Focusing of an inertia - gravity wave packet by a baroclinic shear flow

We investigate the interaction of a small-amplitude internal gravity wave packet in a rotating fluid with a baroclinic shear flow. Ray equations and three-dimensional direct numerical simulations of the Boussinesq equations are solved for this purpose. The shear flow has a simple structure and depends separately on the vertical and horizontal coordinates. We focus on the situation where the intrinsic frequency Ω of the wave packet increases as the packet propagates into the shear flow, due to the horizontal dependence of this flow. The packet is trapped in the neighbourhood of the Ω = N surface (where N is the spatially varying Brunt-Väisälä frequency) and the wave-induced velocity, which first decays because of dispersion, is amplified there. The ray equations show that the packet may undergo multiple reflections within a wave guide formed by sections of the Ω = N surface, and thus penetrate into the shear flow. Three-dimensional numerical simulations of the same problem show that most of the wave packet is actually dissipated once trapped because both the group velocity and the horizontal scale of the packet have strongly decreased through the interaction. Consequently, the wave packet is not able to travel across the shear flow, except when the latter vanishes locally. Present address: Climate and Environmental Physics, Physics Institute, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland.