Dynamics of Three-dimensional Nonlinear Internal Waves Over Topography

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0072145AkylasA common mechanism by which internal gravity waves are generated in nature is flow over topography. The goal of the proposed work is to improve our theoretical understanding of this generation mechanism with particular emphasis on three-dimensional nonlinear disturbances. To this end, an asymptotic theory will be developed to describe the generation of finite-amplitude disturbances by nearly uniformly stratified flow over three-dimensional topography that is more elongated in the spanwise than in the streamwise direction. The proposed theory makes it possible to explore certain features of fully nonlinear waves --- for instance, how wave breaking is influenced by three-dimensional effects --- that, although of primary geophysical interest, so far have defied theoretical treatment. Moreover, the mathematical approach taken here is distinct from prior studies and promises to advance our understanding of nonlinear internal wave propagation from a mathematical standpoint as well.Internal gravity waves are common features in oceans, lakes and in the atmosphere. They owe their existence to the density stratification present in these natural fluid bodies due to variations in temperature and changes in the salinity (in the case of oceans) and pressure (in the case of the atmosphere). Geophysical internal waves are known to possess enormous scales, on the order of kilometers to hundreds of kilometers, so it is not surprising that they are important factors in determining local weather patterns and climate dynamics. The proposed work will provide a mathematical description of the generation of internal waves by flow over topography, modeling the action of wind over mountain ranges in the atmosphere or the flow of currents over a sill in the ocean bottom. Emphasis is placed on particular flow conditions under which internal-wave generation is most violent and is expected to play an important part in geophysical applications (e.g., the development of thunderstorms).