Kolmogorov-Zakharov Spectra of Turbulence Wave Turbulence

Starting at the level of graduate students, this book offers a comprehensive introduction to a rapidly developing field of turbulence.  It also presents the state of the art of the theory of wave turbulence in diverse media for researchers looking for a formalism to solve existing problems or for new research subjects and ideas. The book provides a general theory of developed wave turbulence in different media: plasmas, solids, atmosphere, oceans and space.

The presentation starts with a simple and intuitive dimensional analysis and proceeds to a rigorous analytic theory with exact solutions for the stationary spectra of turbulence, stability theory of such spectra, description of nonstationary regimes and matching spectra with pumping and dissipation regions. The reader is provided with the necessary tools to study nonlinear waves and turbulence: Hamiltonian formalism, statistical description, derivation of kinetics equations and methods of finding their steady and non-steady solutions.

In this second edition the book is brought up to date both in theoretical and experimental/observational aspects. In particular, the authors have updated and revised the description of nonstationary turbulence, turbulent entropy production, etc, and added discussions of master equation and several cases of strong turbulence and nonlocal cascades. The book now includes excercises, some with solutions.

O. Introduction.- 1. Equations of Motion and the Hamiltonian Formalism.- 2. Statistical Description of Weak Wave Turbulence.- 3. Stationary Spectra of Weak Wave Thrbulence.- 4. The Stability Problem and Kolmogorov Spectra.- 5. Physical Applications .- 6. Conclusion.- A. Appendix.- A.1 Variational Derivatives.- A.2 Canonicity Conditions of Transformations.- A.3 Elimination of Nonresonant Terms from the Interaction Hamiltonian .- A.4 Feynman rules and derivation of the renormalized kinetic equations.- A.5 Liouville approach and derivation of the Master Equation.

Vladimir Zakharov was Regent’s Professor Emeritus at University of Arizona, Tucson, USA. He published nine books and around 400 articles in peer reviewed journals, see math.arizona.edu/~zakharov/

Victor Lvov is consultant at the Weizmann Institute of Science. He published three books and above 270 articles in peer reviewed journals, see weizmann.ac.il/chembiophys/lvov/ and in wikipedia.org/wiki/Victor_L%27vov

Gregory Falkovich is a professor at the Weizmann Institute of Science, he published three books and around 200 articles in peer reviewed journals, weizmann.ac.il/complex/falkovich/