The problem of scattering of internal gravity waves by a localised vortex in a stratified medium is considered in the case of incoming waves with large wavelength compared to the size of the vortex. An asymptotic solution is found using a rational expansion of the equations of motion, and the leading-order scattered wave field is calculated.
There are several physically-interesting cases. We consider incoming waves with the same vertical scale as the vortex, and waves which are long in all directions compared to the vortex. We consider the Boussinesq limit, in which the scattered wave field consists entirely of internal gravity waves. The general non-Boussinesq case is also considered, in which case both acoustic and internal waves may be scattered from the vortex. Implications for the interpretation of internal waves are discussed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics