Mathematical Sciences: Geophysical Fluid Dynamics

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This proposal concerns a number of important topics in the fluid dynamics of ocean waves revolving around the central concept of wave-wave and wave-solid interactions. Specifically the proposer will study wave reflection on a sloping beach, parametrically excited edge waves, axisymmetric cross-waves, resonant interactions and Wilton's ripples, and the tidal equations of Laplace with regard to the coupling between surface and internal tides. The study of ocean waves has a long and venerable history, and it remains today a vitally important area of research that includes the motion of ships through water, the diurnal tidal motions, and structures. This proposal will involve looking into the underlying mathematics and physics of these phenomena; the understanding gained from this research will have genuine technological significance.