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Resonant reflection of water waves in a long channel with corrugated boundaries

Published online by Cambridge University Press:  21 April 2006

Philip L.-F. Liu
Philip L.-F. Liu
Affiliation:
Joseph H. DeFrees Hydraulic Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

A one-dimensional wave equation is derived for water-wave propagations in a long channel with corrugated boundaries. The amplitude and the wavelength of boundary undulations are assumed to be smaller than and in the same order of magnitude as the incident wavelength, respectively. When the Bragg reflection condition (i.e. the wavenumber of the boundary undulations is twice that of the incident wavenumber) is nearly satisfied, significant wave reflection could occur. Coupled equations for transmitted and reflected wave fields are derived for the near resonant coupling. The detuning mechanism is attributed to the slight deviation in the wavenumber of the corrugated boundaries from the Bragg wavenumber. Analytical solutions are obtained for the cases where the boundary undulations are within a finite region. The application of the present theory to the design of a harbour resonator is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 371 - 381
Copyright
© 1987 Cambridge University Press

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