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Reflection of water waves in a channel with corrugated bed

Published online by Cambridge University Press:  21 April 2006

T. Brooke Benjamin ,
B. Boczar-Karakiewicz  and
W. G. Pritchard
T. Brooke Benjamin
Affiliation:
Mathematical Institute, 24/29 St Giles, Oxford OX1 3LB, UK
B. Boczar-Karakiewicz
Affiliation:
I.N.R.S.-Océanologie, Université du Québec, Rimouski, Québec G5L 3A1, Canada
W. G. Pritchard
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA
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Abstract

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 & Heathershaw (1984).

In §2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagate 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 effects (§2.2) and approximately for small frictional effects (§2.3). Points of interpretation (§2.4) include accounts of degenerate but non-trivial solutions that apply at frequencies terminating the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in §4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both inside and outside the stopping band. Quantitative comparisons (§4.2 and 4.3) demonstrate close agreements with the theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 249 - 274
Copyright
© 1987 Cambridge University Press

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