Nonlinear Wave Propagation in Fluid Flows

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This project aims at improving the fundamental understanding of the generation of waves on the surface of deep water by an external disturbance. The physical regime of interest is when the waves have wavelength of a few cm; both gravity and capillary effects then become important, and the wave speed attains a minimum value which defines a critical forcing speed: the linear response to external forcing traveling with speed equal to this minimum grows unbounded with time and, apart from damping, nonlinear effects can become important near this resonance. Theoretical models will be used to study the interplay of forcing, nonlinear and damping effects on the wave response under resonant conditions. The theoretical predictions will be compared with laboratory experimental observations reported in the literature.Resonant forcing of gravity-capillary waves is relevant to the generation of ripples by wind, that appear as small-scale roughness on the ocean surface, and to the wave drag associated with the motion of small bodies on a free surface. More generally, this problem is prototypical of resonantly forced wave systems with a phase-speed minimum at finite wavelength, and other potential applications include the response of floating ice sheets to surface vehicles.