Gravity wave focusing on the Antarctic polar vortex using Gaussian-beam approximation in horizontally non-uniform flows

Ray path theory is an asymptotic approximation to the wave equations. It represents efficiently gravity wave propagation in non-uniform background flows so that it is useful to develop schemes of gravity wave effects in general circulation models. One of the main limitations of ray path theory to be applied in realistic flows is in caustics where rays intersect and the ray solution has a singularity. Gaussian beam approximation is a higher-order asymptotic ray path approximation which considers neighboring rays to the central one and thus it is free of the singularities produced by caustics. A previous implementation of the Gaussian beam approximation assumes a horizontally uniform flow. In this work, we extend the Gaussian beam approximation to include horizontally nonuniform flows. Under these conditions the wave packet can undergo horizontal wave refraction producing changes in the horizontal wavenumber, which affects the ray path as well as the ray tube cross-sectional area and so the wave amplitude via wave action conservation. As an evaluation of the Gaussian beam approximation in horizontally nonuniform flows a series of proof-of-concept experiments is conducted comparing the approximation with the linear wave solution given by the WRF model. A very good agreement in the wave field is found. An evaluation is conducted with conditions that mimic the Antarctic polar vortex and the orography of the Southern flank of South America. The Gaussian beam approximation nicely reproduces the expected asymmetry of the wave field. A much stronger disturbance propagates towards higher latitudes (polar vortex) compared to lower latitudes.