Observation of the Inverse Energy Cascade in the modified Korteweg-de Vries Equation
Résumé
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.
Domaines
Mécanique des fluides [physics.class-ph] Mécanique des fluides [physics.class-ph] Analyse numérique [math.NA] Equations aux dérivées partielles [math.AP] Mathématiques générales [math.GM] Physique Générale [physics.gen-ph] Dynamique des Fluides [physics.flu-dyn] Physique Atmosphérique et Océanique [physics.ao-ph] Systèmes Solubles et Intégrables [nlin.SI] Formation de Structures et Solitons [nlin.PS] Dynamique Chaotique [nlin.CD] Physique Numérique [physics.comp-ph]| Origine | Fichiers produits par l'(les) auteur(s) |
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