A theoretical investigation is made of the propagation and interactions of nonlinear internal wave beams in density-stratified fluids. These are fundamental time-harmonic disturbances that derive from the non-isotropic nature of internal gravity-wave motion. Attention is focused on the following specific problems: (i) the instability of wave beams to short-scale subharmonic disturbances, a prominent mechanism of breakdown and turbulence generation according to recent experimental and numerical studies; (ii) three-dimensional reflections of nonlinear beams from a sloping boundary, including the case of near-critical reflection, that occurs when the angle of incidence to the horizontal nearly matches the boundary slope; (iii) three-dimensional collisions of nonlinear beams and the associated scattering of energy. These physical phenomena are tackled by formulating mathematical models that are analyzed by asymptotic and numerical methods. The theoretical predictions are compared against related laboratory experiments and field observations.
Internal wave beams play an important part in natural fluid bodies, like the oceans, lakes, and the atmosphere, where density stratification is mainly caused by temperature variations; there are numerous observations of internal wave beams in the atmosphere due to thunderstorms, as well as in oceans due to the interaction of tidal currents with the continental shelf and sea-floor topography. This project is motivated by the need to understand and model quantitatively the mechanisms responsible for the transfer of energy from tide-generated internal wave beams to deep-ocean mixing, which in turn affects ocean circulation, climate change, pollutant dispersal, and nutrient cycles. Moreover, the results of this study would be of basic value in geophysical fluid dynamics and applied mathematics.