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Weak versus strong wave turbulence in the Majda-McLaughlin-Tabak model

S. Chibbaro1, F. De Lillo2, and M. Onorato2

  • 1Sorbonne Université, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France
  • 2Dipartimento di Fisica, Università di Torino and INFN, Sezione di Torino, Via P. Giuria 1, Torino 10125, Italy

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Phys. Rev. Fluids 2, 052603(R) – Published 30 May, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.052603

Abstract

We consider the one-dimensional Majda-McLaughlin-Tabak (MMT) model that describes the interactions of nonlinear and dispersive waves. We perform a detailed numerical study of the direct energy cascade. Our numerical experiments show the following. (i) In the limit of small nonlinearity the spectral slope observed in the statistical steady regime corresponds to the one predicted by the weak-wave-turbulence (WWT) theory. (ii) As the nonlinearity is increased, the WWT theory breaks down and deviations from its predictions are observed. (iii) It is shown that such departures from the WWT theoretical predictions are accompanied by the phenomenon of intermittency, typical of three-dimensional fluid turbulence. Our results clarify the role played by the wave-turbulence theory in the statistical description of nonlinear-dispersive waves described by the MMT model.

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Phys. Rev. Fluids 2, 052603(R)– Published 30 May, 2017
  • Received 24 September 2016

©2017 American Physical Society

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