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On weak reflection of water waves

Published online by Cambridge University Press:  20 April 2006

Philip L.-F. Liu  and
Ting-Kuei Tsay
Philip L.-F. Liu
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
Ting-Kuei Tsay
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
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Abstract

The weak reflection of monochromatic water waves is studied for the cases of slowly varying water depth. A coupled system of equations for the forward-scattering (transmitted) and the backward-scattering (reflected) wavefields are derived from the mild-slope equation (Smith & Sprinks 1975). Parabolic approximation is then used to simplify the equations for the diffraction factor. An iterative numerical scheme is proposed to compute the resulting equations. The scheme converges very quickly for the cases of weak reflection. The accuracy of the present approach is shown by comparing with numerical results obtained by a hybrid finite-element formulation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 131 , June 1983 , pp. 59 - 71
Copyright
© 1983 Cambridge University Press

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