Detailed investigation of energy transfers in homogeneous stratified turbulence*

TLDR

The study investigates irreversible mechanisms in homogeneous stably stratified turbulence. Using an EDQNM closure with axisymmetry, the authors decompose the velocity–temperature field into vortex and wave components and compute anisotropic energy transfers among vortex kinetic, wave kinetic, and potential energies for eight interaction types. The calculations show that pure vortical interactions generate an irreversible anisotropic structure that blocks the inverse cascade of two‑dimensional turbulence, as illustrated by time‑evolution plots for isotropic and two anisotropic closures.

Abstract

This paper investigates some irreversible mechanisms occurring in homogeneous stably stratified turbulent flows. In terms of the eigenmodes of the linear regime, the velocity-temperature field is decomposed into a vortex and two wavy components. Using an eddy-damped quasinormal Markovian (EDQNM) closure with the axisymmetry hypothesis, an analysis of the anisotropic energy transfers between the vortex kinetic energy, the wave kinetic and potential energy is made. Within the light of triadic exchanges, and by analogy of the resonance condition for three linearly interacting gravity waves, the closure model allows one to compute the detailed transfers for eight types of interactions. Results of the calculations include time evolution plots, for the isotropic closure model as well as two different types of the anisotropic closure. The pure vortical interactions are shown to be responsible for the irreversible anisotropic structure created by stable stratification, and this structure prevents the inverse cascade of two-dimensional turbulence.