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Internal gravity waves in a vertically sheared flow Healey, David Andrew

Abstract

We investigate the propagation of internal gravity waves in a rotating fluid with horizontal and vertical stratification. The modification of these waves by the presence of a vertically sheared geostrophic current is determined, and the rate of energy exchange between waves and current is estimated and compared to exchange rates of other interaction mechanisms. The effect of boundary conditions on the range of frequencies allowed for wave propagation is also considered. The wave amplitude has horizontal exponential dependence due to the horizontal density variation as well as to exchange of energy with the mean shear flow. The solution also shows a phase difference from surface to bottom. For waves propagating normally to a vertically sheared geostrophic current, the energy exchange mechanism is found to be weak when compared to other exchange mechanisms and is likely to be of little importance in the ocean. The imposition of boundary conditions on the wave solution alters the frequency range over which solutions may exist.

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