PMID: 15244765Jul 13, 2004Paper

Noisy spectra, long correlations, and intermittency in wave turbulence

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Y V Lvov, S Nazarenko

Abstract

We study the k-space fluctuations of the wave action about its mean spectrum in the turbulence of dispersive waves. We use a minimal model based on the random phase approximation (RPA) and derive evolution equations for the arbitrary-order one-point moments of the wave intensity in the wave-number space. The first equation in this series is the familiar kinetic equation for the mean wave-action spectrum, whereas the second and higher equations describe the fluctuations about this mean spectrum. The fluctuations exhibit a nontrivial dynamics if some long coordinate-space correlations are present in the system, as it is the case in typical numerical and laboratory experiments. Without such long-range correlations, the fluctuations are trivially fixed at their Gaussian values and cannot evolve even if the wave field itself is non-Gaussian in the coordinate space. Unlike the previous approaches based on smooth initial k-space cumulants, the RPA model works even for extreme cases where the k-space fluctuations are absent or very large and intermittent. We show that any initial non-Gaussianity at small amplitudes propagates without change toward the high amplitudes at each fixed wave number. At each fixed amplitude, however, the prob...Continue Reading

References

Apr 29, 1996·Physical Review Letters·A N Pushkarev, V E Zakharov
Nov 3, 2001·Physical Review Letters·Y V Lvov, E G Tabak
Oct 9, 2002·Physical Review Letters·M OnoratoC Brandini

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Citations

Feb 21, 2006·Physical Review Letters·Boris GershgorinDavid Cai
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Boris GershgorinDavid Cai
May 16, 2007·Physical Review Letters·E FalconC Laroche
Feb 3, 2016·The European Physical Journal. E, Soft Matter·D RosenbergA Pouquet
Jul 18, 2018·Physical Review. E·Wonjung LeeDavid Cai
Aug 31, 2016·Physical Review. E·Sergio Chibbaro, Christophe Josserand
Sep 28, 2017·Physical Review. E·Sergio ChibbaroLamberto Rondoni
Jul 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P Clark di LeoniP D Mininni
Sep 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Elena KartashovaOleksii Rudenko
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Victor S L'vovOleksii Rudenko
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Mitsuhiro Tanaka, Naoto Yokoyama
May 16, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C RoraiA Pouquet

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