Shear-induced breaking of internal gravity waves

TL;DR

This study uses direct numerical simulations to explore how internal gravity waves interact with shear flows in stratified oceans, revealing the development of instabilities and mixing processes relevant to ocean turbulence.

Contribution

It demonstrates the applicability of linear ray tracing theory in nonlinear regimes and characterizes the turbulence and mixing resulting from wave-shear interactions.

Findings

Wave energy accumulates in negative shear regions leading to instabilities.

Shear-driven billow structures dominate mixing over convective rolls.

Turbulent mixing efficiency is similar to Kelvin-Helmholtz instability.

Abstract

Motivated by observations of turbulence in the strongly stratified ocean thermocline, we use direct numerical simulations to investigate the interaction of a sinusoidal shear flow and a large-amplitude internal gravity wave. Despite strong nonlinearities in the flow and a lack of scale separation, we find that linear ray tracing theory is qualitatively useful in describing the early development of the flow as the wave is refracted by the shear. Consistent with the linear theory, the energy of the wave accumulates in regions of negative mean shear where we observe evidence of convective and shear instabilities. Streamwise-aligned convective rolls emerge the fastest, but their contribution to irreversible mixing is dwarfed by shear-driven billow structures that develop later. Although the wave strongly distorts the buoyancy field on which these billows develop, the mixing efficiency of the subsequent turbulence is similar to that arising from Kelvin-Helmholtz instability in a stratified shear layer. We run simulations at Reynolds numbers of 5000 and 8000, and vary the initial amplitude of the internal gravity wave. For high values of initial wave amplitude, the results are qualitatively independent of $Re$. Smaller initial wave amplitudes delay the onset of the instabilities, and allow for significant laminar diffusion of the internal wave, leading to reduced turbulent activity. We discuss the complex interaction between the mean flow, internal gravity wave and turbulence, and its implications for internal wave-driven mixing in the ocean.