Mathematical Sciences: Nonlinear Coupling of Long Internal Waves With Small-Scale Disturbances

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9404673 AKYLAS Internal gravity waves are of considerable geophysical interest. Large-amplitude internal wave disturbances are common features in the ocean thermocline both in deep water and in coastal regions, as well as in the lower atmosphere. This work focuses on understanding the interaction of long large-amplitude internal waves with short-scale disturbances. This is a fully nonlinear mechanism that is relevant to various oceanic and atmospheric phenomena. For example, the coupling of solitary internal waves with short-scale surface waves manifests as surface roughness variations---the so-called 'surface rips'---that often accompany internal waves in the field, and are visible in radar images of the sea surface. The main objective is to obtain an understanding of this nonlinear coupling mechanism both from a physical and a mathematical point of view. Particular emphasis is placed on calculating the amplitude of short-wave tails induced by long internal waves. For this purpose, a singular perturbation technique in the wavenumber domain will be developed for weakly nonlinear disturbances, and fully numerical computations will be carried out for large-amplitude waves.