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

Abstract : Within the spirit of fluid turbulence, we consider the one-dimensional Majda-McLaughlin-Tabak (MMT) model that describes the interactions of nonlinear dispersive waves. We perform a detailed numerical study of the direct energy cascade in the defocusing regime. In particular, we consider a configuration with large-scale forcing and small scale dissipation, and we introduce three non- dimensional parameters: the ratio between nonlinearity and dispersion, {\epsilon}, and the analogues of the Reynolds number, Re, i.e. the ratio between the nonlinear and dissipative time-scales, both at large and small scales. Our numerical experiments show that (i) in the limit of small {\epsilon} 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. We calculate the structure-function as well as the probability density function of the wave field at each scale and show that the degree of intermittency depends on {\epsilon}.
Type de document :
Article dans une revue
Physical Review Fluids, American Physical Society, 2016, 2 (5), pp.052603(R) 〈10.1103/PhysRevFluids.2.052603〉
Liste complète des métadonnées

http://hal.upmc.fr/hal-01540467
Contributeur : Gestionnaire Hal-Upmc <>
Soumis le : vendredi 16 juin 2017 - 13:04:20
Dernière modification le : jeudi 11 janvier 2018 - 06:28:11

Lien texte intégral

Identifiants

Collections

Citation

S. Chibbaro, F. De Lillo, M. Onorato. Weak versus strong wave turbulence in the Majda-McLaughlin-Tabak model. Physical Review Fluids, American Physical Society, 2016, 2 (5), pp.052603(R) 〈10.1103/PhysRevFluids.2.052603〉. 〈hal-01540467〉

Partager

Métriques

Consultations de la notice

31