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Bragg scattering of water waves by a doubly periodic seabed

Published online by Cambridge University Press:  21 April 2006

Mamoun Naciri  and
Chiang C. Mei
Mamoun Naciri
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Chiang C. Mei
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

We extend the recent work on Bragg scattering of water waves by one-dimensional parallel bars of sinusoidal profile to two-dimensional, doubly sinusoidal bed waves. The resonance condition governing the phase matching between the incident, scattered and bed waves is now more complicated and a much richer variety of resonant reflection can occur. In particular, for one normally incident wave there can be two reflected waves forming a standing wave in the transverse direction. Solutions for a wide strip of bed waves are discussed for incident water waves satisfying approximately the Bragg resonance condition. Modifications for a two-dimensional array of hemispheroids are also given. Possible application to the design of submerged breakwaters is suggested.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 51 - 74
Copyright
© 1988 Cambridge University Press

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