Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles

Part 1 One-dimensional waves in nonlinear nondispersive media: the basic equations and statistical problems of the theory of random waves in nondispersive media physical examples of nonlinear waves. Part 2 One-dimensional wave dynamics: exact solution of Burgers equation, Reynolds number Burgers equation solution at large Reynolds numbers evolution of the basic disturbance types Burghers equation, hydrodynamics of noninteracting particles and parabolic equation quasioptics. Part 3 Lagrangian and Eulerian statistics of random fields: connection of the statistical properties of random fields connection of statistical properties of random functions with behaviour of their realizations Lagrangian and Eulerian statistics of random fields. Part 4 Random waves of hydrodynamic type: probability properties of random Riemann waves Riemann wave spectrum density fluctuations of noninteracting particle gas probability properties of density fluctuations fluctuations of the optical wave parameters beyond a random phase screen concentrations of a passive impurity in a flow with random velocity field motion of noninteracting particles under the action of external forces. Part 5 Statistical properties of discontinuous waves: discontinuity influence on the nonlinear wave statistics - initial stage qualitative theory of one-dimensional turbulence at the stage of developed discontinuities self-preservation of random waves in nonlinear dissipative media asymptotic analysis of nonlinear random waves at large Reynolds numbers turbulence at finite Reynolds numbers - final stage of decay statistical properties of the waves in a medium with arbitrary nonlinearity. Part 6 Three-dimensional potential turbulence - the large-scale structure of the Universe: cellular structure formation in three-dimensional potential turbulence asymptotic features of potantial turbulence density fluctuations in model gas. Appendices: Properties of delta-functions and their statistical averages nonlinear gravitational instability of random density waves in the expanding universe, A.L.Melott and S.F.Shandarin singularities and bifurcations of potential flows, V.I.Arnold et al.

Перевод пока недоступен