Spectral Approach to Axisymmetric Turbulence in a Stratified Fluid

Abstract

A spectral non-isotropic approach is used for describing the effects of buoyancy forces on a homogeneous 3D turbulence in a stratified fluid, and characterizing the trends towards two-dimensionality. A unique variable suitably chosen takes into account the fluctuating field of both velocity and temperature. Accordingly, the coupling between the “wave” component of kinetic energy and the potential energy is more easily described, and a specific two-point closure model (EDQNM) is derived. Such a model includes the dispersive and anisotropic character of the gravity waves regime in linear and non-linear interactions. Beyond other approaches based on direct numerical simulations or simplified statistical closures, the analysis presented here allows to scrutinize different contributions of the spectral energy (christened “vortex”, “wave” and “potential”) and provides moreover the angular variability in wave-space of the basic spectra. (dependence on the angle ^θk, between the vertical -axial-direction and the wave vector k). This angular variability is found already in the phase speed of the gravity internal waves N, sinθ_k/k (N is the Brünt-Vaîsala frequency), and leads to anisotropic inertial transfers mediated by non-linear interactions. Our main numerical result is that the spectral kinetic energy concentrates on rather vertical wave vectors. Although a moderate dominance of the “vortex” (versus the “wave”) component is also found, the former tendency questions the classical assumptions of two-dimensionality.