Two problems of nonlinear wave propagation in fluid media will be studied by asymptotic and numerical methods: the unsteady dynamics of fully localized free-surface and interfacial solitary waves, often referred to as "lumps"; and resonant nonlinear interactions of internal gravity wavepackets with higher-mode long waves in a density-stratified fluid. Recent theoretical work has brought out a new class of gravity-capillary lumps, and there is experimental evidence that these lumps can be driven by wind blowing over water. While previous studies have focused on the existence of steady lumps, the present investigation will tackle the question of how such lumps may arise from general initial conditions and by external forcing. The second problem to be addressed is a resonance mechanism by which three-dimensional internal gravity wavepackets can transfer energy to higher-mode obliquely propagating long waves, thus contributing to the generation of smaller vertical scales and enhancing the fine vertical structure of the background mean flow fields (density, velocity, etc).
Gravity-capillary lumps are likely to contribute significantly to the small-scale roughness of the ocean surface. Understanding their dynamics may thus prove useful in interpreting satellite images of the ocean surface. Moreover, similar lumps are expected to arise on floating ice sheets due to loads moving on top of the ice, a problem with several applications, including the use of vehicles on floating ice. Shedding light, on the other hand, on how internal gravity waves in a stratified fluid contribute to the fine vertical structure of the background flow is an important issue in understanding how mixing occurs in the ocean, which in turn is believed to affect climate dynamics, biological productivity and waste disposal.
