An efficient description of weakly nonlinear interactions between subgrid-scale gravity waves (GW) and a large-scale resolved flow can be achieved via Wentzel-Kramer-Brillouin (WKB) theory. Traditional implementations of this theory suffer from the caustics problem that occurs whenever two rays with different wavenumbers cross. Muraschko et al (2015, QJRMS) have shown within a Boussinesq framework that corresponding numerical instabilities can be circumvented by a spectral approach where the wave amplitudes are described by a wave-action density in phase space, spanned by location and wave number. Their study is extended here so as to describe GW dynamics in an atmospheric framework with vertically varying reference-atmosphere density. A Eulerian and a Lagrangian implementation of a weakly nonlinear phase space WKB model are applied to various cases of interactions between GWs and large-scale flow. For validation these simulations are compared with fully nonlinear large eddy simulations (LES) that resolve both GWs and large-scale flow. By prescribing the initial large-scale wind profile several classical cases are investigated such as refraction, reflection, and critical layers. Both static instability and modulational instability of GW packets are addressed as well. It is shown that the phase space WKB models are able to reproduce the reference LES results with a good accuracy. This holds even for highly nonlinear cases as the collapse of a GW packet due to static or modulational instability. Since the Lagrangian WKB model is very efficient these results are of relevance for the development of numerically stable GW parameterizations that allow for horizontal GW propagation and GW transience. Work in progress on the numerical treatment of the interaction between resolved GWs and subgrid-scale GWs shall be reported as well.

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*email: Boeloeni@iau.uni-frankfurt.de
*Preference: Oral