C. Staquet et Fs. Godeferd, STATISTICAL MODELING AND DIRECT NUMERICAL SIMULATIONS OF DECAYING STABLY STRATIFIED TURBULENCE - PART-1 - FLOW ENERGETICS, Journal of Fluid Mechanics, 360, 1998, pp. 295-340
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.