On strongly nonlinear gravity waves in a vertically sheared atmosphere, Part I: Spectral stability of the refracted wave

TL;DR

This paper analyzes the spectral stability of strongly nonlinear gravity waves in a sheared atmosphere, revealing how refraction and mean flow influence wave stability through classical and new instability criteria.

Contribution

It introduces a theoretical framework for understanding the stability of nonlinear gravity waves affected by vertical shear, incorporating both classical and novel instability conditions.

Findings

Wave stability depends on classical modulation criteria for each atmospheric layer.

Instability requires the upper layer wind to be stronger than the lower layer.

New instability bounds relate mean flow and wave amplitude.

Abstract

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.