On the stationary energy spectra of the stratified fluid in a weak turbulence regime

Abstract

A characteristic feature of stratified fluid dynamics is omnipresence of internal gravity waves. In the case of strong stratification the effective non-linearity parameter becomes small and, hence, one may look for wave-dominated turbulent regimes where turbulence is thought of as a “soup ” of random weakly interacting internal gravity waves. Such an approach, called weak turbulence (for a recent review see [1]) is well-known, especially in plasma physics (cf. [2]) and consists in using the perturbation theory in wave amplitudes and Gaussian statistics for an ensemble of weakly nonlinear waves in order to get a kinetic equation for the wave amplitude density. We apply this technique to the stratified fluid in the Boussinesq approximation and obtain in this way essentially anisotropic (in vertical and horizontal components of the wave number) Kolmogorov-type energy spectra as stationary solutions of the kinetic equations.