Idealised Turbulent Wake With Steady, Non-Uniform Ambient Density Stratification

Density stratification in geophysical environments can be non-uniform, particularly in thermohaline staircases and atmospheric layer transitions. Non-uniform stratification, however, is often approximated by the average ambient density change with height. This approximation is frequently made in numerical simulations because it greatly simplifies the calculations. In this paper, direct numerical simulations using $4096 \times 2048 \times 2048$ grid points to resolve an idealised turbulent wake in a non-uniformly stratified fluid are analysed to understand the consequences of assuming linear stratification. For flows with the same average change in density with height, but varied local stratification $d\bar \rho(z)/dz$, flow dynamics are dependent on the ratio $\xi=\delta_{\cal U}/\delta_{\rho}$, where $\delta_{\cal U}$ and $\delta_{\rho}$ are characteristic velocity and density vertical scale heights of the mean flow. Results suggest that a stably stratified flow will demonstrate characteristics similar to nonstratified flow when $\xi > 2$, even though the average stratification is quite strong. In particular, the results show that mixing is enhanced when $\xi > 2$.