Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Flow energetics

The dynamics of a homogeneous turbulent flow subjected to a stable stratification are studied by means of direct numerical simulations (DNS) and by a two-point closure statistical EDQNM model, adapted for anisotropic flows by Cambon. The purpose of this work is to investigate the validity of the anisotropic statistical model, which we refer to as the EDQNM 2 model. The numerical simulations are of high resolution, 256 3 , which permits Reynolds numbers comparable to those of recent laboratory experiments. Thus, detailed comparisons with the wind-tunnel experiments of Lienhardt & Van Atta and Yoon & Warhaft are also presented. The initial condition is chosen so as to test the anisotropic closure assumption of the EDQNM 2 model. This choice yields a ratio of kinetic to potential energy of 2: 1. This important amount of initial potential energy drives the flow dynamics during the first Brunt-Vaisala period. Because stronger transfer rates of potential energy than of kinetic energy occur toward small scales, the heat flux is (persistently) counter gradient at those small scales. The loss of potential energy at large scales is partly made up for by conversion of vertical kinetic energy, and this sets up a down-gradient heat flux at those scales, as if no or little potential energy were present at the initial time