Stratified shear flow instabilities in the non-Boussinesq regime

TL;DR

This paper investigates how non-Boussinesq effects influence wave propagation and shear instability in stratified shear flows, revealing a preference for wave direction that can stabilize the flow, challenging traditional Boussinesq-based interpretations.

Contribution

It introduces a detailed analysis of non-Boussinesq effects on shear flow instabilities across multiple flow configurations, highlighting their stabilizing influence.

Findings

Non-Boussinesq effects alter wave propagation direction.

Wave phase-locking is affected by non-Boussinesq effects.

Non-Boussinesq effects tend to stabilize shear flows.

Abstract

Effects of the baroclinic torque on wave propagation normally neglected under the Boussinesq approximation is investigated here, with a special focus on the associated consequences for the mechanistic interpretation of shear instability arising from the interaction between a pair of vorticity-propagating waves. To illustrate and elucidate the physical effects that modify wave propagation, we consider three examples of increasing complexity: wave propagation supported by a uniform background flow; wave propagation supported on a piecewise-linear basic state possessing one jump; and an instability problem of a piecewise-linear basic state possessing two jumps, which supports the possibility of shear instability. We find that the non-Boussinesq effects introduces a preference for the direction of wave propagation that depends on the sign of the shear in the region where waves are supported. This in turn affects phase-locking of waves that is crucial for the mechanistic interpretation for shear instability, and is seen here to have an inherent tendency for stabilisation.