Robust identification of dynamically distinct regions in stratified turbulence

Abstract

We present a new robust method for identifying three dynamically distinct regions in a stratified turbulent flow, which we characterise as quiescent flow, intermittent layers and turbulent patches. The method uses the cumulative filtered distribution function of the local density gradient to identify each region. We apply it to data from direct numerical simulations of homogeneous stratified turbulence, with unity Prandtl number, resolved on up to $8192\times 8192\times 4096$ grid points. In addition to classifying regions consistently with contour plots of potential enstrophy, our method identifies quiescent regions as regions where $\unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(1)$, layers as regions where $\unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(10)$ and patches as regions where $\unicode[STIX]{x1D716}/\unicode[STIX]{x1D708}N^{2}\sim O(100)$. Here, $\unicode[STIX]{x1D716}$ is the dissipation rate of turbulence kinetic energy, $\unicode[STIX]{x1D708}$ is the kinematic viscosity and $N$ is the (overall) buoyancy frequency. By far the highest local dissipation and mixing rates, and the majority of dissipation and mixing, occur in patch regions, even when patch regions occupy only 5 % of the flow volume. We conjecture that treating stratified turbulence as an instantaneous assemblage of these different regions in varying proportions may explain some of the apparently highly scattered flow dynamics and statistics previously reported in the literature.