Intermittent patches of turbulence in a stratified medium with stable shear

Abstract

Direct numerical simulation (DNS) is used to investigate the evolution of intermittent patches of turbulence in a background flow with the gradient Richardson number, Rig , larger than the critical value of 0.25. The base flow consists of an unstable stratified shear layer (Rig <0.25) located on top of a stable shear layer (Rig >0.25), whose shear and stratification are varied. The unstable shear layer undergoes a Kelvin–Helmholtz shear instability that develops into billows. Vortices associated with the billows are pulled into the bottom shear layer and stretched by the local shear into a horseshoe configuration. The breakdown of the horseshoe vortices generates localized patches of turbulence. Three cases with different levels of shear and stratification, but with the same Rig , in the bottom shear layer are simulated to examine the popular hypothesis that mixing is determined by local Rig . In the case with largest shear and stratification, the vortices are less likely to penetrate the bottom layer and are quickly dissipated due to the strong stratification. In the case with moderate shear and stratification, vortices penetrate across the bottom layer and generate turbulence patches with intense dissipation rate. The case with the mildest level of shear and stratification shows the largest net turbulent mixing integrated over the bottom layer. Analysis of the turbulent kinetic energy budget indicates that the mean kinetic energy in the bottom layer contributes a large amount of energy to the turbulent mixing. In all cases, the mixing efficiency is elevated during the penetration of the vortices and has a value of approximately 0.35 when the turbulence in the patches decays.