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Resonance Clustering in Wave Turbulent Regimes: Integrable Dynamics

Resonance Clustering in Wave Turbulent Regimes: Integrable Dynamics
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Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 5 : pp. 1211–1240

Abstract

Two fundamental facts of the modern wave turbulence theory are 1) existence of power energy spectra in k-space, and 2) existence of "gaps" in this spectra corresponding to the resonance clustering. Accordingly, three wave turbulent regimes are singled out: kinetic, described by wave kinetic equations and power energy spectra;discrete, characterized by resonance clustering; and mesoscopic, where both types of wave field time evolution coexist. In this review paper we present the results on integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes. Using a novel method based on the notion of dynamical invariant we show that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others-only for particular initial conditions. We also identify chaotic behaviour in some cases. Physical implications of the results obtained are discussed.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.110910.160211a

Communications in Computational Physics, Vol. 10 (2011), Iss. 5 : pp. 1211–1240

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

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