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Models for very wide-angle water waves and wave diffraction. Part 2. Irregular bathymetry

Published online by Cambridge University Press:  26 April 2006

Robert A. Dalrymple ,
Kyung Duck Suh ,
James T. Kirby  and
Jang Won Chae
Robert A. Dalrymple
Affiliation:
Ocean Engineering Group, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
Kyung Duck Suh
Affiliation:
Ocean Engineering Group, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
James T. Kirby
Affiliation:
Coastal and Oceanographic Engineering Department, University of Florida, Gainesville, FL 32611, USA
Jang Won Chae
Affiliation:
Ocean Engineering Laboratory, Korea Ocean Research and Development Institute, P.O. Box 29, Panwol Ind., Ansan, 171-14, Korea
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Abstract

A wide-angle model for water-wave propagation on an irregular bathymetry is developed based on the linear mild-slope equation. The spectral model decomposes the incident wavetrain into directional modes, or an angular spectrum. The effect of the bottom topography is shown to force the generation of additional directional wave modes. Nonlinearity is incorporated in the model by correcting the wave parameters iteratively using an empirical nonlinear dispersion relationship which is approximately valid over the entire range of water depths.

Numerical examples are presented for waves incident on a transverse bar field, a laboratory experiment involving wave focusing over an elliptic shoal on a sloping beach for which detailed measurements are available and for waves focusing behind a circular shoal resting on a flat botom. The application of the model is limited to cases in which the model domain is rectangular and the depth variation in the lateral direction is small if waves of large incident angle are modelled.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 201 , April 1989 , pp. 299 - 322
Copyright
© 1989 Cambridge University Press

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