STATISTICAL MODELING AND DIRECT NUMERICAL SIMULATIONS OF DECAYING STABLY STRATIFIED TURBULENCE - PART-1 - FLOW ENERGETICS

The dynamics of a homogeneous turbulent flow subjected to a stable str atification are studied by means of direct numerical simulations (DNS) and by a two-point closure statistical EDQNM model, adapted for aniso tropic flows by Cambon (1989). The purpose of this work is to investig ate the validity of the anisotropic statistical model, which we refer to as the EDQNM(2) model. The numerical simulations are of high resolu tion, 256(3), which permits Reynolds numbers comparable to those of re cent laboratory experiments. Thus, detailed comparisons with the wind- tunnel experiments of Lienhardt & Van Atta (1990) and Yoon & Warhaft ( 1990) are also presented. The initial condition is chosen so as to tes t the anisotropic closure assumption of the EDQNM(2) model. This choic e yields a ratio of kinetic to potential energy of 2 : 1. This importa nt amount of initial potential energy drives the flow dynamics during the first Brunt-Vaisala period. Because stronger transfer rates of pot ential energy than of kinetic energy occur toward small scales, the he at flux is (persistently) counter gradient at those small scales. The loss of potential energy at large scales is partly made up for by conv ersion of vertical kinetic energy, and this sets up a down-gradient he at flux at those scales, as if no or little potential energy were pres ent at the initial time. Thus, common features with wind-tunnel experi ments tin which there is relatively little potential energy just behin d the grid) are found. Interestingly, only one quantity displays a sim ilarity law in the DNS, in the EDQNM(2) model and in the experiments o f Lienhardt & Van Atta (1990) and Yoon & Warhaft (1990) as well: this is the ratio of the vertical heat flux to the dissipation rate of kine tic energy, which can also be interpreted as an instantaneous mixing e fficiency. Thus, this parameter seems to be independent of initial flo w conditions. Our calculations simulate a longer evolution of the flow dynamics than laboratory experiments tin which the flow develops for at most one Brunt-Vaisala period). We find that the flow dynamics chan ge from about 1.5 Brunt-Vaisala periods. At that time, the heat flux c ollapses while the dissipation rate of kinetic energy displays a self- similarity law attesting that this quantity becomes driven by buoyancy forces. This permits us to link the collapse of the largest scales of the flow with the smallest scales being influenced by the buoyancy fo rce. We finally discuss the influence of a geometrical confinement eff ect upon the above results. The EDQNM(2) model compares remarkably wel l with the DNS, with respect to previous statistical models of stably stratified turbulent flows. Insufficient decorrelation between the ver tical velocity and the temperature fluctuations is however observed, b ut with no dynamical significance. The vortex part of the flow is also overestimated by the EDQNM(2) model, but the relative difference betw een the model prediction and the DNS does not exceed 15% after 6 Brunt -Vaisala periods. The EDQNM(2) model offers interesting perpectives be cause of its ability to predict the dynamics of stratified flows at hi gh Reynolds numbers. Knowledge about small-scale behaviour will be esp ecially useful, to build up parameterization of the subgrid scales for instance.