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Resonance Clustering in Wave Turbulent Regimes: Integrable Dynamics

Published online by Cambridge University Press:  20 August 2015

Miguel D. Bustamante  and
Elena Kartashova
Miguel D. Bustamante*
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Elena Kartashova*
Affiliation:
IFA, J. Kepler University, Linz 4040, Austria
*
Email:miguel.bustamante@ucd.ie
Corresponding author.Email:elena.kartaschova@jku.at
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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.

Keywords

47.10.Df47.10.Fg02.70.DhResonance clusteringHamiltonian formulationwave turbulent regimesNR-diagramintegrable dynamics
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1211 - 1240
Copyright
Copyright © Global Science Press Limited 2011

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