Nonlinear Waves and Weak Turbulence: with Applications in Oceanography and Condensed Matter PhysicsThis book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh. |
Contents
| 3 | |
| 4 | |
35 | 50 |
45 | 60 |
2 993 | 67 |
42 | 82 |
97 | 98 |
46 | 108 |
8 | 147 |
9 | 158 |
Modeling Turbulence by Systems of Coupled Gyrostats | 178 |
Solitons Propagation in Optical Fibers with Random | 211 |
Collision Dynamics of Solitary Waves in Nematic | 227 |
Statistical Mechanics Eulers Equation and Jupiters | 238 |
Stochastic Burgers Flows by W A Woyczynski | 279 |
Long Range Prediction and Scaling Limit | 312 |
Hidden Symmetries of Hamiltonian Systems over | 121 |
Wave Spectra of Developed Seas by R E Glazman | 129 |
A Remark on Shocks in Inviscid Burgers Turbulence | 339 |
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Common terms and phrases
action-angle variables algebraic amplitude angular anisotropic assume Burgers capillary waves coefficient collision integral conserved constant correlation functions corresponding defined density described dimensional dispersion dissipation distribution dynamics energy flux equilibrium Euler equation Falkovich finite flow Fluid Mech frequency Glazman gravity waves gyrostats Hamiltonian flows Hamiltonian system holomorphic curves Hopf equation inertial interval initial instability interaction inverse cascade isotropic k₁ kinetic equation Kolmogorov Kolmogorov spectrum Larraza layer length scale limit linear modes momentum motion n-tuple nonlinear nonlinear Schrödinger equation obtained parameters Phys physical problem propagation random range resonant Schrödinger soliton stable stationary solutions statistical stochastic stratified turbulence surface Theorem theory tion Toda lattice transform two-dimensional variables vector velocity viscosity wave action wave age wave field wave numbers wave spectra wave turbulence wavenumbers weak turbulence wind wo(r Woyczynski Zakharov zero ΣΦ