ISBN: 3-540-66697-4
TITLE: Nonlinear MHD Waves and Turbulence
AUTHOR: Passot, Thierry; Sulem, Pierre-Louis (Eds.)
TOC:

Nonlinear Phenomena Involving Dispersive Alfvn Waves 1
P.K. Shukla, L. Stenflo
1 Introduction 1
2 Dispersive Alfvn waves in a uniform plasma 3
3 Generation of Alfvn waves 5
4 Nonlinear effects caused by inertial Alfvn waves 10
5 Amplitude modulation of kinetic Alfvn waves 14
6 Modulation of EMICA waves 16
7 Self-interaction between dispersive Alfvn waves in nonuniform plasmas 18
8 Chaos in Alfvnic turbulence 24
9 Summary and conclusions 26
References 28
Whistler Solitons, Their Radiation and the Self-Focusing of Whistler Wave Beams 31
V.I. Karpman
1 Introduction 31
2 Basic equations. Slab ducts 32
3 Full wave solutions for the slab ducts 37
4 Slab whistler solitons 41
5 Self-focusing of whistler wave beams 44
6 Concluding remarks 51
References 52
Alfvn Wave Filamentation and Plasma Heating 54
S. Champeaux, A. Gazol, T. Passot, P.L. Sulem
1 Introduction 54
2 Filamentation of dispersive Alfvn waves 56
3 Filamentation of weakly dispersive wave trains 64
4 Filamentation in the weakly dispersive longwavelength regime 74
5 Conclusions 80
References 81
Nonlinear Quasiresonant Alfvn Oscillations in a One-Dimensional Magnetic Cavity 83
L. Nocera, M.S. Ruderman
1 Introduction 83
2 Basic equations and assumptions 84
3 Derivation of the governing equations 87
4 Energetics 90
5 Multistability 91
6 Solutions with shocks and high-Reynolds-number bifurcations 98
7 Conclusions 101
References 102
On the Reflection of Alfvn Waves in the Inhomogeneous Solar Wind 104
L.M.B.C. Campos, N.L. Isaeva, P.J.S. Gil
1 Introduction 104
2 Effects of stratification, Hall currents, non-uniform magnetic fields and mean flow 107
3 Models combining radial stratification, mean flow and monopole external magnetic field 132
References 156
Relativistic Alfvn Solitons and Acceleration of Cosmic Rays 160
G. Pelletier
1 Introduction 160
2 The nonlinear relativistic wavefront 161
3 Generation of a parallel electric field 166
4 Electron-positron plasma 168
5 Relativistic Fermi acceleration 169
6 Astrophysics consequences and head on collision of solitons 174
7 Cosmic rays scattering off magnetic disturbances 176
8 Conclusion 179
References 180
Reduced Models of Magnetohydrodynamic Turbulence in the Interstellar Medium and the Solar Wind 182
A. Bhattacharjee, C.S. Ng
1 Introduction 182
2 The four-field model 185
3 The NI-MHD model 188
4 Four-field simulations: implications for pressure fluctuations 190
5 Anisotropic spectra in weak turbulence theory 192
References 196
Alfvnic Turbulence and Wave Propagation in the Corona and Heliosphere 198
M. Velli
1 Alfvn waves observed in the solar wind 198
2 Basic features of linear propagation 199
3 Observations of Alfvn wave generation 204
4 Non-linear propagation in the lower atmosphere: Parametric decay and filamentation 208
5 Alfvn solitons in the solar wind 215
6 Conclusions 220
References 221
Nonlinear Alfvn Wave Interaction with Large-Scale Heliospheric Current Sheet 222
P. Veltri, F. Malara, L. Primavera
1 Introduction 222
2 A model for Alfvn wave interaction with heliospheric current sheet 225
3 Numerical results 230
4 The effects of an inhomogeneous entropy distribution 238
5 Discussion and conclusions 245
References 248
Coherent Electrostatic Nonlinear Waves in Collisionless Space Plasmas 251
C. Salem, A. Mangeney, J.-L. Bougeret
1 Introduction 251
2 Coherent ion acoustic waves in the solar wind 252
3 Review of the observational evidence on coherent waves in the Earth's environment 258
4 Theoretical interpretations 263
5 Conclusion 265
References 265
Modeling the Dissipation Range of Magnetofluid Turbulence 269
M.L. Goldstein, S. Ghosh, E. Siregar, V. Jayanti
1 Observational background 269
2 More realistic dissipation operators 276
3 Summary and conclusions 286
References 287
A Weak Turbulence Theory for Incompressible MHD 291
S. Galtier, S. Nazarenko, A.C. Newell, A. Pouquet
1 Introduction and general discussion 291
2 The derivation of the kinetic equations 298
3 General properties of the kinetic equations 304
4 Asymptotic solution of the 3D kinetic equations 308
5 Two-dimensional problem 308
6 Front propagation 318
7 Nonlocal isotropic 3D MHD turbulence 323
8 Conclusion 324
References 328
Shell Models for MHD Turbulence 331
P. Giuliani
1 Introduction 331
2 Models with nearest neighbour interactions 332
3 Models with nearest and next-nearest interactions 333
4 Dynamo action in MHD shell models 335
5 Spectral properties in stationary forced state 338
6 Fluxes, inertial range and intermittency 339
7 Conclusions 343
References 344
Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD 346
E.A. Kuznetsov, V.P. Ruban
1 Introduction 346
2 General remarks 349
3 Vortex line representation 353
4 Variational principle 356
5 Integrable hydrodynamics 357
6 Lagrangian description of MHD 359
7 Frozen-in MHD fields 361
8 Relabeling symmetry in MHD 364
9 Variational principle for incompressible MHD 366
References 367
Quasi-Two-Dimensional Hydrodynamics and Interaction of Vortex Tubes 369
V.E. Zakharov
1 Introduction 369
2 Quasi-two-dimensional hydrodynamics 370
3 Dynamics of the isolated vortex tube 373
4 Vortex tube in an external flow 378
5 Interaction of vortex tubes 380
6 Instability and collapse of traveling vortex pair 381
7 Solitons on the co-rotating vortex pair 383
References 385
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