Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation - Archive ouverte HAL Access content directly
Journal Articles EPL - Europhysics Letters Year : 2014

Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation

Abstract

In this Lettre we demonstrate for the first time the formation of the inverse energy cascade in the focusing modified Korteweg-de Vries (mKdV) equation. We study numerically the properties of this cascade such as the dependence of the spectrum shape on the initial excitation parameter (amplitude), perturbation magnitude and the size of the spectral domain. Most importantly we found that the inverse cascade is always accompanied by the direct one and they both form a very stable quasi-stationary structure in the Fourier space in the spirit of the FPU-like reoccurrence phenomenon. The formation of this structure is intrinsically related to the development of the nonlinear stage of the Modulational Instability (MI). These results can be used in several fields such as the internal gravity water waves, ion-acoustic waves in plasmas and others.
Fichier principal
Vignette du fichier
DD_ET-2014a.pdf (11.67 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00991944 , version 1 (16-05-2014)
hal-00991944 , version 2 (11-06-2014)

Identifiers

Cite

Denys Dutykh, Elena Tobisch. Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation. EPL - Europhysics Letters, 2014, 107, pp.14001. ⟨10.1209/0295-5075/107/14001⟩. ⟨hal-00991944v2⟩
443 View
166 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More