On strongly nonlinear gravity waves in a vertically sheared atmosphere

Abstract

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thinvertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same orderof magnitude as the background flow and hence the self-induced mean flow alters the modulation propertiesto leading order. In this theoretical study, we show that the stability of such a refracted wave depends on theclassical 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 windand the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind inthe upper layer is stronger than the wind in the lower layer.Keywords:Internal gravity waves; Modulation equations; Shea