Abstract
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.
Highlights
The importance of gravity waves for the atmospheric dynamics and for weather and climate forecasting was established in [6] and [18]
We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind
Horizontally periodic, non-hydrostatic, and strongly nonlinear gravity waves in the unbounded x-z-plane which we model by Grimshaw’s modulation equations [1, 15, 24]
Summary
The importance of gravity waves for the atmospheric dynamics and for weather and climate forecasting was established in [6] and [18]. Excited in the troposphere, gravity waves may persist deep into the upper atmospheric layers [11,12,13] On their journey through the atmospheric layers they may interact with the mean ow. They exert drag onto the horizontal mean- ow, produce heat when dissipating [2], and induce mixing of tracer constituents such as green-house gases [22]. To this day, many questions regarding the sources, propagation and dissipation of gravity waves are still to be answered
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