Effects of equatorially-confined shear flow on MRG and Rossby waves

TL;DR

This study investigates how equatorially confined shear flows influence MRG and Rossby waves using linear stability analysis within rotating shallow water equations, revealing significant effects on wave dispersion, confinement, and stability in different coordinate systems.

Contribution

It provides a detailed comparison of wave behavior under shear in both β-plane and spherical models, highlighting the importance of full spherical analysis for equatorially confined flows.

Findings

Shear significantly affects wave dispersion at high wavenumbers.

Waves are more confined in the equatorial easterly flow, especially in the β-plane system.

Exponential instabilities occur in the β-plane but not in the full spherical system.

Abstract

Linear modal stability analysis of a mean zonal shear flow is carried out in the framework of rotating shallow water equations (RSWE), both under the $\beta$-plane approximation and in the full spherical coordinate system. Two base flows -- equatorial easterly (EE) and westerly (EW) -- with Gaussian profiles highly confined to small latitudes are analyzed. At low Froude number, mixed Rossby-gravity (MRG) and Rossby waves are found to be particularly affected by shear, with prominent changes at higher wavenumbers. These waves become practically non-dispersive at large wavenumbers in EE. The perturbations are found to be more confined equatorially in EE than in EW with the degree of confinement being more pronounced in the $\beta$-plane system compared to the full spherical system. At high Froude number, the phase speeds are significantly larger in the $\beta$-plane system for all families of waves. Under the $\beta$-plane approximation, exponentially unstable modes can be excited, having negative (positive) phase speed in EE (EW). Strikingly, this flow is always neutrally stable with the full spherical system. This speaks for the importance of studying the whole spherical system even for equatorially confined shear.