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Nonlinear refraction–diffraction of waves in shallow water

Published online by Cambridge University Press:  20 April 2006

Philip L.-F. Liu ,
Sung B. Yoon  and
James T. Kirby
Philip L.-F. Liu
Affiliation:
Joseph H. DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
Sung B. Yoon
Affiliation:
Joseph H. DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853
James T. Kirby
Affiliation:
Marine Sciences Research Center, State University of New York at Stony Brook, Stony Brook, NY 11794 Present address: Department of Coastal and Oceanographic Engineering, University of Florida, Gainesville, FL 32611
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Abstract

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K–P equation (Kadomtsev & Petviashvili 1970) to include varying depth in two dimensions. Comparisons are made between present numerical results, experimental data (Whalin 1971) and previous numerical calculations (Madsen & Warren 1984).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 153 , April 1985 , pp. 185 - 201
Copyright
© 1985 Cambridge University Press

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