On the stability of Kolmogorov spectra of a weak turbulence
type: Item
instance of: scholarly article
title: On the stability of Kolmogorov spectra of a weak turbulence
zbMATH Open document ID: 0631.76052
DOI: 10.1016/0167-2789(87)90039-X
author: G. E. Fal'kovich
author: A. V. Shafarenko
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: The stability problem of Kolmogorov spectra of a weak turbulence is analytically solved for the first time in the framework of a three-wave kinetic equation. The spectrum of isotropic perturbations of a stationary not-in-equilibrium distribution is found for the capillary waves on a shallow water surface. It is shown, in the isotropic case, that the Kolmogorov solution is stable with respect to excitations local in k- space. The perturbations drift to the damping region without growth of the magnitude. The structural instability of the isotropic spectrum is found by computer simulation: a small pumping anisotropy causes the spectrum to be essentially anisotropic within the inertial range.
Mathematics Subject Classification ID: 76F05
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4027042
zbMATH Keywords: stability problem of Kolmogorov spectra
zbMATH Keywords: weak turbulence
zbMATH Keywords: three-wave kinetic equation
zbMATH Keywords: spectrum of isotropic perturbations
zbMATH Keywords: stationary not-in- equilibrium distribution
zbMATH Keywords: capillary waves
zbMATH Keywords: shallow water surface
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4027042