Abstract
The generation of wind waves at the surface of a pre-existing underlying vertically sheared water flow of constant vorticity is considered. Emphasis is put on the role of the vorticity in water on wind-wave generation. The amplitude growth rate increases with the vorticity except for quite old waves. A limit to the wave energy growth is found in the case of negative vorticity, corresponding to the vanishing of the growth rate.
Highlights
Wind-wave generation is a central problem in physical oceanography
We have shown that gravity waves propagating at the surface of water flows of constant vorticity behave practically like waves in infinite depth providing that kh > π
Beji and Nadaoka [5] and Stiassnie et al [6] have investigated wind wave generation on a still water while we have considered the role of an undelying vortical water flow on wind wave generation
Summary
Miles [1] is one the first to provide a theoretical framework to understand how wind energy is transferred to ocean surface waves He considered the linear stability of an inviscid parallel shear flow described by a boundary layer in the air above a flat surface of water at rest. Note that Hristov et al [2] found from open ocean experiments that the structure of the wave-induced air flow is in agreement with the critical layer theory. This instability corresponds to a resonant interaction between the wave-induced pressure fluctuations and the surface waves.
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