The Dynamics of Asymmetric Stratified Shear Instabilities

TL;DR

This paper investigates how asymmetry in stratified shear flows influences instability development, revealing mixed Holmboe and Kelvin-Helmholtz features, asymmetric mixing patterns, and reduced parameter dependence in turbulence.

Contribution

It introduces a framework to analyze asymmetric shear instabilities, combining linear stability theory and simulations, highlighting their mixed characteristics and impact on mixing.

Findings

Asymmetric instabilities show features of both Holmboe and KH modes.

Asymmetry leads to asymmetric mixing with overturning and scouring flows.

Reduced dependence on initial parameters in asymmetric KH simulations.

Abstract

Most idealized studies of stratified shear instabilities assume that the shear interface and the buoyancy interface are coincident. We discuss the role of asymmetry on the evolution of shear instabilities. Using linear stability theory and direct numerical simulations, we show that asymmetric shear instabilities exhibit features of both Holmboe and Kelvin-Helmholtz (KH) instabilities, and develop a framework to determine whether the instabilities are more Holmboe-like or more KH-like. Further, the asymmetric instabilities produce asymmetric mixing that exhibits features of both overturning and scouring flows and that tends to realign the shear and buoyancy interfaces. In all but the symmetric KH simulations, we observe a collapse in the distribution of gradient Richardson number ($Ri_g$), suggesting that asymmetry reduces the parameter dependence of KH-driven mixing events. The observed dependence of the turbulent dynamics on small-scale details of the shear and stratification has important implications for the interpretation of oceanographic data.