This comprehensive introduction to a modern and rapidly developing field starts at a level suitable for graduate students and young researchers. Written by leading experts in the field, it provides a general theory of developed turbulence with a consistent description of phenomena in different media such as plasmas, solids, the atmosphere, oceans and space.

Klappentext

This comprehensive introduction into a modern and rapidlydeveloping field starts on the level of graduates and youngresearchers. It provides a general theory of developedturbulence with a consistent description of phenomena indifferent media such as plasmas, solids, atmosphere, oceansand space.Starting from simple dimensional analysis the expositionproceeds to rigorous theory with exact solutions for thestationary spectra of turbulence, the solution of thestability problem, matching of Kolmogorov-like spectra withpumping and damping. The reader is provided with thenecessary tools for studying nonlinear waves andturbulence:Hamiltonian formalisms, methods of statistical description,derivation of kinetic equations and solutions.

Inhalt

0. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 1.1 The Hamiltonian Formalism for Waves in Continuous Media.- 1.2 The Hamiltonian Formalism in Hydrodynamics.- 1.3 Hydrodynamic-Type Systems.- 1.4 Spin Waves.- 1.5 Universal Models.- 2. Statistical Description of Weak Wave Turbulence.- 2.1 Kinetic Wave Equation.- 2.2 General Properties of Kinetic Wave Equations.- 3. Stationary Spectra of Weak Wave Turbulence.- 3.1 Kolmogorov Spectra of Weak Turbulence in Scale-Invariant Isotropic Media.- 3.2 Kolmogorov Spectra of Weak Turbulence in Nearly Scale-Invariant Media.- 3.3 Kolmogorov Spectra of Weak Turbulence in Anisotropic Media.- 3.4 Matching Kolmogorov Distributions with Pumping and Damping Regions.- 4. The Stability Problem and Kolmogorov Spectra.- 4.1 The Linearized Kinetic Equation and Neutrally Stable Modes.- 4.2 Stability Problem for Kolmogorov Spectra of Weak Turbulence.- 4.3 Nonstationary Processes and the Formation of Kolmogorov Spectra.- 5. Physical Applications.- 5.1 Weak Acoustic Turbulence.- 5.2 Wave Turbulence on Water Surfaces.- 5.3 Turbulence Spectra in Plasmas, Solids, and the Atmosphere.- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian.- References.