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Towards a New Picture of Wave Turbulence

Shrira, V. I.; Annenkov, S. Y.


S. Y. Annenkov


The existing wave turbulence paradigm assumes, in particular, a proximity to stationarity and spatial homogeneity of the wave field under consideration, which is often violated in nature. In this review, we outline a new theoretical approach free from these restrictive assumptions. We present and discuss a novel approach to the direct numerical simulation (DNS) of random wind wave fields, based on the Zakharov equation. This approach can be used in situations when the statistical theory is not applicable. It can be also used to provide an independent corroboration to the wave turbulence theory. We review the experimental evidence indicating that often wave fields evolve much faster than the existing theory predicts, we then employ the DNS to study the fast evolution of wave fields far from equilibrium. These fields evolve on the dynamic timescale typical of coherent wave processes, rather than on the kinetic timescale typical of broadband random wave fields. This phenomenon of “fast evolution”, its causes, the specifics of its mathematical description and implications are the main focus of the review. We also present a generalisation of the existing statistical theory of wave turbulence, based on the new generalised kinetic equation. This equation is free of the assumption of quasi-stationarity and can account for both the fast and kinetic-scale processes in wave fields. Throughout the review water waves are used as a typical example of weakly nonlinear wave field, however, the new approach is equally valid for any random broadband weakly nonlinear wave field evolving due to nonlinear resonant interactions, either triad or quartic; the specificity of wave field is only in the form of the interaction coefficients.

Online Publication Date May 2, 2013
Publication Date 2013-06
Deposit Date Dec 8, 2023
Publisher World Scientific Publishing
Pages 239-281
Book Title Advances in Wave Turbulence
ISBN 9789814366939