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An angular spectrum model for propagation of Stokes waves

Published online by Cambridge University Press:  26 April 2006

Kyung Duck Suh ,
Robert A. Dalrymple  and
James T. Kirby
Kyung Duck Suh
Affiliation:
Center for Applied Coastal Research, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA Present address: Virginia Institute of Marine Science, Gloucester Point, VA 23062, USA.
Robert A. Dalrymple
Affiliation:
Center for Applied Coastal Research, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
James T. Kirby
Affiliation:
Center for Applied Coastal Research, Department of Civil Engineering, University of Delaware, Newark, DE 19716, USA
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Abstract

An angular spectrum model for predicting the transformation of Stokes waves on a mildly varying topography is developed, including refraction, diffraction, shoaling and nonlinear wave interactions. The equations governing the water-wave motion are perturbed using the method of multiple scales and Stokes expansions for the velocity potential and free-surface displacement. The first-order solution is expressed as an angular spectrum, or directional modes, of the wave field propagating on a beach with straight iso-baths whose depth is given by laterally averaged depths. The equations for the evolution of the angular spectrum due to the effects of bottom variation and cubic resonant interaction are obtained from the higher-order problems. Comparison of the present model with existing models is made for some simple cases. Numerical examples of the time-independent version of the model are presented for laboratory experiments for wave diffraction behind a breakwater gap and wave focusing over submerged shoals: an elliptic shoal on a sloping beach and a circular shoal on a flat bottom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 205 - 232
Copyright
© 1990 Cambridge University Press

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