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Wave turbulence. (English) Zbl 1220.76006

Lecture Notes in Physics 825. Berlin: Springer (ISBN 978-3-642-15941-1/pbk; 978-3-642-15942-8/ebook). xvi, 279 p. (2011).
The book, structured in four main parts, constitutes a compact text which should be accessible for graduate students and non-specialist mature researchers who would like to learn about wave turbulence and possibly apply it in their own fields.
After introducing wave turbulence, in Part I, “Primer on wave turbulence” (Chapters 2 through 4), the author places wave turbulence in the general turbulence context and provides a wave turbulence “primer” (a set of useful shortcut techniques for reproducing the most important wave turbulence results) in known applications.
Part II, “Wave turbulence closure” (Chapters 5 through 7), focuses on the basic statistical objects, formulating the basic theoretical assumptions and deriving the main steps in the wave turbulence closures with all important details, explained using the Petviashvilli wave model.
In Part III, “Wave turbulence predictions” (Chapters 8 through 12), the author studies the properties of wave turbulence, important solutions and predictions which arise from the wave turbulence closure.
Part IV, “Selected applications” (Chapters 13 through 16), presents a detailed discussion of three selected physical applications: nonlocal drift/Rossby wave turbulence in geophysical fluids and in plasmas, MHD turbulence and Bose-Einstein condensation. These descriptions explain specific features characterizing these applications, including the nonlocality, finite-size effects, the coexistence of wave turbulence with strong turbulence, zonal jets, vortices and coherent condensates.

MSC:

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76Fxx Turbulence
86Axx Geophysics
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