Nonlinear Diffraction of Ocean Gravity Waves
WOODS HOLE OCEANOGRAPHIC INSTITUTION MA
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In an irregular sea, waves having different wave numbers interact nonlinearly, giving rise to long waves at the difference frequency and wavenumber. The long waves are associated with motions that have large characteristics time and space scales. The method of multiple scales in time and in space, in conjunction with perturbation expansions, enables us to separate the flow into components for the general case when there are wave-trains propagating in different directions. In particular, it is of great interest to study the effect of modification of the short waves by diffraction, refraction, reflection and radiation. Using the method of matched asymptotics we determine the long-wave, that consists of forced waves travelling with the short-wave groups and of an additional wave that propagates away from the zone of modification at the long-wave velocity gh to the 12 power. The resulting theory has a wide range of applications. We have studied the following problems a Slow sway of a moored floating body in water of finite depth b Wave trapping on a shelf and c Excitation of interfacial waves in the lee of a breakwater. The present method of analysis, and in particular the multiple scales expansion, proves to be a useful tool in studying modulation and nonlinearity in several aspects at wave propagation, and can be extended to the study of a heretofore unexplored aspect of harbor resonance.
- Physical and Dynamic Oceanography
- Fluid Mechanics