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Refraction-diffraction model for weakly nonlinear 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

A model equation is derived for calculating transformation and propagation of Stokes waves. With the assumption that the water depth is slowly varying, the model equation, which is a nonlinear Schrödinger equation with variable coefficients, describes the forward-scattering wavefield. The model equation is used to investigate the wave convergence over a semicircular shoal. Numerical results are compared with experimental data (Whalin 1971). Nonlinear effects, which generate higher-harmonic wave components, are definitely important in the focusing zone. Mean free-surface set-downs over the shoal are also computed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 265 - 274
Copyright
© 1984 Cambridge University Press

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