Reflection of Water Waves in a Channel with Corrugated Beds.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Intended as a contribution towards understanding the multiple processes entailed in the development of coastal sand bars due to wave action, this theoretical and experimental study deals with the Bragg reflection of long-crested surface waves in a water channel whose bed is corrugated sinusoidally. The present findings complement and in a few respects improve upon those in previous investigations, particularly Davies and Heathershaw 1984. In chapter 2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagates into a channel with a limited stretch of corrugations on its bed and an imperfectly absorbing beach at its far end. Allowance is made fully for dispersive effect and approximately for small frictional effect. Points of interpretation include accounts of degenerate but nontrivial solutions that apply at frequencies terminating at the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in chapter 4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both outside the stopping band. Quantitative comparisons demonstrate close agreements with the theory. Keywords Water waves Sand bars.
- Fluid Mechanics
- Hydrology, Limnology and Potamology