Statistical properties of a model of a turbulent patch arising from a breaking internal wave

Abstract

The turbulent patch arising from internal gravity wave breaking is investigated with direct numerical simulation of a stably stratified flow over a two-dimensional hill. The turbulent patch is distinguished from the non-turbulent wave region with potential vorticity. The turbulent patch is highly intermittent, and its location fluctuates with space and time. The buoyancy Reynolds number slowly decays with time in the turbulent patch and the mixing efficiency stays around 0.2. The turbulent patch is separated from the non-turbulent wave region by a turbulent/non-turbulent interfacial (TNTI) layer, whose thickness is about five times the Kolmogorov scale. The kinetic energy dissipation rate also sharply decreases from the turbulent to the wave region while the potential energy dissipation rate has a large peak within the TNTI layer. Both shear and stable stratification are strong in the upper area of the turbulent patch. On the other hand, the lower area has a small mean density gradient, i.e., weak stratification, which is related to the strong intermittency of the turbulent patch in the lower area. Furthermore, weak stratification in the lower area results in a low gradient Richardson number, which is below the critical value for the shear instability, and the roller vortex appears. The outer edge of the turbulent patch aligns with the perimeter of the roller vortex, and the vortex affects the spatial distribution of the turbulent patch.