Linear and nonlinear stability of a quasi-geostrophic mixing layer subject to a uniform background shear

TL;DR

This study revisits the stability of a quasi-geostrophic mixing layer with background shear using the kernel-wave perspective, revealing how shear direction influences instability and the role of Rossby deformation radius.

Contribution

It introduces a kernel-wave perspective to analyze QG mixing layer stability, highlighting the effects of background shear and Rossby deformation radius on instability.

Findings

Adverse shear stabilizes the system.

Favorable shear enhances instability.

QG environment weakens instability, especially for m > 0.

Abstract

The aim of this work is to shed light by revisiting - through the kernel-wave (KW) perspective - the breakdown of a quasi-geostrophic (QG) mixing layer (or vortex strip/filament) in atmosphere under the influence of a background shear. The QG mixing layer is modelled with a family of quasi-Rayleigh velocity profiles in which the potential vorticity (PV) is constant in patches. In the KW perspective a counter-propagating Rossby wave (CRW) is created at each PV edge, i.e. the edge where a PV jump is located. The important parameters of our study are (i) the vorticity of the uniform shear m and (ii) the Rossby deformation radius Ld, which indicates how far the pressure perturbations can vertically propagate. While an adverse shear (m < 0) stabilizes the system, a favorable shear (m > 0) strengthens the instability. This is due to how the background shear affects the two uncoupled CRWs by shifting the optimal phase difference towards large (small) wavenumber when m < 0 (m > 0). As the QG environment is introduced a general weakening of the instability is noticed, particularly for m > 0...