetic and timing arguments, MHD processes can produce strongly anisotropic gamma rays with an observable flux out to distances of about 1-2 Gpc. Here we show that sheared Alfven waves propagating along open magnetospheric field lines at the poles of magnetized neutron stars transfer their energy dissipationally to the current sustaining the field misalignment and thereby focus their power into a spatial region about 1000 times smaller than that of the crustal disturbance. This produces a strong (observable) flux enhancement along certain directions. We apply this model to a source population of 'turned-off' pulsars that have nonetheless retained their strong magnetic fields and have achieved alignment at a period of approximately greater than 5 sec.
Energy Technology Data Exchange (ETDEWEB)
Evans, R. M. [NASA Goddard Space Flight Center, Space Weather Lab, Greenbelt, MD 20771 (United States); Opher, M. [Astronomy Department, Boston University, 675 Commonwealth Avenue, Boston, MA 02215 (United States); Oran, R.; Van der Holst, B.; Sokolov, I. V.; Frazin, R.; Gombosi, T. I. [Center for Space Environment Modeling, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 (United States); Vasquez, A., E-mail: Rebekah.e.frolov@nasa.gov [Instituto de Astronomia y Fisica del Espacio (CONICET-UBA) and FCEN (UBA), CC 67, Suc 28, Ciudad de Buenos Aires (Argentina)
2012-09-10
The heating and acceleration of the solar wind is an active area of research. Alfven waves, because of their ability to accelerate and heat the plasma, are a likely candidate in both processes. Many models have explored wave dissipation mechanisms which act either in closed or open magnetic field regions. In this work, we emphasize the boundary between these regions, drawing on observations which indicate unique heating is present there. We utilize a new solar corona component of the Space Weather Modeling Framework, in which Alfven wave energy transport is self-consistently coupled to the magnetohydrodynamic equations. In this solar wind model, the wave pressure gradient accelerates and wave dissipation heats the plasma. Kolmogorov-like wave dissipation as expressed by Hollweg along open magnetic field lines was presented in van der Holst et al. Here, we introduce an additional dissipation mechanism: surface Alfven wave (SAW) damping, which occurs in regions with transverse (with respect to the magnetic field) gradients in the local Alfven speed. For solar minimum conditions, we find that SAW dissipation is weak in the polar regions (where Hollweg dissipation is strong), and strong in subpolar latitudes and the boundaries of open and closed magnetic fields (where Hollweg dissipation is weak). We show that SAW damping reproduces regions of enhanced temperature at the boundaries of open and closed magnetic fields seen in tomographic reconstructions in the low corona. Also, we argue that Ulysses data in the heliosphere show enhanced temperatures at the boundaries of fast and slow solar wind, which is reproduced by SAW dissipation. Therefore, the model's temperature distribution shows best agreement with these observations when both dissipation mechanisms are considered. Lastly, we use observational constraints of shock formation in the low corona to assess the Alfven speed profile in the model. We find that, compared to a polytropic solar wind model, the wave
Clack, C
2009-01-01
The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas, 15, 2310 (2008)] and Alfv\\'en resonance by Clack \\emph{et al.} [A&A,494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfv\\'{e}n dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of ener...
Hybrid Model of Inhomogeneous Solar Wind Plasma Heating by Alfven Wave Spectrum: Parametric Studies
Ofman, L.
2010-01-01
Observations of the solar wind plasma at 0.3 AU and beyond show that a turbulent spectrum of magnetic fluctuations is present. Remote sensing observations of the corona indicate that heavy ions are hotter than protons and their temperature is anisotropic (T(sub perpindicular / T(sub parallel) >> 1). We study the heating and the acceleration of multi-ion plasma in the solar wind by a turbulent spectrum of Alfvenic fluctuations using a 2-D hybrid numerical model. In the hybrid model the protons and heavy ions are treated kinetically as particles, while the electrons are included as neutralizing background fluid. This is the first two-dimensional hybrid parametric study of the solar wind plasma that includes an input turbulent wave spectrum guided by observation with inhomogeneous background density. We also investigate the effects of He++ ion beams in the inhomogeneous background plasma density on the heating of the solar wind plasma. The 2-D hybrid model treats parallel and oblique waves, together with cross-field inhomogeneity, self-consistently. We investigate the parametric dependence of the perpendicular heating, and the temperature anisotropy in the H+-He++ solar wind plasma. It was found that the scaling of the magnetic fluctuations power spectrum steepens in the higher-density regions, and the heating is channeled to these regions from the surrounding lower-density plasma due to wave refraction. The model parameters are applicable to the expected solar wind conditions at about 10 solar radii.
Alfv\\'en wave phase-mixing and damping in the ion cyclotron range of frequencies
Threlfall, J W; De Moortel, I
2010-01-01
Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfv\\'en waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k^2di^2 where k is wavenumber and di is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k^2di^2>>1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispers...
Hybrid Model of Inhomogeneous Solar Wind Plasma Heating by Alfven Wave Spectrum: Parametric Studies
Ofman, L.
2010-01-01
Observations of the solar wind plasma at 0.3 AU and beyond show that a turbulent spectrum of magnetic fluctuations is present. Remote sensing observations of the corona indicate that heavy ions are hotter than protons and their temperature is anisotropic (T(sub perpindicular / T(sub parallel) >> 1). We study the heating and the acceleration of multi-ion plasma in the solar wind by a turbulent spectrum of Alfvenic fluctuations using a 2-D hybrid numerical model. In the hybrid model the protons and heavy ions are treated kinetically as particles, while the electrons are included as neutralizing background fluid. This is the first two-dimensional hybrid parametric study of the solar wind plasma that includes an input turbulent wave spectrum guided by observation with inhomogeneous background density. We also investigate the effects of He++ ion beams in the inhomogeneous background plasma density on the heating of the solar wind plasma. The 2-D hybrid model treats parallel and oblique waves, together with cross-field inhomogeneity, self-consistently. We investigate the parametric dependence of the perpendicular heating, and the temperature anisotropy in the H+-He++ solar wind plasma. It was found that the scaling of the magnetic fluctuations power spectrum steepens in the higher-density regions, and the heating is channeled to these regions from the surrounding lower-density plasma due to wave refraction. The model parameters are applicable to the expected solar wind conditions at about 10 solar radii.
Oblique non-neutral solitary Alfven modes in weakly nonlinear pair plasmas
Energy Technology Data Exchange (ETDEWEB)
Verheest, Frank [Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B-9000 Gent (Belgium); School of Physics, Howard College Campus, University of KwaZulu-Natal, Durban 4041 (South Africa); Lakhina, G S [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410218 (India); Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
2005-04-01
The equal charge-to-mass ratio for both species in pair plasmas induces a decoupling of the linear eigenmodes between waves that are charge neutral or non-neutral, also at oblique propagation with respect to a static magnetic field. While the charge-neutral linear modes have been studied in greater detail, including their weakly and strongly nonlinear counterparts, the non-neutral mode has received less attention. Here the nonlinear evolution of a solitary non-neutral mode at oblique propagation is investigated in an electron-positron plasma. Employing the framework of reductive perturbation analysis, a modified Korteweg-de Vries equation (with cubic nonlinearity) for the lowest-order wave magnetic field is obtained. In the linear approximation, the non-neutral mode has its magnetic component orthogonal to the plane spanned by the directions of wave propagation and of the static magnetic field. The linear polarization is not maintained at higher orders. The results may be relevant to the microstructure in pulsar radiation or to the subpulses.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Energy Technology Data Exchange (ETDEWEB)
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Explaining Signatures of Auroral Arcs based on the Stationary Inertial Alfven Wave
Nogami, Sh; Koepke, Me; Knudsen, Dj; Gillies, Dm; Donovan, E.; Vincena, S.
2016-10-01
Optical emission data from the THEMIS array of All Sky Imagers are analyzed to determine the lifetime of an auroral arc (i.e., the elapsed time during which an arc is visible). Lifetime is an important temporal signature related to the arc generation mechanism, by which arcs can be distinguished. An arc with a lifetime greater than ten minutes is consistent with arc generation by Stationary Inertial Alfven Wave (StIAW) which supports a steady-state wave electric field component parallel to a background magnetic field. An StIAW is a non-fluctuating, non-travelling, spatially periodic pattern of perturbed ion density that is static in the laboratory frame. StIAWs are the predicted result of the interaction between a magnetic-field-aligned electron current and plasma convection perpendicular to a background magnetic field. Electrostatic probes measure the fixed pattern of perturbed ion density in LAPD-U. Electron acceleration due to StIAWs is being investigated as a mechanism for the formation and support of long-lived auroral arcs. Preliminary evidence of electron acceleration from laboratory experiment is reported. This work was supported by NSF Grant PHY-130-1896, Grants from the Canadian Space Agency, and the THEMIS ASI teams at UCalgary and UC Berkeley. Facility use and experimental assistance from BaPSF is gratefully acknowledged.
Kinetic Alfven wave instability in a Lorentzian dusty plasma: Non-resonant particle approach
Energy Technology Data Exchange (ETDEWEB)
Rubab, N.; Biernat, H. K. [Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042 Graz (Austria); Institute of Physics, University of Graz, Universitaetplatz 5, A-8010 Graz (Austria); Erkaev, V. [Institute of Computational Modelling, 660036 Krasnoyarsk, Russia and Siberian Federal University, 660041 Krasnoyarsk (Russian Federation); Langmayr, D. [Virtual Vehicle Competence Center (vif), Inffeldgasse 21a, 8010 Graz (Austria)
2011-07-15
Analysis of the electromagnetic streaming instability is carried out which is related to the cross field drift of kappa distributed ions. The linear dispersion relation for electromagnetic wave using Vlasov-fluid equations in a dusty plasma is derived. Modified two stream instability (MTSI) in a dusty plasma has been discussed in the limit {omega}{sub pd}{sup 2}/c{sup 2}k{sub perpendicular}{sup 2}<<1. Numerical calculations of the growth rate of instability have been carried out. Growth rates of kinetic Alfven instability are found to be small as compared to MTSI. Maximum growth rates for both instabilities occur in oblique directions for V{sub 0}{>=}V{sub A}. It is shown that the presence of both the charged dust particles and perpendicular ion beam sensibly modify the dispersion relation of low-frequency electromagnetic wave. The dispersion characteristics are found to be insensible to the superthermal character of the ion distribution function. Applications to different intersteller regions are discussed.
Study of kinetic Alfven wave (KAW) in plasma - sheet-boundary- layer
Energy Technology Data Exchange (ETDEWEB)
Shukla, Nidhi; Varma, P; Tiwari, M S, E-mail: tiwarims@rediffmail.co, E-mail: poornimavarma@yahoo.co, E-mail: nidhiphy.shukla@gmail.co [Department of Physics and Electronics, Dr. H. S. Gour University, Sagar (M.P.), 470003 (India)
2010-02-01
The effect of parallel electric field with general loss-cone distribution function on the dispersion relation and damping rate/growth rate of the kinetic Alfven wave (KAW) is evaluated by kinetic approach. The generation of KAW by the combined effect of parallel electric field and loss-cone distribution indices (J) at a particular range of k{sub p}erpendicular{rho}{sub i} (k{sub p}erpendicular{rho}{sub i} <1 and k{sub p}erpendicular{rho}{sub i} >1) is noticed, where k{sub p}erpendicular is perpendicular wave number and {rho}{sub i} is the ion-gyro radius. Thus the propagation of KAW and loss of the Poynting flux from plasma sheet boundary layer (PSBL) to the ionosphere can be explained on the basis of present investigation. It is found that the present study also shows that the loss-cone distribution index is an important parameter to study KAW in the PSBL.
Current-vortex filament model of nonlinear Alfven perturbations in a finite-pressure plasma
Lakhin, V. P.; Schep, T. J.; Westerhof, E.
1998-01-01
A low-beta, two-fluid model is shown to possess solutions in the form of current-vortex filaments. The model can be viewed as that of reduced magnetohydrodynamics, extended with electron inertia, the Hall term and parallel electron pressure. These drift-Alfven filaments are the plasma analogs of poi
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Rankin, R.; Sydorenko, D.
2015-12-01
Results from a 3D global numerical model of Alfven wave propagation in a warm multi-species plasma in Earth's magnetosphere are presented. The model uses spherical coordinates, accounts for a non-dipole magnetic field, vertical structure of the ionosphere, and an air gap below the ionosphere. A realistic density model is used. Below the exobase altitude (2000 km) the densities and the temperatures of electrons, ions, and neutrals are obtained from the IRI and MSIS models. Above the exobase, ballistic (originating from the ionosphere and returning to ionosphere) and trapped (bouncing between two reflection points above the ionosphere) electron populations are considered similar to [Pierrard and Stegen (2008), JGR, v.113, A10209]. Plasma parameters at the exobase provided by the IRI are the boundary conditions for the ballistic electrons while the [Carpenter and Anderson (1992), JGR, v.97, p.1097] model of equatorial electron density defines parameters of the trapped electron population. In the simulations that are presented, Alfven waves with frequencies from 1 Hz to 0.01 Hz and finite azimuthal wavenumbers are excited in the magnetosphere and compared with Van Allen Probes data and ground-based observations from the CARISMA array of ground magnetometers. When short perpendicular scale waves reflect form the ionosphere, compressional Alfven waves are observed to propagate across the geomagnetic field in the ionospheric waveguide [e.g., Lysak (1999), JGR, v.104, p.10017]. Signals produced by the waves on the ground are discussed. The wave model is also applied to interpret recent Van Allen Probes observations of kinetic scale ULF waves that are associated with radiation belt electron dynamics and energetic particle injections.
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves
Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.
1992-01-01
The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
Energy Technology Data Exchange (ETDEWEB)
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... that at resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Kinetic Alfven Waves and the Depletion of the Thermal Population in Extragalactic Jets
Jafelice, L. C.; Opher, R.
1990-11-01
evident that both problems are intimately related to one another. Jafe- lice and Opher (1987a)(Astrophys. Space Sci. 137, 303)showed that an abundant generation of kinetic Alfven waves (KAw) within EJ and ERS is expected. In the present work we study the chain of processes: a) KAW accelerate thermal electrons along the background magnetic field producing suprathermal runaway electrons; b) which generate Langmuir waves and c) which in turn further accelerate a fraction of the runaway electrons to moderately relativistic energies. We show that assuming that there is no other source of a thermal population but the original one, the above sequence of processes can account for the consumption of thermal electrons in a time scale the source lifetime. Key o : GALAXIES-JETS - HYDROMAGNETICS
Wang, C B; Lee, L C
2014-01-01
A scenario is proposed to explain the preferential heating of minor ions and differential streaming velocity between minor ions and protons observed in the solar corona and in the solar wind. It is demonstrated by test particle simulations that minor ions can be nearly fully picked up by intrinsic Alfv\\'en-cyclotron waves observed in the solar wind based on the observed wave energy density. Both high frequency ion-cyclotron waves and low frequency Alfv\\'en waves play crucial roles in the pickup process. A minor ion can first gain a high magnetic moment through the resonant wave-particle interaction with ion-cyclotron waves, and then this ion with a large magnetic moment can be trapped by magnetic mirror-like field structures in the presence of the lower-frequency Alfv\\'en waves. As a result, the ion is picked up by these Alfv\\'en-cyclotron waves. However, minor ions can only be partially picked up in the corona due to low wave energy density and low plasma beta. During the pickup process, minor ions are stoch...
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Interpreting Ulysses data using inverse scattering theory: Oblique Alfv\\'en waves
Wheeler, Harry R; Hamilton, R L
2015-01-01
Solitary wave structures observed by the Ulysses spacecraft in the solar wind were analyzed using both inverse scattering theory as well as direct numerical integration of the derivative nonlinear Schr\\"odinger (DNLS) equation. Several of these structures were found to be consistent with soliton solutions of the DNLS equation. Such solitary structures have been commonly observed in the space plasma environment and may, in fact, be long-lived solitons. While the generation of these solitons may be due to an instability mechanism, e.g., the mirror instability, they may be observable far from the source region due to their coherent nature.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
Energy Technology Data Exchange (ETDEWEB)
Shukla, Nidhi; Mishra, Ruchi; Varma, P; Tiwari, M S [Department of Physics and Electronics, Dr H S Gour University, Sagar (MP) 470003 (India)
2008-02-15
This work studies the effect of ion and electron beam on kinetic Alfven wave (KAW) with general loss-cone distribution function. The kinetic theory has been adopted to evaluate the dispersion relation and damping rate of the wave in the presence of loss-cone distribution indices J. The variations in wave frequency {omega} and damping rate with perpendicular wave number k{sub perpendicular}{rho}{sub i} (k{sub perpendicular} is perpendicular wave number and {rho}{sub i} is ion gyroradius) and parallel wave number k{sub parallel} are studied. It is found that the distribution index J and ion beam velocity enhance the wave frequency at lower k{sub perpendicular}{rho}{sub i}, whereas the electron beam velocity enhances the wave frequency at higher k{sub perpendicular}{rho}{sub i}. The calculated values of frequency correspond to the observed values in the range 0.1-4 Hz. Increase in damping rate due to higher distribution indices J and ion beam velocity is observed. The effect of electron beam is to reduce the damping rate at higher k{sub perpendicular}{rho}{sub i}. The plasma parameters appropriate to plasma sheet boundary layer are used. The results may explain the transfer of Poynting flux from the magnetosphere to the ionosphere. It is also found that in the presence of the loss-cone distribution function the ion beam becomes a sensitive parameter to reduce the Poynting flux of KAW propagating towards the ionosphere.
Hahn, Michael
2013-01-01
We present a measurement of the energy carried and dissipated by Alfv\\'en waves in a polar coronal hole. Alfv\\'en waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease with height in coronal holes, which is a signature of wave damping, but have been unable to quantify the energy lost by the waves. This is because line widths depend on both the non-thermal velocity v_nt and the ion temperature T_i. We have implemented a means to separate the T_i and v_nt contributions using the observation that at low heights the waves are undamped and the ion temperatures do not change with height. This enables us to determine the amount of energy carried by the waves at low heights, which is proportional to v_nt. We find the initial energy flux density present was 6.7 +/- 0.7 x 10^5 erg cm^-2 s^-1, which is sufficient to heat the coronal hole and acccelerate the solar wind during the 2007 - 2009 solar minimum. Additionally, we find tha...
Exact solitary wave solutions of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
A self-consistent theory of collective alpha particle losses induced by Alfvenic turbulence
Energy Technology Data Exchange (ETDEWEB)
Biglari, H. (Princeton Univ., NJ (United States). Plasma Physics Lab.); Diamond, P.H. (California Univ., San Diego, La Jolla, CA (United States). Dept. of Physics)
1992-01-01
The nonlinear dynamics of kinetic Alfven waves, resonantly excited by energetic ions/alpha particles, is investigated. It is shown that {alpha}-particles govern both linear instability and nonlinear saturation dynamics, while the background MHD turbulence results only in a nonlinear real frequency shift. The most efficient saturation mechanism is found to be self-induced profile modification. Expressions for the fluctuation amplitudes and the {alpha}-particle radial flux are self-consistently derived. The work represents the first self-consistent, turbulent treatment of collective {alpha}-particle losses by Alfvenic fluctuations.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Diffusive shock acceleration with magnetic field amplification and Alfvenic drift
Kang, Hyesung
2012-01-01
We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfvenic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is greater than 2x10^{-4}, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfven speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfvenic drift predicts that the postshock CR pressure saturates roughly at 10 % of the shock ram pressure for strong shocks...
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed.......Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
Hansen, Shelley C
2012-01-01
Alfv\\'en waves may be difficult to excite at the photosphere due to low ionization fraction and suffer near-total reflection at the transition region (TR). Yet they are ubiquitous in the corona and heliosphere. To overcome these difficulties, we show that they may instead be generated high in the chromosphere by conversion from reflecting fast magnetohydrodynamic waves, and that Alfv\\'enic transition region reflection is greatly reduced if the fast reflection point is within a few scale heights of the TR. The influence of mode conversion on the phase of the reflected fast wave is also explored. This phase can potentially be misinterpreted as a travel speed perturbation, with implications for the practical seismic probing of active regions.
Tsiklauri, D
2015-01-01
Our magnetohydrodynamic (MHD) simulations and analytical calculations show that, when a background flow is present, mathematical expressions for the Alfv\\'en wave (AW) damping via phase mixing are modified by a following substitution $C_A^\\prime(x) \\to C_A^\\prime(x)+V_0^\\prime(x)$, where $C_A$ and $V_0$ are AW phase and the flow speeds and prime denotes derivative in the direction across the background magnetic field. In uniform magnetic field and over-dense plasma structures, in which $C_A$ is smaller compared to surrounding plasma, the flow, that is confined to the structure, in the same direction as the AW, reduces the effect of phase mixing, because on the edges of the structure $C_A^\\prime$ and $V_0^\\prime$ have opposite sign. Thus, the wave damps via phase mixing {\\it slower} compared to the case without the flow. This is the consequence of the co-directional flow reducing the wave front stretching in the transverse direction. Although, the result is generic and is applicable to different laboratory or ...
Alfven波在微电离大气中的衰减特性研究%Attenuation of Alfven Waves in Weakly Ionized Near Earth Atmosphere
Institute of Scientific and Technical Information of China (English)
刘元涛; 赵华; 李磊; 王劲东; 周斌; 冯永勇
2011-01-01
利用简单的偶极子地磁场模型以及大气电子密度和电导率模式,分析地面产生的磁扰动以Alfven波的模式传播到近地空间区域.这种地面的磁扰动可能干扰近地空间卫星对空间磁扰动的观测.通过对地面磁扰动Alfven 波模式1000km高度内的衰减情况进行模拟,认为在近地空间采用地磁偶极子模型是合理的.由于衰减随扰动频率的增大而急剧增强,分析还得到了近地卫星能够探测到地面磁扰动的最大频率.计算结果表明,Alfven波的衰减主要集中在高度50km以下,这个区域内的大气电导率极其微弱,使Alfven波的传播受到极大衰减.0.4Hz 以下的Alfven波沿磁力线传播到1000 km高度后衰减结为原来扰动幅度的千分之一,因此频率在0.4 Hz以下的Alfven波可能会干扰低轨卫星探测磁场脉动.%Alfven waves, produced on the ground by artificial or by soundstorm, propagating to the near-earth space along the geomagnetic field lines, would decay greatly with distance.A dipole geomagnetic field model in near earth space, plasma density and conductivity models derived from observational data are used in this study to investigate the attenuation of Alfven waves below 1000 km altitude by numerical simulation methods.The frequency that would be detected by magnetometer carried by satellite was also found.The result showed that: Alfven waves will decay sharply in the height of less than 50 km for the much weak electrical conductivity in this region; it is 0.4 Hz Alfven waves, when transmitted to 1000 km, that becomes about one-thousandth of the original, so Alfven waves below 0.4 Hz can be detected by LEO satellites.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Nonlinear Dispersion Relation in Wave Transformation
Institute of Scientific and Technical Information of China (English)
李瑞杰; 严以新; 曹宏生
2003-01-01
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1＜kh＜1.5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
Statistical distribution of nonlinear random wave height
Institute of Scientific and Technical Information of China (English)
HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi
2006-01-01
A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Nonlinear mhd simulations of wave dissipation in flux tubes
Poedts, S.; Toth, G.; Belien, A. J. C.; Goedbloed, J. P.
1997-01-01
The phase mixing and resonant dissipation of Alfven waves is studied in both the 'closed' magnetic loops and the 'open' coronal holes observed in the hot solar corona. The resulting energy transfer from large to small length scales contributes to the heating of these magnetic str
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Optical evidence for Alfven wave breaking in the near-Earth magnetosphere
Semeter, J.; Blixt, M.
2006-12-01
Alfvén waves propagating obliquely to the Earth's magnetic lines of force become dispersive when the perpendicular wavelength approaches the collisionless electron skin depth. The dispersion results in two simultaneous effects: (1) wave energy becomes coupled to particle kinetic energy such that parallel acceleration of electrons is possible, and (2) wave energy spreads azimuthally across the background magnetic field, with phase- and group-velocities oppositely directed. Validation of this mechanism requires two-dimensional, time-dependent measurements of the dispersing wave packet. Such evidence should be available in video measurements of the aurora-borealis. An analysis of high-speed, narrow-field, intensified video of dynamic aurora event is presented, confirming the salient predictions for inertial Alfvén wave dispersion.
On the polarization of nonlinear gravitational waves
Poplawski, Nikodem J.
2011-01-01
We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.
Nature and dynamics of overreflection of Alfven waves in MHD shear flows
Gogichaishvili, D; Chanishvili, R; Lominadze, J
2014-01-01
Our goal is to gain new insights into the physics of wave overreflection phenomenon in MHD nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, ${\\bf U}_0=(Sy,0,0)$, that contain two different types of Alfv${\\rm \\acute{e}}$n waves. These waves are reduced to pseudo- and shear shear-Alfv${\\rm \\acute{e}}$n waves when wavenumber along $Z$-axis equals zero (i.e., when $k_z=0$). Therefore, for simplicity, we labelled these waves as: P-Alfv${\\rm \\acute{e}}$n and S-Alfv${\\rm \\acute{e}}$n waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetri...
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Effect of dust particles on kinetic Alfven wave in earth's magnetoplasma
Energy Technology Data Exchange (ETDEWEB)
Varma, P; Shukla, Nidhi; Agarwal, Priyanka; Tiwari, M S, E-mail: poornimavarma@yahoo.co, E-mail: tiwarims@rediffmail.co [Department of Physics and Electronics, Dr. H .S. Gour University, Sagar (M.P.) - 470003 (India)
2010-02-01
Kinetic Alfve'n waves are examined in the presence of density and charge of dust particles with bi-Maxwellian distribution function. The theory of particle aspect analysis is used to evaluate the dispersion relation and growth rate. It is assumed that a low {beta} (ratio of plasma pressure to magnetic pressure) plasma consist the resonant and non-resonant particles. The resonant particles participate in the energy exchange with the wave whereas non-resonant particles support the oscillatory motion of the wave. It is assumed that the dusty plasma model modify the scenario of the KAW. The density of dust particles enhanced the frequency of the KAW. The presence of charged dust grains gives rise to new kinds of waves. The finding may be applicable for the laboratory plasma and has wide applications in magnetosphere as well as space plasma which modify the propagational characteristics of KAW.
Energy Technology Data Exchange (ETDEWEB)
Yamaguchi, Y [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Ichimura, M [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Higaki, H [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Kakimoto, S [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Nakagome, K [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Nemoto, K [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Katano, M [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Nakajima, H [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan); Fukuyama, A [Department of Nuclear Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501 (Japan); Cho, T [Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577 (Japan)
2006-08-15
The formation of eigenmodes with the m = 1 fast Alfven waves in the ion-cyclotron range of frequency are investigated in the axisymmetric central cell of the GAMMA 10 tandem mirror. When the fast waves with frequencies near the fundamental ion-cyclotron frequency have been used for the plasma production, the saturation in the density has been observed. The spatial structure of the excited wave field is calculated in the central cell using a two-dimensional full wave code. The results of numerical analysis indicate that the increase in plasma density depends strongly on the eigenmode formations associated with the boundary conditions. The results of numerical analysis are compared with the results of measurements of the waves with magnetic probes. A very good degree of agreement is found between the theoretical results and the experimental results. It is suggested that the simultaneous excitation of several radial eigenmodes with high-harmonic fast waves is effective for higher density plasma production.
Sahraoui, Fouad; Goldstein, Melvyn L.
2010-01-01
Over the past few decades, large-scales solar wind (SW) turbulence has been studied extensively, both theoretically and observationally. Observed power spectra of the low frequency turbulence, which can be described in the magnetohydrodynamic (MHD) limit, are shown to obey the Kolmogorov scaling, $k"{ -5/3 }$, down the local proton gyrofrequency ($C{ci} \\sim O.l$-Hz). Turbulence at frequencies above $C{ci}$ has not been thoroughly investigated and remains far less well understood. Above $C{ ci}$ the spectrum steepens to $\\sim f"{ -2.5}$ and a debate exists as to whether the turbulence has become dominated by dispersive kinetic Alfven waves (KA W) or by whistler waves, before it is dissipated at small scales, In a case study Sahraoui et al., PRL (2009) have reported the first direct determination of the dissipation range of solar wind turbulence near the electron gyroscale using the high resolution Cluster magnetic and electric field data (up to $10"2$-Hz in the spacecraft reference frame). Above the Doppler-shifted proton scale $C{\\rho i}$ a new inertial range with a scaling $\\sim f"{ -2.3}$ has been evidenced and shown to remarkably agree with theoretical predictions of a quasi-two-dimensional cascade into KA W turbulence. Here, we use a wider sample of data sets of small scale SW turbulence under different plasma conditions, and investigate under which physical criteria the KA W (or the whistler) turbulence may be observed to carry out the cascade at small scales, These new observations/criteria are compared to the predictions on the cascade and the (kinetic) dissipation from the Vlasov theory. Implications of the results on the heating problem of the solar wind will be discussed.
Nonlinear surface waves over topography
Janssen, T.T.
2006-01-01
As ocean surface waves radiate into shallow coastal areas and onto beaches, their lengths shorten, wave heights increase, and the wave shape transforms from nearsinusoidal to the characteristic saw-tooth shapes at the onset of breaking; in the ensuing breaking process the wave energy is cascaded to
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Nonlinear surface waves in photonic hypercrystals
Ali, Munazza Zulfiqar
2017-08-01
Photonic crystals and hyperbolic metamaterials are merged to give the concept of photonic hypercrystals. It combines the properties of its two constituents to give rise to novel phenomena. Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation. Both dielectric and metallic photonic hypercrystals are studied and it is found that nonlinearity limits the infinite divergence of wave vectors of the surface waves. These states exist in the frequency region where the linear surface waves do not exist. It is also shown that the nonlinearity can be used to engineer the group velocity of the resulting surface wave.
Nonlinear water waves with soluble surfactant
Lapham, Gary; Dowling, David; Schultz, William
1998-11-01
The hydrodynamic effects of surfactants have fascinated scientists for generations. This presentation describes an experimental investigation into the influence of a soluble surfactant on nonlinear capillary-gravity waves in the frequency range from 12 to 20 Hz. Waves were generated in a plexiglass wave tank (254 cm long, 30.5 cm wide, and 18 cm deep) with a triangular plunger wave maker. The tank was filled with carbon- and particulate-filtered water into which the soluble surfactant Triton-X-100® was added in known amounts. Wave slope was measured nonintrusively with a digital camera running at 225 fps by monitoring the position of light beams which passed up through the bottom of the tank, out through the wavy surface, and onto a white screen. Wave slope data were reduced to determine wave damping and the frequency content of the wave train. Both were influenced by the presence of the surfactant. Interestingly, a subharmonic wave occurring at one-sixth the paddle-driving frequency was found only when surfactant was present and the paddle was driven at amplitudes high enough to produce nonlinear waves in clean water. Although the origins of this subharmonic wave remain unclear, it appears to be a genuine manifestation of the combined effects of the surfactant and nonlinearity.
Longitudinal nonlinear wave propagation through soft tissue.
Valdez, M; Balachandran, B
2013-04-01
In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Erkaev, NV; Shaidurov, VA; Semenov, VS; Biernat, HK; Heidorn, D; Lakhina, GS
2006-01-01
A ratio of the maximal and minimal cross sections of the magnetic tube (contraction ratio) is a crucial parameter which affects very strongly on reflections of MHD wave pulses propagating along a narrowing magnetic flux tube. In cases of large contraction ratios of magnetospheric magnetic tubes, the
Alfven Eigenmode And Ion Bernstein Wave Studies For Controlling Fusion Alpha Particles
Heeter, R F
1999-01-01
In magnetic confinement fusion reactor plasmas, the charged fusion products (such as alpha particles in deuterium-tritium plasmas) will be the dominant power source, and by controlling these charged fusion products using wave-particle interactions the reactor performance could be optimized. This thesis studies two candidate waves: Mode-Converted Ion Bernstein Waves (MCIBWs) and Alfvén Eigenmodes (AEs). Rates of MCIBW-driven losses of alpha-like fast deuterons, previously observed in the Tokamak Fusion Test Reactor (TFTR), are reproduced by a new model so that the wave-particle diffusion coefficient can be deduced. The MCIBW power in TFTR is found to be ∼ 1/3 that needed for collisionless alpha particle control. A reasonable reactor power scaling is derived. To study AEs, existing magnetic fluctuation probes at the Joint European Torus (JET) have been absolutely calibrated from 30–500 kHz for the first time, allowing fluctuation measurements with &vbm0;dBpol&vbm0;/B0&am...
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Nonlinear ship waves and computational fluid dynamics
National Research Council Canada - National Science Library
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
.... Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design...
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...
The Nonlinear Talbot Effect of Rogue Waves
Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-01-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a \\pi-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Proton heating and beam formation via parametrically unstable Alfven-cyclotron waves
Marsch, Eckart; Araneda, Jaime; -Vinas, Adolfo F.
Vlasov theory and one-dimensional hybrid simulations are used to study the effects that compressible fluctuations driven by parametric instabilities of Alfvén/cyclotron waves have on proe ton velocity distributions. Field-aligned proton beams are generated during the saturation phase of the wave-particle interaction, with a drift speed which is slightly greater than the Alfvén speed and is maintained until the end of the simulation. The main part of the dise tribution becomes anisotropic due to phase mixing as is typically observed in the velocity distributions measured in the fast solar wind. We identify the key instabilities and also find that even in the parameter regime, where fluid theory appears to be appropriate, strong kinetic effects still prevail.
Coffey, Victoria; Chandler, Michael; Singh, Nagendra
2008-01-01
The role that the cleft/cusp has in ionosphere/magnetosphere coupling makes it a very dynamic region having similar fundamental processes to those within the auroral regions. With Polar passing through the cusp at 1 Re in the Spring of 1996, we observe a strong correlation between ion heating and broadband ELF (BBELF) emissions. This commonly observed relationship led to the study of the coupling of large field-aligned currents, burst electric fields, and the thermal O+ ions. We demonstrate the role of these measurements to Alfvenic waves and stochastic ion heating. Finally we will show the properties of the resulting density cavities.
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Brady, C S
2016-01-01
Two of the central problems in our understanding of the solar chromosphere are how the upper chromosphere is heated and what drives spicules. Estmates of the required chromospheric heating, based on radiative and conductive losses suggest a rate of $\\sim 0.1 \\mathrm{\\:erg\\:cm^{-3}\\:s^{-1}}$ in the lower chromosphere dropping to $\\sim 10^{-3} \\mathrm{\\:erg\\:cm^{-3}\\:s^{-1}}$ in the upper chromosphere (\\citet{Avrett1981}). The chromosphere is also permeated by spicules, higher density plasma from the lower atmosphere propelled upwards at speeds of $\\sim 10-20 \\mathrm{\\:km\\:s^{-1}}$, for so called Type-I spicules (\\citet{Pereira2012,Zhang2012}, reaching heights of $\\sim 3000-5000 \\mathrm{\\:km}$ above the photosphere. A clearer understanding of chromospheric dynamics, its heating and the formation of spicules, is thus of central importance to solar atmospheric science. For over thirty years it has been proposed that photospheric driving of MHD waves may be responsible for both heating and spicule formation. This ...
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A. [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS—University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2014-10-15
In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
Nonlinear Interaction of Waves in Geomaterials
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Optics in a nonlinear gravitational wave
Harte, Abraham I
2015-01-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. The commonly-used predictions of linear perturbation theory are shown to be generically overshadowed---even for very weak gravitational waves---by nonlinear effects when considering observations of sufficiently distant sources; higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Optics in a nonlinear gravitational plane wave
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Simulations of the Mg II k and Ca II 8542 lines from an Alfv\\'en Wave-heated flare chromosphere
Kerr, Graham S; Russell, Alexander J B; Allred, Joel C
2016-01-01
We use radiation hydrodynamic simulations to examine two models of solar flare chromospheric heating: Alfv\\'en wave dissipation and electron beam collisional losses. Both mechanisms are capable of strong chromospheric heating, and we show that the distinctive atmospheric evolution in the mid-to-upper chromosphere results in Mg II k-line emission that should be observably different between wave-heated and beam-heated simulations. We also present Ca II 8542A profiles which are formed slightly deeper in the chromosphere. The Mg II k-line profiles from our wave-heated simulation are quite different from those from a beam-heated model and are more consistent with IRIS observations. The predicted differences between the Ca II 8542A in the two models are small. We conclude that careful observational and theoretical study of lines formed in the mid-to-upper chromosphere holds genuine promise for distinguishing between competing models for chromospheric heating in flares.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
LIU Xiao; XU JiYao; MA RuiPing
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75-85 km, z =90-110 km and z= 115-130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the horizontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90-110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Nonlinear plasma wave in magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Bulanov, Sergei V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Prokhorov Institute of General Physics, Russian Academy of Sciences, Moscow 119991 (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region 141700 (Russian Federation); Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Hosokai, Tomonao; Zhidkov, Alexei G. [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Japan Science and Technology Agency, CREST, 2-1, Yamadaoka, Suita, Osaka 565-0871 (Japan); Kodama, Ryosuke [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871 (Japan)
2013-08-15
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic “Four-Ray Star” pattern.
Study of Linear and Nonlinear Wave Excitation
Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick
2013-10-01
We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.
Wave-kinetic description of nonlinear photons
Marklund, M; Brodin, G; Stenflo, L
2004-01-01
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner-Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to break-up and focusing of ultra-high intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser-plasma systems.
A nonlinear Schroedinger wave equation with linear quantum behavior
Energy Technology Data Exchange (ETDEWEB)
Richardson, Chris D.; Schlagheck, Peter; Martin, John; Vandewalle, Nicolas; Bastin, Thierry [Departement de Physique, University of Liege, 4000 Liege (Belgium)
2014-07-01
We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schroedinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear Dispersion Effect on Wave Transformation
Institute of Scientific and Technical Information of China (English)
LI Ruijie; Dong-Young LEE
2000-01-01
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986), and which has a better approximation to Hedges＇ empirical relation than the modilied relations by Hedges (1987). Kirby and Dahymple (1987) for shallow waters. The new dispersion relation is simple in form. thus it can be used easily in practice. Meanwhile. a general explicil approximalion to the new dispersion rela tion and olher nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking inlo account weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed vith the new dispersion relation predicts wave translornation over complicated topography quite well.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-06-15
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Directory of Open Access Journals (Sweden)
T. K. Suzuki
2008-03-01
Full Text Available We review our recent results of global one-dimensional (1-D MHD simulations for the acceleration of solar and stellar winds. We impose transverse photospheric motions corresponding to the granulations, which generate outgoing Alfvén waves. We treat the propagation and dissipation of the Alfvén waves and consequent heating from the photosphere by dynamical simulations in a self-consistent manner. Nonlinear dissipation of Alfven waves becomes quite effective owing to the stratification of the atmosphere (the outward decrease of the density. We show that the coronal heating and the solar wind acceleration in the open magnetic field regions are natural consequence of the footpoint fluctuations of the magnetic fields at the surface (photosphere. We find that the properties of the solar wind sensitively depend on the fluctuation amplitudes at the solar surface because of the nonlinearity of the Alfvén waves, and that the wind speed at 1 AU is mainly controlled by the field strength and geometry of flux tubes. Based on these results, we point out that both fast and slow solar winds can be explained by the dissipation of nonlinear Alfvén waves in a unified manner. We also discuss winds from red giant stars driven by Alfvén waves, focusing on different aspects from the solar wind.
Characterizing Electron Trapping Nonlinearity in Langmuir Waves
Strozzi, D J; Rose, H A; Hinkel, D E; Langdon, A B; Banks, J W
2012-01-01
We assess when electron trapping nonlinearities are expected to be important in Langmuir waves. The basic criterion is that the effective lifetime, t_d, of resonant electrons in the trapping region of velocity space must exceed the period of trapped motion for deeply-trapped electrons, tau_B = (n_e/delta n)^{1/2} 2pi/omega_pe. A unitless figure of merit, the "bounce number" N_B = t_d/tau_B, encapsulates this condition and allows an effective threshold amplitude for which N_B=1 to be defined. The lifetime is found for convective loss (transverse and longitudinal) out of a spatially finite Langmuir wave. Simulations of driven waves with a finite transverse profile, using the 2D-2V Vlasov code Loki, show trapping nonlinearity increases continuously with N_B for side loss, and is significant for N_B ~ 1. The lifetime due to Coulomb collisions (both electron-electron and electron-ion) is also found, with pitch-angle scattering and parallel drag and diffusion treated in a unified way. A simple way to combine convec...
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity ($\\delta I/I\\sim \\delta n/n$). The waves are evident as significant density fluctuations that vary with height, and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Nonlinear Plasma Wave in Magnetized Plasmas
Bulanov, Sergei V; Kando, Masaki; Koga, James K; Hosokai, Tomonao; Zhidkov, Alexei G; Kodama, Ryosuke
2013-01-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern which has been observed in the image of the electron bunch in experiments [T. Hosokai, et al., Phys. Rev. Lett. 97, 075004 (2006)].
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Saturation process of nonlinear standing waves
Institute of Scientific and Technical Information of China (English)
马大猷; 刘克
1996-01-01
The sound pressure of the nonlinear standing waves is distorted as expected, but also tends to saturate as being found in standing-wave tube experiments with increasing sinusoidal excitation. Saturation conditions were not actually reached, owing to limited excitation power, but the evidence of tendency to saturation is without question. It is the purpose of this investigation to find the law of saturation from the existing experimental data. The results of curve fitting indicate that negative feedback limits the growth of sound pressure with increasing excitation, the growth of the fundamental and the second harmonic by the negative feedback of their sound pressures, and the growth of the third and higher harmonics, however, by their energies (sound pressures squared). The growth functions of all the harmonics are derived, which are confirmed by the experiments. The saturation pressures and their properties are found.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...
Highly Alfvenic Slow Solar Wind
Roberts, D. Aaron
2010-01-01
It is commonly thought that fast solar wind tends to be highly Alfvenic, with strong correlations between velocity and magnetic fluctuations, but examples have been known for over 20 years in which slow wind is both Alfvenic and has many other properties more typically expected of fast solar wind. This paper will present a search for examples of such flows from more recent data, and will begin to characterize the general characteristics of them. A very preliminary search suggests that such intervals are more common in the rising phase of the solar cycle. These intervals are important for providing constraints on models of solar wind acceleration, and in particular the role waves might or might not play in that process.
Nonlinear wave propagation in constrained solids subjected to thermal loads
Nucera, Claudio; Lanza di Scalea, Francesco
2014-01-01
The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such "residual" energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Kaladze, Tamaz; Kahlon, Laila
Nonlinear dynamics of coupled internal-gravity (IG) and alfven electromagnetic planetary waves in the weakly ionized ionospheric E-layer is investigated. Under such coupling new type of alfven waves is revealed. It is shown that such short wavelength turbulence of IG and alfvén waves is unstable with respect to the excitation of low-frequency and large-scale perturbations of the zonal flow and magnetic field. A set of coupled equations describing the nonlinear interaction of coupled IG and alfven waves with zonal flows is derived. The nonlinear mechanism of the instability is driven by the advection of vorticity and is based on the parametric excitation of convective cells by finite-amplitude coupled IG and alfven waves leading to the inverse energy cascade toward the longer wavelength. The growth rates of the corresponding instability and the conditions for driving them are determined. The possibility of generation of the intense mean magnetic field is shown.
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
The nonlinear standing wave inside the space of liquid
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Spectral stability of Alfven filament chains
Bergmans, J.; Kuvshinov, B. N.; Lakhin, V. P.; Schep, T. J.
2000-01-01
The two-fluid model of nonlinear Alfven perturbations has singular solutions in the form of current-vortex filaments. We investigate analytically and numerically the spectral stability of single and double rows of filaments. Staggered and non-staggered double rows (von Karman streets) are studied. I
Spectral stability of Alfven filament configurations
Bergmans, J.; Kuvshinov, B. N.; Lakhin, V. P.; Schep, T. J.
2000-01-01
The two-fluid plasma equations that describe nonlinear Alfven perturbations have singular solutions in the form of current-vortex filaments. These filaments are analogous to point vortices in ideal hydrodynamics and geostrophic fluids. In this work the spectral (linear) stability of current-vortex f
Pfaff, R. F.
2009-01-01
On December 14,2002, a NASA Black Brant X sounding rocket was launched equatorward from Ny Alesund, Spitzbergen (79 N) into the dayside cusp and subsequently cut across the open/closed field line boundary, reaching an apogee of771 km. The launch occurred during Bz negative conditions with strong By negative that was changing during the flight. SuperDarn (CUTLASS) radar and subsequent model patterns reveal a strong westward/poleward convection, indicating that the rocket traversed a rotational reversal in the afternoon merging cell. The payload returned DC electric and magnetic fields, plasma waves, energetic particle, suprathermal electron and ion, and thermal plasma data. We provide an overview of the main observations and focus on the DC electric field results, comparing the measured E x B plasma drifts in detail with the CUTLASS radar observations of plasma drifts gathered simultaneously in the same volume. The in situ DC electric fields reveal steady poleward flows within the cusp with strong shears at the interface of the closed/open field lines and within the boundary layer. We use the observations to discuss ionospheric signatures of the open/closed character of the cusp/low latitude boundary layer as a function of the IMF. The electric field and plasma density data also reveal the presence of very strong plasma irregularities with a large range of scales (10 m to 10 km) that exist within the open field line cusp region yet disappear when the payload was equatorward of the cusp on closed field lines. These intense low frequency wave observations are consistent with strong scintillations observed on the ground at Ny Alesund during the flight. We present detailed wave characteristics and discuss them in terms of Alfven waves and static irregularities that pervade the cusp region at all altitudes.
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...... of a constantly maintained pump wave is derived and a general dispersion relation describing the modulation of the high frequency wave due to different low frequency responses is obtained. Particular attention is devoted to a purely growing modulation. The relative importance of the ponderomotive force...
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Distribution of the nonlinear random ocean wave period
Institute of Scientific and Technical Information of China (English)
HOU Yijun; LI Mingjie; SONG Guiting; SI Guangcheng; QI Peng; HU Po
2009-01-01
Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (υ=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Nonlinear numerical simulation on extreme-wave kinematics
Institute of Scientific and Technical Information of China (English)
NING Dezhi; TENG Bin; LIU Shuxue
2009-01-01
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is "adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media (where distortion can be cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
Experimental characterization of nonlinear processes of whistler branch waves
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Ganguli, G.; Rudakov, L.
2016-05-01
Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.
Belova, Elena; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.
2016-10-01
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4-9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfven wave (KAW) that occurs on the high-field side at the Alfven resonance location. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. This mechanism provides an alternative explanation to the observed reduced heating of the plasma core in the NSTX. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power. This research was supported by the U.S. DOE contract # DE-AC02-09CH11466.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Rapid energization of radiation belt electrons by nonlinear wave trapping
Directory of Open Access Journals (Sweden)
Y. Katoh
2008-11-01
Full Text Available We show that nonlinear wave trapping plays a significant role in both the generation of whistler-mode chorus emissions and the acceleration of radiation belt electrons to relativistic energies. We have performed particle simulations that successfully reproduce the generation of chorus emissions with rising tones. During this generation process we find that a fraction of resonant electrons are energized very efficiently by special forms of nonlinear wave trapping called relativistic turning acceleration (RTA and ultra-relativistic acceleration (URA. Particle energization by nonlinear wave trapping is a universal acceleration mechanism that can be effective in space and cosmic plasmas that contain a magnetic mirror geometry.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube
Institute of Scientific and Technical Information of China (English)
DUAN Wen-Shan
2004-01-01
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrodinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change,depending on what kind of inhomogeneity the tube has.
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
Indian Academy of Sciences (India)
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
The periodic wave solutions for two systems of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
王明亮; 王跃明; 张金良
2003-01-01
The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long-short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
The period ratio P_1/P_2 of torsional Alfv\\'en waves with steady flows in spicules
Ebadi, H; Farahani, S Vasheghani
2016-01-01
The aim here is to model the standing torsional oscillations in solar spicules in the presence of density stratification, magnetic field expansion, and steady flows. By implementing cylindrical geometry, the eigenfrequencies, eigenfunctions, and the period ratio P_1/P_2 of these waves is obtained for finite plasma-beta. The shifts created by the steady flow justifies the divergence of the observed period ratio for the first and second periods from the number 2.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2010-10-15
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Nonlinear spin-wave excitations at low magnetic bias fields
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Nonlinear electron acoustic waves in presence of shear magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
Statistical distribution of nonlinear random wave height in shallow water
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution.The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated.The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution.The effect of wave steepness in shallow water is similar to that in deep water;but the factor of shallow water lowers the wave height distribution of the general wave with the reduced factor of wave steepness.It also makes the wave height distribution of shallow water more centralized.The results indicate that the new distribution fits the in situ measurements much better than other distributions.
Development of A Fully Nonlinear Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
陈永平; 李志伟; 张长宽
2004-01-01
A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method,the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Nonlinear volume holography for wave-front engineering.
Hong, Xu-Hao; Yang, Bo; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2014-10-17
The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Exact Nonlinear Internal Equatorial Waves in the f-plane
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Experimental observations of nonlinear effects of the Lamb waves
Institute of Scientific and Technical Information of China (English)
DENG Mingxi; D.C. Price; D.A.Scott
2004-01-01
The experimental observations of nonlinear effects of the primary Lamb waves have been reported. Firstly, the brief descriptions have been made for the nonlinear acoustic measurement system developed by Ritec. The detailed considerations for the acoustic experiment system established for observing of the nonlinear effects of the primary Lamb waves have been carried out. Especially, the analysis focuses on the time-domain responses of second harmonics of the primary Lame waves by employing a straightforward model. Based on the existence conditions of strong nonlinearity of the primary Lamb waves, the wedge transducers are designed to generate and detect the primary and secondary waves on the surface of an aluminum sheet. For the different distances between the transmitting and receiving wedge transducers,the amplitudes of the primary waves and the second harmonics on the sheet surface have been measured within a specified frequency range. In the immediate vicinity of the driving frequency,where the primary and the double frequency Lamb waves have the same phase velocities, the quantitative relations of second-harmonic amplitudes with the propagation distance have been analyzed. It is experimentally verified that the second harmonics of the primary Lamb waves do have a cumulative growth effect along with the propagation distance.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Quantification and prediction of rare events in nonlinear waves
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Linear and nonlinear propagation of water wave groups
Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.
1992-01-01
Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.
GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS
Institute of Scientific and Technical Information of China (English)
GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan
2005-01-01
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
Wave Propagation In Strongly Nonlinear Two-Mass Chains
Wang, Si Yin; Herbold, Eric B.; Nesterenko, Vitali F.
2010-05-01
We developed experimental set up that allowed the investigation of propagation of oscillating waves generated at the entrance of nonlinear and strongly nonlinear two-mass granular chains composed of steel cylinders and steel spheres. The paper represents the first experimental data related to the propagation of these waves in nonlinear and strongly nonlinear chains. The dynamic compressive forces were detected using gauges imbedded inside particles at depths equal to 4 cells and 8 cells from the entrance gauge detecting the input signal. At these relatively short distances we were able to detect practically perfect transparency at low frequencies and cut off effects at higher frequencies for nonlinear and strongly nonlinear signals. We also observed transformation of oscillatory shocks into monotonous shocks. Numerical calculations of signal transformation by non-dissipative granular chains demonstrated transparency of the system at low frequencies and cut off phenomenon at high frequencies in reasonable agreement with experiments. Systems which are able to transform nonlinear and strongly nonlinear waves at small sizes of the system are important for practical applications such as attenuation of high amplitude pulses.
Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides
Institute of Scientific and Technical Information of China (English)
Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing
2013-01-01
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Sergej Flach; Mikhail Ivanchenko; Nianbei Li
2011-11-01
We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd indications for an asymptotic low-temperature ∼ 4 and intermediate temperature ∼ 2 laws. These ﬁndings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).
Nonlinear mixing of laser generated narrowband Rayleigh surface waves
Bakre, Chaitanya; Rajagopal, Prabhu; Balasubramaniam, Krishnan
2017-02-01
This research presents the nonlinear mixing technique of two co-directionally travelling Rayleigh surface waves generated and detected using laser ultrasonics. The optical generation of Rayleigh waves on the specimen is obtained by shadow mask method. In conventional nonlinear measurements, the inherently small higher harmonics are greatly influenced by the nonlinearities caused by coupling variabilities and surface roughness between the transducer and specimen interface. The proposed technique is completely contactless and it should be possible to eliminate this problem. Moreover, the nonlinear mixing phenomenon yields not only the second harmonics, but also the sum and difference frequency components, which can be used to measure the acoustic nonlinearity of the specimen. In this paper, we will be addressing the experimental configurations for this technique. The proposed technique is validated experimentally on Aluminum 7075 alloy specimen.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Nonlinear wave propagation in a rapidly-spun fiber.
McKinstrie, C J; Kogelnik, H
2006-09-04
Multiple-scale analysis is used to study linear wave propagation in a rapidly-spun fiber and its predictions are shown to be consistent with results obtained by other methods. Subsequently, multiple-scale analysis is used to derive a generalized Schroedinger equation for nonlinear wave propagation in a rapidly-spun fiber. The consequences of this equation for pulse propagation and four-wave mixing are discussed briefly.
Nonlinear propagation of planet-generated tidal waves
Rafikov, Roman
2001-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process sp...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
Energy Technology Data Exchange (ETDEWEB)
Xie, Xi-Yang; Tian, Bo, E-mail: tian_bupt@163.com; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Simulation of Fully Nonlinear 3-D Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
张晓兔; 滕斌; 宁德志
2004-01-01
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Nonlinear diffraction of water waves by offshore stuctures
Directory of Open Access Journals (Sweden)
Matiur Rahman
1986-01-01
Full Text Available This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Nonlinear Alfvén wave dynamics in plasmas
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Diffractive optics based four-wave, six-wave, ..., nu-wave nonlinear spectroscopy.
Miller, R J Dwayne; Paarmann, Alexander; Prokhorenko, Valentyn I
2009-09-15
A detailed understanding of chemical processes requires information about both structure and dynamics. By definition, a reaction involves nonstationary states and is a dynamic process. Structure describes the atomic positions at global minima in the nuclear potential energy surface. Dynamics are related to the anharmonicities in this potential that couple different minima and lead to changes in atomic positions (reactions) and correlations. Studies of molecular dynamics can be configured to directly access information on the anharmonic interactions that lead to chemical reactions and are as central to chemistry as structural information. In this regard, nonlinear spectroscopies have distinct advantages over more conventional linear spectroscopies. Because of this potential, nonlinear spectroscopies could eventually attain a comparable level of importance for studying dynamics on the relevant time scales to barrier crossings and reactive processes as NMR has for determining structure. Despite this potential, nonlinear spectroscopy has not attained the same degree of utility as linear spectroscopy largely because nonlinear studies are more technically challenging. For example, unlike the linear spectrometers that exist in almost all chemistry departments, there are no "black box" four-wave mixing spectrometers. This Account describes recent advances in the application of diffractive optics (DOs) to nonlinear spectroscopy, which reduces the complexity level of this technology to be closer to that of linear spectroscopy. The combination of recent advances in femtosecond laser technology and this single optic approach could bring this form of spectroscopy out of the exclusive realm of specialists and into the general user community. However, the real driving force for this research is the pursuit of higher sensitivity limits, which would enable new forms of nonlinear spectroscopy. This Account chronicles the research that has now extended nonlinear spectroscopy to six-wave
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be...
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Nonlinear scattering of radio waves by metal objects
Shteynshleyger, V. B.
1984-07-01
Nonlinear scattering of radio waves by metal structures with resulting harmonic and intermodulation interference is analyzed from both theoretical and empirical standpoints, disregarding nonlinear effects associated with the nonlinear dependence of the electric or magnetic polarization vector on respectively the electric or magnetic field intensity in the wave propagating medium. Nonlinear characteristics of metal-oxide-metal contacts where the thin oxide film separation two metal surfaces has properties approximately those of a dielectric or a high-resistivity semiconductor are discussed. Tunneling was found to be the principal mechanism of charge carrier transfer through such a contact with a sufficiently thin film, the contact having usually a cubic or sometimes an integral sign current-voltage characteristic at 300 K and usually S-form or sometimes a cubic current-voltage characteristic at 77 K.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
The Gouy phase shift in nonlinear interactions of waves
Lastzka, Nico; Schnabel, Roman
2007-06-01
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ(2)interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
Jo, Young Hyun; Lee, Hae June; Mikhailenko, Vladimir V.; Mikhailenko, Vladimir S.
2016-01-01
It was derived that the drift-Alfven instabilities with the shear flow parallel to the magnetic field have significant difference from the drift-Alfven instabilities of a shearless plasma when the ion temperature is comparable with electron temperature for a finite plasma beta. The velocity shear not only modifies the frequency and the growth rate of the known drift-Alfven instability, which develops due to the inverse electron Landau damping, but also triggers a combined effect of the velocity shear and the inverse ion Landau damping, which manifests the development of the ion kinetic shear-flow-driven drift-Alfven instability. The excited unstable waves have the phase velocities along the magnetic field comparable with the ion thermal velocity, and the growth rate is comparable with the frequency. The development of this instability may be the efficient mechanism of the ion energization in shear flows. The levels of the drift--Alfven turbulence, resulted from the development of both instabilities, are determined from the renormalized nonlinear dispersion equation, which accounts for the nonlinear effect of the scattering of ions by the electromagnetic turbulence. The renormalized quasilinear equation for the ion distribution function, which accounts for the same effect of the scattering of ions by electromagnetic turbulence, is derived and employed for the analysis of the ion viscosity and ions heating, resulted from the interactions of ions with drift-Alfven turbulence. In the same way, the phenomena of the ion cyclotron turbulence and anomalous anisotropic heating of ions by ion cyclotron plasma turbulence has numerous practical applications in physics of the near-Earth space plasmas. Using the methodology of the shearing modes, the kinetic theory of the ion cyclotron turbulence of the plasma with transverse current with strong velocity shear has been developed.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-06-27
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
From solitary wave to traveling surge
Institute of Scientific and Technical Information of China (English)
宋礼庭
1995-01-01
The solution of kinetic Alfven wave under action of anomalous resistance has two branches: the slow wave, VP
Nonlinear waves in a fluid-filled thin viscoelastic tube
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the expo-η, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries (KdV)-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves
Directory of Open Access Journals (Sweden)
Hongjuan Yan
2015-01-01
Full Text Available The nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients β and δ are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients β′ and δ′ versus stress and fatigue life. The relative nonlinear coefficients β′ and δ′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient β′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient δ′, however, the experiment data does not accord with the theoretical model.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Shallow water modal evolution due to nonlinear internal waves
Badiey, Mohsen; Wan, Lin; Luo, Jing
2017-09-01
Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Nonlinear reflection of internal gravity wave onto a slope
Raja, Keshav; Sommeria, Joel; Staquet, Chantal; Leclair, Matthieu; Grisouard, Nicolas; Gostiaux, Louis
2016-04-01
The interaction of internal waves on sloping topography is one of the processes that cause mixing and transport in oceans. The mixing caused by internal waves is considered to be an important source of energy that is needed to bring back deep, dense water from the abyss to the surface of the ocean, across constant density surfaces. Apart from the vertical transport of heat (downwards) and mass (upwards), internal waves are also observed to irreversibly induce a mean horizontal flow. Mixing and wave induced mean flow may be considered as the processes that transfer wave induced energy to smaller and larger scales respectively. The process of mixing has been a subject of intense research lately. However, the process of wave induced mean flow and their dynamic impact await thorough study. The present study involves this wave induced mean flow, its generation and energetics. The nonlinear subcritical reflection of internal waves from a sloping boundary is studied using laboratory experiments carried out on the Coriolis Platform at Grenoble and, 2D and 3D numerical simulations done using a non-hydrostatic code. In the experiment, a plane wave is produced using a wave generator and is made to reflect normally on a sloping bottom in a uniformly stratified fluid. We consider both rotating and non-rotating cases. The numerical simulation mimicks the laboratory setup with an initial condition of an analytical plane wave solution in a vertical plane limited by a smooth envelope to simulate the finite wave generator. The interaction of the incident and reflected waves produce, apart from higher harmonics, an irreversible wave induced mean flow which grows in time and is localised in the interacting region. The finite extent of the wave generator allows the mean flow to recirculate in the horizontal plane, resulting in a dipolar potential vorticity field. Moreover, the generation of mean flow and higher harmonics, along with dissipative effects, diminishes the amplitude of
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Analysis of nonlinear internal waves in the New York Bight
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Nonlinear dynamics of Airy-Vortex 3D wave packets: Emission of vortex light waves
Driben, Rodislav
2014-01-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Due to the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and non-zero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse, especially those having small width.
Nonlinear dynamics of Airy-vortex 3D wave packets: emission of vortex light waves.
Driben, Rodislav; Meier, Torsten
2014-10-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Because of the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and nonzero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse.
Linear and Nonlinear Surface Waves in Electrohydrodynamics
Hunt, Matthew; Vanden-broeck, Jean-Marc; Papageorgiou, Demetrios
2015-01-01
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, Ba Phi [Central University of Construction, Tuy Hoa (Viet Nam); Kim, Ki Hong [Ajou University, Suwon (Korea, Republic of)
2014-02-15
We study numerically the dynamics of an initially localized wave packet in one-dimensional nonlinear Schroedinger lattices with both local and nonlocal nonlinearities. Using the discrete nonlinear Schroedinger equation generalized by including a nonlocal nonlinear term, we calculate four different physical quantities as a function of time, which are the return probability to the initial excitation site, the participation number, the root-mean-square displacement from the excitation site and the spatial probability distribution. We investigate the influence of the nonlocal nonlinearity on the delocalization to self-trapping transition induced by the local nonlinearity. In the non-self-trapping region, we find that the nonlocal nonlinearity compresses the soliton width and slows down the spreading of the wave packet. In the vicinity of the delocalization to self-trapping transition point and inside the self-trapping region, we find that a new kind of self-trapping phenomenon, which we call partial self-trapping, takes place when the nonlocal nonlinearity is sufficiently strong.
A Numerical Wave Tank for Nonlinear Waves with Passive Absorption
Institute of Scientific and Technical Information of China (English)
周宗仁; 尹彰; 石瑞祥
2001-01-01
A numerical wave tank with passive absorption for irregular waves is considered in this paper. Waves with spectralshapes corresponding to that of the Mitsuyasu-Bretschneider type are used as the initial condition at one end of theflume. An absorbing boundary is imposed at the other end of the wave flume to minimize reflection. By use of aLagrangian description for the surface elevation, and finite difference for approximation of the time derivative, the problem is then solved by the boundary element method. The effects of the absorbing boundary are investigated by varyingthe values of the absorption coefficient μ, and studying the time histories of the surface elevations "recorded" on pre-se-lected locations.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Nonlinear wave mechanics from classical dynamics and scale covariance
Energy Technology Data Exchange (ETDEWEB)
Hammad, F. [Departement TC-SETI, Universite A.Mira de Bejaia, Route Targa Ouzemmour, 06000 Bejaia (Algeria)], E-mail: fayhammad@yahoo.fr
2007-10-29
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed.
Non-Linear Langmuir Wave Modulation in Collisionless Plasmas
DEFF Research Database (Denmark)
Dysthe, K. B.; Pécseli, Hans
1977-01-01
A non-linear Schrodinger equation for Langmuir waves is presented. The equation is derived by using a fluid model for the electrons, while both a fluid and a Vlasov formulation are considered for the ion dynamics. The two formulations lead to significant differences in the final results, especially...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Exact controllability for a nonlinear stochastic wave equation
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The exact controllability for a semilinear stochastic wave equation with a boundary control is established. The target and initial spaces are L 2 ( G × H −1 ( G with G being a bounded open subset of R 3 and the nonlinear terms having at most a linear growth.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
An inhomogeneous wave equation and non-linear Diophantine approximation
DEFF Research Database (Denmark)
Beresnevich, V.; Dodson, M. M.; Kristensen, S.;
2008-01-01
A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution...... is studied. Both the Lebesgue and Hausdorff measures of this set are obtained....
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
NUMERICAL SIMULATIONS OF NONLINEAR WAVE TRANSFORMATION AROUND WAVE-PERMEABLE STRUCTURE
Institute of Scientific and Technical Information of China (English)
Li Xi; YAN Yi-xin
2005-01-01
The problem of wave partial/full reflection and transmission by wave-permeable structure is approached by solving the shape-related function with focus on the understanding of wave attenuation.2D depth-averaged Boussinesq type wave equations are given with new damping item in simulating the nonlinear wave transmission through wave-permeable structure.1D wave equation is examined to give the analytical expression of the absorbing coefficient, and is compared with laboratory data in flume to calibrate the coefficients, and the expression is applied directly in modified Boussinesq type equations.Compared with wave basin data for various incident wave conditions,the accurate predictions of combined diffraction-refraction effects in simulating nonlinear wave going through wave-permeable breakwater in the engineering application can be obtained.It shows that wave-permeable breakwaters with proper absorbing effects can be used as an effective alternative to massive gravity breakwaters in reduction of wave transmission in shallow water.
Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types
Remillieux, Marcel C.; Guyer, Robert A.; Payan, Cédric; Ulrich, T. J.
2016-03-01
In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.
Nonlinear single Compton scattering of an electron wave-packet
Angioi, A; Di Piazza, A
2016-01-01
In the presence of a sufficiently intense electromagnetic laser field, an electron can absorb on average a large number of photons from the laser and emit a high-energy one (nonlinear single Compton scattering). The case of nonlinear single Compton scattering by an electron with definite initial momentum has been thoroughly investigated in the literature. Here, we consider a more general initial state of the electron and use a wave-packet obtained as a superposition of Volkov wave functions. In particular, we investigate the energy spectrum of the emitted radiation at fixed observation direction and show that in typical experimental situations the sharply peaked structure of nonlinear single Compton scattering spectra of an electron with definite initial energy is almost completely washed out. Moreover, we show that at comparable uncertainties, the one in the momentum of the incoming electron has a larger impact on the photon spectra at a fixed observation direction than the one on the laser frequency, relate...
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
The nonlinear evolution of rogue waves generated by means of wave focusing technique
Hu, HanHong; Ma, Ning
2011-01-01
Generating the rogue waves in offshore engineering is investigated, first of all, to forecast its occurrence to protect the offshore structure from being attacked, to study the mechanism and hydrodynamic properties of rouge wave experimentally as well as the rouge/structure interaction for the structure design. To achieve these purposes demands an accurate wave generation and calculation. In this paper, we establish a spatial domain model of fourth order nonlinear Schrödinger (NLS) equation for describing deep-water wave trains in the moving coordinate system. In order to generate rogue waves in the experimental tank efficiently, we take care that the transient water wave (TWW) determines precisely the concentration of time/place. First we simulate the three-dimensional wave using TWW in the numerical tank and modeling the deepwater basin with a double-side multi-segmented wave-maker in Shanghai Jiao Tong University (SJTU) under the linear superposing theory. To discuss its nonlinearity for guiding the experiment, we set the TWW as the initial condition of the NLS equation. The differences between the linear and nonlinear simulations are presented. Meanwhile, the characteristics of the transient water wave, including water particle velocity and wave slope, are investigated, which are important factors in safeguarding the offshore structures.
Energy Technology Data Exchange (ETDEWEB)
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Evolution of Nonlinear Internal Waves in China Seas
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Weak bond detection in composites using highly nonlinear solitary waves
Singhal, Taru; Kim, Eunho; Kim, Tae-Yeon; Yang, Jinkyu
2017-05-01
We experimentally investigate a diagnostic technique for identifying a weak bond in composites using highly nonlinear solitary waves (HNSWs). We set up a one-dimensional chain of granular crystals, consisting of spherical particles with nonlinear interactions, to generate HNSWs. These solitary wave packets are transmitted into an inspection area of composites by making a direct contact with the chain. We demonstrate that a strong type of solitary waves injected to the weak bond area can break the weak bond of laminates, thereby causing delamination. Then, to identify the creation of the delamination, we transmit a weak type of solitary waves by employing the same apparatus, and measure the solitary waves reflected from the specimens. By analyzing these reflected solitary waves, we differentiate the weak bond samples with the pristine bond ones in an efficient and fast manner. The diagnostic results based on the proposed method are compared with the strength and energy release rate at bond interfaces, which are measured via standard testing methods such as three point bending and end notched flexure tests. This study shows the potential of solitary wave-based detection of weak bonds for hot spot monitoring of composite-based structures.
Nonlinear interaction of waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1979-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed by using the method of multiple scales. For the case of two waves, a strong nonlinear interaction exists if one of the frequencies w2 is twice the other frequency w1. Numerical results for flow past a flat plate show that this interaction mechanism is strongly destabilizing even in regions where either the fundamental or its harmonic is damped in the absence of the interaction. For the case of three waves, a strong nonlinear interaction exists when w3 = w2- w1. This combination resonance causes the amplitude of the wave with the difference frequency w3 to multiply many times in magnitude in a short distance even if it is damped in the absence of the interaction. The initial amplitudes play a dominant role in determining the changes in the amplitudes of the waves in both of these mechanisms.
Nonlinear dynamic behaviors of a floating structure in focused waves
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear interaction of two waves in boundary-layer flows
Nayfeh, A. H.; Bozatli, A. N.
1980-01-01
First-order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary-layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates
Institute of Scientific and Technical Information of China (English)
CAI Hong-Qiang; YANG Shu-Rong; XUE Ju-Kui
2011-01-01
The dynamics of the weak nonlinear matter solitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful to understand the dynamics of nonlinear matter waves in spinor BEGs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation freauencv are also obtained.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
Nonlinear waves in electromigration dispersion in a capillary
Christov, Ivan C
2016-01-01
We construct exact solutions to an unusual nonlinear advection--diffusion equation arising in the study of Taylor--Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions ({\\it i.e.}, non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approx...
Liu, Chang
2015-01-01
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the ?first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
On a nonlinear gravitational wave. Geodesics
Culetu, Hristu
2016-01-01
An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\\rho$ and the pressure $p_{z}$ are negative but finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, $Oz$ axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Characteristics of Short Wavelength Compressional Alfven Eigenmodes
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E D; Podesta, M; Bortolon, A; Crocker, N A; Gerhardt, S P; Bell, R E; Diallo, A; LeBlanc, B; Levinton, F M
2012-12-19
Most Alfvenic activity in the frequency range between Toroidal Alfven Eigenmodes and roughly one half of the ion cyclotron frequency on NSTX [M. Ono, et al., Nucl. Fusion 40 (2000) 557], that is, approximately 0.3 MHz up to ≈ 1.2 MHz, are modes propagating counter to the neutral beam ions. These have been modeled as Compressional and Global Alfven Eigenmodes (CAE and GAE) and are excited through a Doppler-shifted cyclotron resonance with the beam ions. There is also a class of co-propagating modes at higher frequency than the counter-propagating CAE and GAE. These modes have been identified as CAE, and are seen mostly in the company of a low frequency, n=1 kink-like mode. In this paper we present measurements of the spectrum of these high frequency CAE (hfCAE), and their mode structure. We compare those measurements to a simple model of CAE and present evidence of a curious non-linear coupling of the hfCAE and the low frequency kink-like mode.
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and cur...
Energy Technology Data Exchange (ETDEWEB)
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2006-08-15
Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method is applied to three nonlinear evolution equations. As a result, many exact travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions.
Generation and propagation of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.
2007-01-01
During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
Focusing of Spherical Nonlinear Pulses for Nonlinear Wave Equations Ⅲ. Subcritical Case
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper studied spherical pulses of solutions of the system of semilinear wave equations with the pulses focusing at a point in three space variables. It is shown that there is no nonlinear effect at leading terms of pulses, when the initial data is subcritical.
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Geodesic deviation in a nonlinear gravitational wave spacetime
Culetu, Hristu
2016-01-01
The tidal effects generated by a nonlinear gravitational wave are investigated in double-null v - u coordinates, as an exact solution of Einstein's field equations. The components $\\xi^{v}$ and $\\xi^{u}$ of the separation vector behave as in flat space but the transversal components $\\xi^{x}$ and $\\xi^{y}$ depend nonlinearly on $v$ through the Bessel and Neumann functions, far from the null surface $v = 0$. We show that the same results are obtained by means of the tetrad formalism.
Traveling wave solutions for some factorized nonlinear PDEs
Cornejo-Pérez, Octavio
2009-01-01
In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers-Fisher equation, the Burgers-Fisher equation and a nonlinear dispersive-dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive-dissipative equation are provided.
Detecting nonlinear acoustic waves in liquids with nonlinear dipole optical antennae
Maksymov, Ivan S
2015-01-01
Ultrasound is an important imaging modality for biological systems. High-frequency ultrasound can also (e.g., via acoustical nonlinearities) be used to provide deeply penetrating and high-resolution imaging of vascular structure via catheterisation. The latter is an important diagnostic in vascular health. Typically, ultrasound requires sources and transducers that are greater than, or of order the same size as the wavelength of the acoustic wave. Here we design and theoretically demonstrate that single silver nanorods, acting as optical nonlinear dipole antennae, can be used to detect ultrasound via Brillouin light scattering from linear and nonlinear acoustic waves propagating in bulk water. The nanorods are tuned to operate on high-order plasmon modes in contrast to the usual approach of using fundamental plasmon resonances. The high-order operation also gives rise to enhanced optical third-harmonic generation, which provides an important method for exciting the higher-order Fabry-Perot modes of the dipole...
Energy Technology Data Exchange (ETDEWEB)
Testa, D [CRPP, Association EURATOM-Confederation Suisse, EPFL, Lausanne (Switzerland); Fasoli, A [CRPP, Association EURATOM-Confederation Suisse, EPFL, Lausanne (Switzerland); Borba, D [Associacao EURATOM/IST (Portugal); EDFA-CSU, Culham Science Centre (United Kingdom); Baar, M de [FOM-Instituut Voor Plasmafysica, Rijnhuizen (Netherlands); Bigi, M [Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon (United Kingdom); Brzozowski, J [NADA VR-Euratom Association, Royal Institute of Technology, Stockholm (Sweden); Vries, P de [Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon (United Kingdom)
2004-07-01
We have investigated the effect of different ion cyclotron resonance frequency (ICRF) heating schemes, of error field modes, of the plasma shape and edge magnetic shear, and of the ion {nabla}B drift direction on the stability of Alfven eigenmodes (AEs). The use of multi-frequency or 2nd harmonic minority ICRF heating at high plasma density gives rise to a lower fast ion pressure gradient in the plasma core and to a reduced mode activity in the Alfven frequency range. Externally excited low-amplitude error fields lead to a much larger AE instability threshold, which we attribute to a moderate radial redistribution of the fast ions. The edge plasma shape has a clear stabilizing effect on high-n, radially localized AEs. The damping rate of n = 1 toroidal AEs is a factor 3 higher when the ion {nabla}B drift is directed towards the divertor. These results represent a useful step towards the extrapolation of current scenarios to the inclusion of fusion-born alpha particles in ITER, with possible application for feedback control schemes for the various ITER operating regimes.
NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER
Institute of Scientific and Technical Information of China (English)
菅永军; 鄂学全; 柏威
2003-01-01
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
Collapse of Nonlinear Gravitational Waves in Moving-Puncture Coordinates
Hilditch, David; Weyhausen, Andreas; Dietrich, Tim; Bruegmann, Bernd; Montero, Pedro J; Mueller, Ewald
2013-01-01
We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data -- Brill and Teukolsky waves -- and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters -- in particular negative amplitudes -- Brill data can be evolved with moving-puncture coordinates, and behave similarly t...
2-D Composite Model for Numerical Simulations of Nonlinear Waves
Institute of Scientific and Technical Information of China (English)
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
The Nonlinear Landau Damping Rate of a Driven Plasma Wave
Energy Technology Data Exchange (ETDEWEB)
Benisti, D; Strozzi, D J; Gremillet, L; Morice, O
2009-08-04
In this Letter, we discuss the concept of the nonlinear Landau damping rate, {nu}, of a driven electron plasma wave, and provide a very simple, practical, analytic formula for {nu} which agrees very well with results inferred from Vlasov simulations of stimulated Raman scattering. {nu} actually is more complicated an operator than a plain damping rate, and it may only be seen as such because it assumes almost constant values before abruptly dropping to 0. The decrease of {nu} to 0 is moreover shown to occur later when the wave amplitude varies in the direction transverse to its propagation.
Optimal Control Of Nonlinear Wave Energy Point Converters
DEFF Research Database (Denmark)
Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten
2013-01-01
In this paper the optimal control law for a single nonlinear point absorber in irregular sea-states is derived, and proven to be a closed-loop controller with feedback from measured displacement, velocity and acceleration of the floater. However, a non-causal integral control component dependent...... idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states......, absorbs almost the same power as the optimal controller....
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Multisymplectic five-point scheme for the nonlinear wave equation
Institute of Scientific and Technical Information of China (English)
WANG Yushun; WANG Bin; YANG Hongwei; WANG Yunfeng
2003-01-01
In this paper, we introduce the multisymplectic structure of the nonlinear wave equation, and prove that the classical five-point scheme for the equation is multisymplectic. Numerical simulations of this multisymplectic scheme on highly oscillatory waves of the nonlinear Klein-Gordon equation and the collisions between kink and anti-kink solitons of the sine-Gordon equation are also provided. The multisymplectic schemes do not need to discrete PDEs in the space first as the symplectic schemes do and preserve not only the geometric structure of the PDEs accurately, but also their first integrals approximately such as the energy, the momentum and so on. Thus the multisymplectic schemes have better numerical stability and long-time numerical behavior than the energy-conserving scheme and the symplectic scheme.
Collapse of nonlinear electron plasma waves in a plasma layer
Grimalsky, V.; Koshevaya, S.; Rapoport, Yu; Kotsarenko, A.
2016-10-01
The excitation of nonlinear electron plasma waves in the plasma layer is investigated theoretically. This excitation is realized by means of initial oscillatory perturbations of the volume electron concentration or by initial oscillatory distributions of the longitudinal electron velocity. The amplitudes of the initial perturbations are small and the manifestation of the volume nonlinearity is absent. When the amplitudes of the initial perturbations exceed some thresholds, the values of the electron concentration near the plasma boundary increase catastrophically. The maxima of the electron concentration reach extremely high magnitudes, and sharp peaks in the electron concentration occur, which are localized both in the longitudinal and transverse directions. This effect is interpreted as wave collapse near the plasma boundary.
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Numerical Simulation of Seabed Response and Liquefaction due to Non-linear Waves
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-feng; ZHANG Qing-he; HAN Tao; QIN Chong-ren
2005-01-01
Based on Biot's consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-linearity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Indian Academy of Sciences (India)
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes
Lesur, Maxime
2011-01-01
The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of high-energy ions produced by the fusion reaction. Such particles can excite Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. To develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, is required. In the case of an isolated single resonance, the problem is homothetic to the so-called Berk-Breizman (BB) problem, which is an extension of the classic bump-on-tail electrostatic problem, including external damping to a thermal plasma, and collisions. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes. The c...
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.
Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi
2008-03-01
In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.
Identification and determination of solitary wave structures in nonlinear wave propagation
Energy Technology Data Exchange (ETDEWEB)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs.
Spectrograms of ship wakes: identifying linear and nonlinear wave signals
Pethiyagoda, Ravindra; Moroney, Timothy J
2016-01-01
A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified three additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. Further, we show that additional features in the experimental data are caused by nonlinearity. Finally, we explain a discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceler...
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Lepri, Stefano, E-mail: stefano.lepri@isc.cnr.it [Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (Italy); Pikovsky, Arkady [Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str 24/25, Potsdam (Germany); Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
Nonlinear Propagation of Planet-Generated Tidal Waves
Rafikov, R. R.
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to shock formation and wake dissipation, is followed in the weakly nonlinear regime. The 2001 local approach of Goodman and Rafikov is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of approx. 10(exp 6)-10(exp 7) yr, even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed that could be incorporated into the study of gap formation in a gaseous disk around the planet.
Nonlinear propagation of planet-generated tidal waves
Rafikov, R R
2002-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process spanning a significant fraction of the disk. Torques induced by the planet could be significant drivers of disk evolution on timescales of the order 1-10 Myr even in the absence of strong background viscosity. A global prescription for angular momentum deposition is developed which could be incorporated into the study of gap formation in a gaseous disk around the planet.
New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
Rezzolla, L
2002-01-01
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Probabilistic approach to nonlinear wave-particle resonant interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2017-02-01
In this paper we provide a theoretical model describing the evolution of the charged-particle distribution function in a system with nonlinear wave-particle interactions. Considering a system with strong electrostatic waves propagating in an inhomogeneous magnetic field, we demonstrate that individual particle motion can be characterized by the probability of trapping into the resonance with the wave and by the efficiency of scattering at resonance. These characteristics, being derived for a particular plasma system, can be used to construct a kinetic equation (or generalized Fokker-Planck equation) modeling the long-term evolution of the particle distribution. In this equation, effects of charged-particle trapping and transport in phase space are simulated with a nonlocal operator. We demonstrate that solutions of the derived kinetic equations agree with results of test-particle tracing. The applicability of the proposed approach for the description of space and laboratory plasma systems is also discussed.
Analytical description of nonlinear acoustic waves in the solar chromosphere
Litvinenko, Yuri E.; Chae, Jongchul
2017-02-01
Aims: Vertical propagation of acoustic waves of finite amplitude in an isothermal, gravitationally stratified atmosphere is considered. Methods: Methods of nonlinear acoustics are used to derive a dispersive solution, which is valid in a long-wavelength limit, and a non-dispersive solution, which is valid in a short-wavelength limit. The influence of the gravitational field on wave-front breaking and shock formation is described. The generation of a second harmonic at twice the driving wave frequency, previously detected in numerical simulations, is demonstrated analytically. Results: Application of the results to three-minute chromospheric oscillations, driven by velocity perturbations at the base of the solar atmosphere, is discussed. Numerical estimates suggest that the second harmonic signal should be detectable in an upper chromosphere by an instrument such as the Fast Imaging Solar Spectrograph installed at the 1.6-m New Solar Telescope of the Big Bear Observatory.
Nonlinear Electromagnetic Waves in a Degenerate Electron-Positron Plasma
El-Labany, S. K.; El-Taibany, W. F.; El-Samahy, A. E.; Hafez, A. M.; Atteya, A.
2015-08-01
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed.
Irregular Wave Forces on Monopile Foundations. Effect af Full Nonlinearity and Bed Slope
DEFF Research Database (Denmark)
Schløer, Signe; Bredmose, Henrik; Bingham, Harry B.
2011-01-01
Forces on a monopile from a nonlinear irregular unidirectional wave model are investigated. Two seabed profiles of different slopes are considered. Morison’s equation is used to investigate the forcing from fully nonlinear irregular waves and to compare the results with those obtained from linear...... wave theory and with stream function wave theory. The latter of these theories is only valid on a flat bed. The three predictions of wave forces are compared and the influence of the bed slope is investigated. Force-profiles of two selected waves from the irregular wave train are further compared...... with the corresponding forceprofiles from stream function theory. The results suggest that the nonlinear irregular waves give rise to larger extreme wave forces than those predicted by linear theory and that a steeper bed slope increases the wave forces both for linear and nonlinear waves. It is further found...
Feng, Q S; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T
2016-01-01
The properties of the nonlinear frequency shift (NFS) especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas have been researched by Vlasov simulation. The pictures of the nonlinear frequency shift from harmonic generation and particles trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given and the results of Vlasov simulation are consistent to the theoretical result of multi-ion species plasmas. When the wave number $k\\lambda_{De}$ is small, such as $k\\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will reach as large as nearly $15\\%$ when the wave amplitude $|e\\phi/T_e|\\sim0.1$, which indicates that in the condition of small $k\\lambda_{De}$, the fluid NFS dominates in the saturation of stimulated Brillouin scattering especially when the nonlinear IAW amplitude is large.
Nonlinear Wave-Currents interactions in shallow water
Lannes, David
2015-01-01
We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of such waves. These equations couple the surface elevation to the vertically averaged horizontal velocity and are therefore independent of the vertical variable. In the presence of vorticity, the dependence on the vertical variable cannot be removed from the vorticity equation but it was however shown in [?] that the motion of the waves could be described using an extended Green-Naghdi system. In this paper we propose an analysis of these equations, and show that they can be used to get some new insight into wave-current interactions. We show in particular that solitary waves may have a drastically different behavior in the presence of vorticity and show the existence of solitary waves of maximal amplitude with a peak at their crest, whose angle depends on the vorticity. We als...
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
Excitation of nonlinear ion acoustic waves in CH plasmas
Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T
2016-01-01
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ k\\lambda_{De} $ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\\lambda_{De}$ increasing. When $k\\lambda_{De}$ is not large, such as $k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\\lambda_{De}$ is large, such as $k\\lambda_{De}=0.7$, the linear ...
Nonlinear electrostatic waves in inhomogeneous dense dusty magnetoplasmas
Energy Technology Data Exchange (ETDEWEB)
Mahmood, S., E-mail: shahzad_mahmoodpk@yahoo.co [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan); Haque, Q. [Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan)
2010-01-25
The nonlinear electrostatic drift waves are studied using quantum hydrodynamic model in dusty quantum magnetoplasmas. The dissipative effects due to collisions between ions and dust particles have also been taken into account. The Korteweg-de Vries Burgers (KdVB) like equation is derived and analytical solution is obtained using tanh method. The limiting cases of KdV type solitary waves, Burger type monotonic shock waves and oscillatory shock solutions are also presented. It is found that both hump and dip type solitary structures are possible in quantum dusty plasmas. However, amplitude and width of the nonlinear structure depend on the dust charge polarity and its concentration in electron-ion quantum plasmas. The monotonic shock like structure is independent of the quantum parameter. It is found that shock strength is increased in the presence of positively charged particles in comparison with negatively charged dust particles. The oscillatory shock structures are also obtained and it is found that change in dust charge polarity only shifts the phase of the oscillatory shock in plasmas. The numerical results are also presented for illustration.
Rotation-induced nonlinear wavepackets in internal waves
Energy Technology Data Exchange (ETDEWEB)
Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk [Department of Mathematics, University College London, London WC1E 6BT (United Kingdom)
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Rotation-induced nonlinear wavepackets in internal waves
Whitfield, A. J.; Johnson, E. R.
2014-05-01
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Enhanced continuous-wave four-wave mixing efficiency in nonlinear AlGaAs waveguides.
Apiratikul, Paveen; Wathen, Jeremiah J; Porkolab, Gyorgy A; Wang, Bohan; He, Lei; Murphy, Thomas E; Richardson, Christopher J K
2014-11-03
Enhancements of the continuous-wave four-wave mixing conversion efficiency and bandwidth are accomplished through the application of plasma-assisted photoresist reflow to reduce the sidewall roughness of sub-square-micron-modal area waveguides. Nonlinear AlGaAs optical waveguides with a propagation loss of 0.56 dB/cm demonstrate continuous-wave four-wave mixing conversion efficiency of -7.8 dB. Narrow waveguides that are fabricated with engineered processing produce waveguides with uncoated sidewalls and anti-reflection coatings that show group velocity dispersion of +0.22 ps²/m. Waveguides that are 5-mm long demonstrate broadband four-wave mixing conversion efficiencies with a half-width 3-dB bandwidth of 63.8-nm.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Beach steepness effects on nonlinear infragravity-wave interactions : A numerical study
de Bakker, A. T M; Tissier, M. F S; Ruessink, B. G.
2016-01-01
The numerical model SWASH is used to investigate nonlinear energy transfers between waves for a diverse set of beach profiles and wave conditions, with a specific focus on infragravity waves. We use bispectral analysis to study the nonlinear triad interactions, and estimate energy transfers to deter
Nonlinear acoustic waves in a collisional self-gravitating dusty plasma
Institute of Scientific and Technical Information of China (English)
Guo Zhi-Rong; Yang Zeng-Qiang; Yin Bao-Xiang; Sun Mao-Zhu
2010-01-01
Using the reductive perturbation method,we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma.The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation,and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles.
Effect of scalar nonlinearity on zonal flow generation by Rossby waves
Mikhailovskii, A. B.; Lominadze, J. G.; Erokhin, N. N.; Erokhin, N. S.; Smolyakov, A. I.; Tsypin, V. S.
2007-01-01
Effects of scalar nonlinearity on the generation of zonal flow by Rossby waves in shallow rotating fluid are considered. Zonal flows are generated via the action of Reynolds stress due to vector nonlinearity together with the effects of scalar nonlinearity. It is shown that the scalar nonlinearity r
Optical Multi-hysteresises and "Rogue Waves" in Nonlinear Plasma
Kaplan, A E
2010-01-01
An overdense plasma layer irradiated by an intense light can exhibit dramatic nonlinear-optical effects due to a relativistic mass-effect of free electrons: highly-multiple hysteresises of reflection and transition, and emergence of gigantic "rogue waves". Those are trapped quasi-soliton field spikes inside the layer, sustained by an incident radiation with a tiny fraction of their peak intensity once they have been excited by orders of magnitude larger pumping. The phenomenon persists even in the layers with "soft" boundaries, as well as in a semi-infinite plasma with low absorption.
Exact travelling wave solutions of nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-04-15
An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.
Fourth order wave equations with nonlinear strain and source terms
Liu, Yacheng; Xu, Runzhang
2007-07-01
In this paper we study the initial boundary value problem for fourth order wave equations with nonlinear strain and source terms. First we introduce a family of potential wells and prove the invariance of some sets and vacuum isolating of solutions. Then we obtain a threshold result of global existence and nonexistence. Finally we discuss the global existence of solutions for the problem with critical initial condition I(u0)[greater-or-equal, slanted]0, E(0)=d. So the Esquivel-Avila's results are generalized and improved.
Critical exponent for damped wave equations with nonlinear memory
Fino, Ahmad
2010-01-01
We consider the Cauchy problem in $\\mathbb{R}^n,$ $n\\geq 1,$ for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\\to\\infty$ of small data solutions have been established in the case when $1\\leq n\\leq3.$ Moreover, we derive a blow-up result under some positive data for in any dimensional space. It turns out that the critical exponent indeed coincides with the one to the corresponding semilinear heat equation.
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...
Theoretical Study of Wave Breaking for Nonlinear Water Waves Propagating on a Sloping Bottom
Chen, Y. Y.; Hsu, H. C.; Li, M. S.
2012-04-01
In this paper, a third-order asymptotic solution in a Lagrangian framework describing nonlinear water wave propagation on the surface of a uniform sloping bottom is presented. A two-parameter perturbation method is used to develop a new mathematical derivation. The particle trajectories, wave pressure and Lagrangian velocity potential are obtained as a function of the nonlinear wave steepness and the bottom slope perturbed to third order. This theoretical solution in Lagrangian form satisfies state of the normal pressure at the free surface. The condition of the conservation of mass flux is examined in detail for the first time. The two important properties in Lagrangian coordinates, Lagrangian wave frequency and Lagrangian mean level, are included in the third-order solution. The solution can also be used to estimate the mean return current for waves progressing over the sloping bottom. The Lagrangian solution untangle the description of the features of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the process of successive deformation of a wave profile and water particle trajectories leading to wave breaking. A series of experiment was conducted to validate the obtained theoretical solution. The proposed solution will be used to determine the wave shoaling and breaking process and the comparisons between the experimental and theoretical results are excellent. For example, the variations of phase velocity on sloping bottom are obtained by 7 set of two close wave gauges and the theoretical result could accurately predict the measured phase velocity. The theoretical wave breaking index can be derived by use of the kinematic stability parameter (K.P.S). The comparisons between the theory, experiment (present study, Iwagali et al.(1974), Deo et al.(2003) and Tsai et al.(2005)) and empirical formula of Goda (2004) for the breaking index(u/C) versus the relative water depth(d/L) under two different bottom slopes shows that the
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
On global attraction to stationary states for wave equations with concentrated nonlinearities
Kopylova, E.
2016-01-01
The global attraction to stationary states is established for solutions to 3D wave equations with concentrated nonlinearities: each finite energy solution converges as $t\\to\\pm\\infty$ to stationary states. The attraction is caused by nonlinear energy radiation.
Nonlinear dynamics of soliton gas with application to "freak waves"
Shurgalina, Ekaterina
2017-04-01
So-called "integrable soliton turbulence" attracts much attention of scientific community nowadays. We study features of soliton interactions in the following integrable systems: Korteweg - de Vries equation (KdV), modified Korteweg - de Vries equation (mKdV) and Gardner equations. The polarity of interacted solitons dramatically influences on the process of soliton interaction. Thus if solitons have the same polarity the maximum of the wave field decreases during the process of nonlinear interactions as well statistical moments (skewness and kurtosis). In this case there is no abnormally large wave formation and this scenario is possible for all considered equation. Completely different results can be obtained for a soliton gas consisted of solitons with different polarities: such interactions lead to an increase of resulting impulse and kurtosis. Tails of distribution functions can grow significantly. Abnormally large waves (freak waves) appear in such solitonic fields. Such situations are possible just in case of mKdV and Gardner equations which admit the existence of bipolar solitons. New effect of changing a defect's moving direction in soliton lattices and soliton gas is found in the present study. Manifestation of this effect is possible as the result of negative phase shift of small soliton in the moment of nonlinear interaction with large solitons. It is shown that the effect of negative velocity is the same for KdV and mKdV equations and it can be found from the kinematic assumption without applying the kinetic theory. Averaged dynamics of the "smallest" soliton (defect) in a soliton gas, consisting of solitons with random amplitudes is investigated. The averaged criterion of velocity sign change confirmed by numerical simulation is obtained.
Nonlinear interactions of electromagnetic waves with the auroral ionosphere
Wong, Alfred Y.
1999-09-01
The ionosphere provides us with an opportunity to perform plasma experiments in an environment with long confinement times, very large-scale lengths, and no confining walls. The auroral ionosphere with its nearly vertical magnetic field geometry is uniquely endowed with large amount of free energy from electron and ion precipitation along the magnetic field and mega-ampere current across the magnetic field. To take advantage of this giant outdoor laboratory, two facilities HAARP and HIPAS, with frequencies ranging from the radio to optical bands, are now available for active probing of and interaction with this interesting region. The ponderomotive pressures from the self-consistent wave fields have produced significant local perturbations of density and particle distributions at heights where the incident EM frequency matches a plasma resonance. This paper will review theory and experiments covering the nonlinear phenomena of parametric decay instability to wave collapse processes. At HF frequencies plasma lenses can be created by preconditioning pulses to focus what is a normally divergent beam into a high-intensity spot to further enhance nonlinear phenomena. At optical wavelengths a large rotating liquid metal mirror is used to focus laser pulses up to a given height. Such laser pulses are tuned to the same wavelengths of selected atomic and molecular resonances, with resulting large scattering cross sections. Ongoing experiments on dual-site experiments and excitation of ELF waves will be presented. The connection of such basic studies to environmental applications will be discussed. Such applications include the global communication using ELF waves, the ozone depletion and remediation and the control of atmospheric CO2 through the use of ion cyclotron resonant heating.
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...
Energy Technology Data Exchange (ETDEWEB)
Tsuchiya, T. [Dia Consultants Company, Tokyo (Japan)
1996-10-01
Nonlinear full-wave tomography (FWT) is under investigation to improve the estimation accuracy of Vp/Vs distributions. Full-wave tomography is one of the underground structure exploration methods mainly using Tarantola`s nonlinear local optimization method (LOM). Numerical experiment for FWT was carried out assuming relatively weak nonlinear underground structure. In the case of inversion by local optimization method, adequate preconditioning is important. Utilization of geological information is also effective in estimating low-frequency components of a model. As far as data are obtained under proper observation arrangement, even in actual field, precise estimation of Vp/Vs distributions is possible by FWT using explosion in a hole as wave source. In full-wave tomography, selection of observation arrangement is essential for both Vp and Vs. However, the proper arrangement is different between Vp and Vs. Approach to different analyses for Vp and Vs is also necessary by using only proper data for Vp and Vs among obtained data sets. 4 figs.
Pressure-gradient-induced Alfven eigenmodes: 2. Kinetic excitation with ion temperature gradient
Bierwage, Andreas; Zonca, Fulvio
2009-01-01
The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfven eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as alpha-induced toroidal Alfven eigenmodes (alphaTAE); that is, bound states trapped between pressure-gradient-induced potential barriers of the Schroedinger equation for shear Alfven waves. Using numerical tools, we examine in detail the effect of kinetic thermal ion compression on alphaTAEs; both non-resonant coupling to ion sound waves and wave-particle resonances. It is shown that the Alfvenic ITG instability thresholds (e.g., the critical temperature gradient) are determined by two resonant absorption mechanisms: Landau damping and continuum damping. The numerical results are interpreted on the basis of a theoretical framework previously derived from a variational f...
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
On the Amplitude Equations for Weakly Nonlinear Surface Waves
Benzoni-Gavage, Sylvie; Coulombel, Jean-François
2012-09-01
Nonlocal generalizations of Burgers' equation were derived in earlier work by Hunter (Contemp Math, vol 100, pp 185-202. AMS, 1989), and more recently by Benzoni-Gavage and Rosini (Comput Math Appl 57(3-4):1463-1484, 2009), as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage (Differ Integr Equ 22(3-4):303-320, 2009) under an appropriate stability condition originally pointed out by Hunter. The same stability condition has also been shown to be necessary for well-posedness in Sobolev spaces in a previous work of the authors in collaboration with Tzvetkov (Benzoni-Gavage et al. in Adv Math 227(6):2220-2240, 2011). In this article, we show how the verification of Hunter's stability condition follows from natural stability assumptions on the original hyperbolic boundary value problem, thus avoiding lengthy computations in each particular situation. We also show that the resulting amplitude equation has a Hamiltonian structure when the original boundary value problem has a variational origin. Our analysis encompasses previous equations derived for nonlinear Rayleigh waves in elasticity.
Recent progress in nonlinear kinetic Alfvén waves
Directory of Open Access Journals (Sweden)
D. J. Wu
2004-01-01
Full Text Available This paper presents a review of recent progress in nonlinear kinetic Alfvén wave (KAW hereafter. We start with the two-fluid theory of KAWs and show how the difference between the motions of electrons and ions in small-scale fields of KAWs modifies the Alfvén wave properties. Then, we focus on nonlinear solitary structures of KAWs. A general criterion of the existence for solitary KAW (SKAW hereafter and its exact analytical solution in a low-β plasma (βe/mi are presented, where the electron drift velocity along the background magnetic field is larger than the thermal speed within a SKAW, and hence can excite, for instance, ion acoustic turbulence as showed by in situ observations of satellites in space plasmas. In consequence, the turbulence results in kinetic dissipation of the SKAW and dynamical evolution in its structure. We further discuss the structure of the dissipated SKAW (DSKAW hereafter that evolves from the SKAW due to the dissipation. The result shows that the DSKAW has a local shock-like structure in its density profile and a net electric potential drop over the shock-like structure. In particular, the electric potential drop of the DSKAW can be expected to accelerate electrons efficiently to the order of the local Alfvén speed. The application of the DSKAW acceleration mechanism to the auroral electron acceleration is also discussed. Finally, a few perspectives of KAW studies in future are presented.
Matda, Y.; Crawford, F. W.
1974-01-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described.
Nguyen, Vu A.; Palo, Scott E.; Lieberman, Ruth S.; Forbes, Jeffrey M.; Ortland, David A.; Siskind, David E.
2016-07-01
Theory and past observations have provided evidence that atmospheric tides and other global-scale waves interact nonlinearly to produce additional secondary waves throughout the space-atmosphere interaction region. However, few studies have investigated the generation region of nonlinearly generated secondary waves, and as a result, the manifestation and impacts of these waves are still poorly understood. This study focuses on the nonlinear interaction between the quasi 2 day wave (2dayW3) and the migrating diurnal tide (DW1), two of the largest global-scale waves in the atmosphere. The fundamental goals of this effort are to characterize the forcing region of the secondary waves and to understand how it relates to their manifestation on a global scale. First, the Fast Fourier Synoptic Mapping method is applied to Thermosphere Ionosphere Mesosphere Energetics and Dynamics-Sounding of the Atmosphere using Broadband Emission Radiometry satellite observations to provide new evidence of secondary waves. These results show that secondary waves are only significant above 80 km. The nonlinear forcing for each secondary wave is then computed by extracting short-term primary wave information from a reanalysis model. The estimated nonlinear forcing quantities are used to force a linearized tidal model in order to calculate numerical secondary wave responses. Model results show that the secondary waves are significant from the upper mesosphere to the middle thermosphere, highlighting the implications for the atmosphere-space weather coupling. The study also concludes that the secondary wave response is most sensitive to the nonlinear forcing occurring in the lower and middle mesosphere and not coincident with the regions of strongest nonlinear forcing.
Nonlinear processes in the strong wave-plasma interaction
Pegoraro, Francesco; Califano, Francesco; Attico, Nicola; Bulanov, Sergei
2000-10-01
Nonlinear interactions in hot laboratory and/or astrophysical plasmas are a very efficient mechanism able to transfer the energy from the large to the small spatial scales of the system. As a result, kinetic processes are excited and play a key role in the plasma dynamics since the typical fluid dissipative length scales (where the nonlinear cascade is stopped) are (much) smaller then the kinetic length scales. Then, the key point is the role of the kinetic effects in the global plasma dynamics, i.e. whether the kinetic effects remains confined to the small scales of the system or whether there is a significant feedback on the large scales. Here we will address this problem by discussing the nonlinear kinetic evolution of the electromagnetic beam plasma instability where phase space vortices, as well as large scale vortex like magnetic structures in the physical space, are generated by wave - particle interactions. The role and influence of kinetic effects on the large scale plasma dynamics will be also discussed by addressing the problem of collisionless magnetic reconection.
Lp-decay rates to nonlinear diffusion waves for p-system with nonlinear damping
Institute of Scientific and Technical Information of China (English)
ZHU Changjiang; JIANG Mina
2006-01-01
In this paper, we study the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (-v(x, t), -u(x, t)) governed by the classical Darcy's law provided that the corresponding prescribed initial error function (w0(x), z0(x))lies in (H3 × H2) (R) and |v+ - v-| + ‖w0‖3 + ‖z0‖2 is sufficiently small.Furthermore, the Lp (2 ≤ p ≤ +∞) convergence rates of the solutions are also obtained.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value
Directory of Open Access Journals (Sweden)
Thanh Long Nguyen
2004-09-01
Full Text Available We consider the initial-boundary value problem for the nonlinear wave equation $$displaylines{ u_{tt}-u_{xx}+f(u,u_{t}=0,quad xin Omega =(0,1,; 0
Weak Turbulence in the Magnetosphere: Formation of Whistler Wave Cavity by Nonlinear Scattering
Crabtree, C; Ganguli, G; Mithaiwala, M; Galinsky, V; Shevchenko, V
2011-01-01
We consider the weak turbulence of whistler waves in the in low-\\beta\\ inner magnetosphere of the Earth. Whistler waves with frequencies, originating in the ionosphere, propagate radially outward and can trigger nonlinear induced scattering by thermal electrons provided the wave energy density is large enough. Nonlinear scattering can substantially change the direction of the wave vector of whistler waves and hence the direction of energy flux with only a small change in the frequency. A portion of whistler waves return to the ionosphere with a smaller perpendicular wave vector resulting in diminished linear damping and enhanced ability to pitch-angle scatter trapped electrons. In addition, a portion of the scattered wave packets can be reflected near the ionosphere back into the magnetosphere. Through multiple nonlinear scatterings and ionospheric reflections a long-lived wave cavity containing turbulent whistler waves can be formed with the appropriate properties to efficiently pitch-angle scatter trapped e...
Abbasnia,Arash; Ghiasi,Mahmoud
2014-01-01
Fully nonlinear wave interaction with a fixed breakwater is investigated in a numerical wave tank (NWT). The potential theory and high-order boundary element method are used to solve the boundary value problem. Time domain simulation by a mixed Eulerian-Lagrangian (MEL) formulation and high-order boundary integral method based on non uniform rational B-spline (NURBS) formulation is employed to solve the equations. At each time step, Laplace equation is solved in Eulerian frame and fully non-l...
Alfven cyclotron instability and ion cyclotron emission
Energy Technology Data Exchange (ETDEWEB)
Gorelenkov, N.N.; Cheng, C.Z.
1995-07-01
Two-dimensional solutions of compressional Alfven eigenmodes (CAE) are studied in the cold plasma approximation. For finite inverse aspect ratio tokamak plasmas the two-dimensional eigenmode envelope is localized at the low magnetic field side with the radial and poloidal localization on the order of a/{radical}m and a/(fourth root of m), respectively, where m is the dominant poloidal mode number. Charged fusion product driven Alfven Cyclotron Instability (ACI) of the compressional Alfven eigenmodes provides the explanation for the ion cyclotron emission (ICE) spectrum observed in tokamak experiments. The ACI is excited by fast charged fusion products via Doppler shifted cyclotron wave-particle resonances. The ion cyclotron and electron Landau dampings and fast particle instability drive are calculated perturbatively for deuterium-deuterium (DD) and deuterium-tritium (DT) plasmas. Near the plasma edge at the low field side the velocity distribution function of charged fusion products is localized in both pitch angle and velocity. The poloidal localization of the eigenmode enhances the ACI growth rates by a factor of {radical}m in comparison with the previous results without poloidal envelope. The thermal ion cyclotron damping determines that only modes with eigenfrequencies at multiples of the edge cyclotron frequency of the background ions can be easily excited and form an ICE spectrum similar to the experimental observations. Theoretical understanding is given for the results of TFTR DD and DT experiments with {upsilon}{sub {alpha}0}/{upsilon}{sub A} < 1 and JET experiments with {upsilon}{sub {alpha}0}/{upsilon}{sub A} > 1.
Dipole AlfvenVortex with Finite Ion Larmor Radius in a Low-Beta Plasma
Institute of Scientific and Technical Information of China (English)
WANG Xu-Yu; HE Xian-Tu; LIU Zhen-Xing; CAO Jin-Bin
2000-01-01
A set of nonlinear fluid equations which include the effects of ion gyroradius is derived to describe Alfven vortex. The correction of finite ion gyroradius to the Alfven vortex in the inertial region is much more significant than that in the kinetic region. The amplitude of the vortex is enhanced in both regions. The scale of the vortex in the kinetic region becomes larger whereas it becomes smaller in the inertial region.
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, R.
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of {minus}100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k{sub p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase transition point
Nixon, Sean; Yang, Jianke
2012-01-01
Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.
Institute of Scientific and Technical Information of China (English)
WU; Shaoping(吴少平); YI; Fan(易帆)
2002-01-01
By using FICE scheme, a numerical simulation of nonlinear propagation of gravity wave packet in three-dimension compressible atmosphere is presented. The whole nonlinear propagation process of the gravity wave packet is shown; the basic characteristics of nonlinear propagation and the influence of the ambient winds on the propagation are analyzed. The results show that FICE scheme can be extended in three-dimension by which the calculation is steady and kept for a long time; the increase of wave amplitude is faster than the exponential increase according to the linear gravity theory; nonlinear propagation makes the horizontal perturbation velocity increase greatly which can lead to enhancement of the local ambient winds; the propagation path and the propagation velocity of energy are different from the results expected by the linear gravity waves theory, the nonlinearity causes the change in propagation characteristics of gravity wave; the ambient winds alter the propagation path and group velocity of gravity wave.
Study of nonlinear waves in astrophysical quantum plasmas
Energy Technology Data Exchange (ETDEWEB)
Hossen, M.R.; Mamun, A.A., E-mail: rasel.plasma@gmail.com [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh)
2015-10-01
The nonlinear propagation of the electron acoustic solitary waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system has been investigated theoretically. Our considered model consisting of two distinct groups of electrons (one of inertial non-relativistic cold electrons and other of inertialess ultrarelativistic hot electrons) and positively charged static ions. The Korteweg-de Vries (K-dV) equation has been derived by employing the reductive perturbation method and numerically examined to identify the basic features (speed, amplitude, width, etc.) of EASWs. It is shown that only rarefactive solitary waves can propagate in such a quantum plasma system. It is found that the effect of degenerate pressure and number density of hot and cold electron fluids, and positively charged static ions, significantly modify the basic features of EASWs. It is also noted that the inertial cold electron fluid is the source of dispersion for EA waves and is responsible for the formation of solitary structures. The applications of this investigation in astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are briefly discussed. (author)
A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up
Filippini, A. G.; Kazolea, M.; Ricchiuto, M.
2016-04-01
In this paper we evaluate hybrid strategies for the solution of the Green-Naghdi system of equations for the simulation of fully nonlinear and weakly dispersive free surface waves. We consider a two step solution procedure composed of: a first step where the non-hydrostatic source term is recovered by inverting the elliptic coercive operator associated to the dispersive effects; a second step which involves the solution of the hyperbolic shallow water system with the source term, computed in the previous phase, which accounts for the non-hydrostatic effects. Appropriate numerical methods, that can be also generalized on arbitrary unstructured meshes, are used to discretize the two stages: the standard C0 Galerkin finite element method for the elliptic phase; either third order Finite Volume or third order stabilized Finite Element method for the hyperbolic phase. The discrete dispersion properties of the fully coupled schemes obtained are studied, showing accuracy close to or better than that of a fourth order finite difference method. The hybrid approach of locally reverting to the nonlinear shallow water equations is used to recover energy dissipation in breaking regions. To this scope we evaluate two strategies: simply neglecting the non-hydrostatic contribution in the hyperbolic phase; imposing a tighter coupling of the two phases, with a wave breaking indicator embedded in the elliptic phase to smoothly turn off the dispersive effects. The discrete models obtained are thoroughly tested on benchmarks involving wave dispersion, breaking and run-up, showing a very promising potential for the simulation of complex near shore wave physics in terms of accuracy and robustness.
Computation of nonlinear water waves with a high-order Boussinesq model
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.; Bingham, Harry
2005-01-01
-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...
Kink wave determined by parabola solution of a nonlinear ordinary differential equation
Institute of Scientific and Technical Information of China (English)
LI Ji-bin; LI Ming; NA Jing
2007-01-01
By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.
Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V.R.; Vegt, van der J.J.W.; Bokhove, O.
2014-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
The Nonlinear Interaction Process in the Wave Assimilation Model and Its Experiments
Institute of Scientific and Technical Information of China (English)
杨永增; 纪永刚; 袁业立
2003-01-01
This paper presents a composite interaction formula based on the discrete-interactionoperator of wave-wave nonlinear interaction for deriving its adjoint source function in the wave assimilation model. Assimilation experiments were performed using the significant wave heights observed by the TOPES/POSEIDON satellite, and the gradient distribution in the physical space wasalso analyzed preliminarily.
Reduced order prediction of rare events in unidirectional nonlinear water waves
Cousins, Will
2015-01-01
We consider the problem of short-term prediction of rare, extreme water waves in unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the dispersive mixing of different harmonics, can grow significantly due to localized nonlinear focusing. Here we show how the interplay between i) statistical properties captured through linear information such as the waves power spectrum and ii) nonlinear dynamical properties of focusing localized wave groups defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the "trigger" of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, short-term predictors of large water waves. Specifically, we sho...
An improved wave-vector frequency-domain method for nonlinear wave modeling.
Jing, Yun; Tao, Molei; Cannata, Jonathan
2014-03-01
In this paper, a recently developed wave-vector frequency-domain method for nonlinear wave modeling is improved and verified by numerical simulations and underwater experiments. Higher order numeric schemes are proposed that significantly increase the modeling accuracy, thereby allowing for a larger step size and shorter computation time. The improved algorithms replace the left-point Riemann sum in the original algorithm by the trapezoidal or Simpson's integration. Plane waves and a phased array were first studied to numerically validate the model. It is shown that the left-point Riemann sum, trapezoidal, and Simpson's integration have first-, second-, and third-order global accuracy, respectively. A highly focused therapeutic transducer was then used for experimental verifications. Short high-intensity pulses were generated. 2-D scans were conducted at a prefocal plane, which were later used as the input to the numerical model to predict the acoustic field at other planes. Good agreement is observed between simulations and experiments.