Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy

Abstract

Stably stratified freely decaying homogeneous turbulence is investigated by means of direct numerical simulations (DNS) and a two-point closure statistical model of the EDQNM type; a careful comparison with laboratory experiments is also made. Several aspects of anisotropy in the flow are studied, both at large and small scales. DNS and EDQNM approaches give very similar results up to the finest indicators of the flow, namely anisotropic spectra of velocity fields. Hence the statistical model predicts the structure of the flow at all scales.

Large-scale anisotropy appears in the Reynolds stress components and in the directional integral length scales. The well-known collapse of vertical turbulent motion, which yields the organization of the flow into quasi-horizontal vertically decorrelated vortex structures, is retrieved and quantified. Thus, the thickness of the vortex structures is shown to be set by their Froude number being of order one, in agreement with a previous dimensional analysis for an inviscid flow. Small-scale anisotropy is quantified from the components of the velocity and temperature gradients, whereby models for the dissipation rate of kinetic energy and available potential energy are discussed. The mixing properties of the flow are also investigated: the counter-gradient heat flux that exists at small scales appears to inhibit mixing when diffusivity is low enough and the Cox number varies linearly with the parameter $\epsilon/\nu N^2$.

All results agree very well with laboratory experiments on stably stratified grid turbulence, though the initial condition of our computations is different from the flow just behind the grid. This suggests a relative independence of decaying stably stratified turbulence of initial conditions.