A turbulent patch arising from a breaking internal wave

Abstract

Results of direct numerical simulations of the development of a breaking internal gravity wave are presented. The wave was forced by the imposition of an appropriate bottom boundary shape (a two-dimensional cosine hill) within a density-stratified domain having a uniform upstream velocity and density gradient. The focus is on turbulence generation and maintenance within the turbulent patch generated by the wave breaking. Pathlines, density contours, temporal and spatial spectra, and second moments of the velocity and density fluctuations and turbulent kinetic energy balance terms obtained from the data averaged over the span in the mixed zone are all used in the analysis of the flow. Typical Reynolds numbers, based on the vertical scale of the breaking region and the upstream velocity, were around 6000 and the fully resolved computations yielded sufficient resolution to capture the fine-scale transition processes as well as the subsequent fully developed turbulence. It is shown that globally, within the turbulent patch, there is an approximate balance in the production, dissipation and transport processes for turbulent kinetic energy, so that the patch remains quasi-steady over a significant time. Although it is far from being axially homogeneous, with turbulence generation occurring largely near the upstream bottom part of the patch where the mean velocity shear is particularly large, it has features not dissimilar to those of a classical turbulent wake.