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Models for very wide-angle water waves and wave diffraction

Published online by Cambridge University Press:  21 April 2006

Robert A. Dalrymple  and
James T. Kirby
Robert A. Dalrymple
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 32601, USA
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Abstract

For a bathymetry consisting of parallel bottom contours, wide-angle parabolic models are developed to describe the diffraction of linear water waves. The first model, developed by operator correspondence, extends the validity of conventional forms of the parabolic model for wave angles up to 70° from the assumed wave direction. Through the use of Fourier decomposition, wave models valid to 90° are developed for three different lateral boundary conditions. By application, it is shown that the diffraction of waves through gaps or around structures is governed by the initial wave condition at the structure, which can be expanded into progressive and evanescent wave modes. Away from the structure, the wave field consists of only the progressive wave modes, which disperse according to their direction of propagation, the water depth and Snell's Law. Examples are shown for oblique waves through a gap, directional seas past a breakwater, a plane wave with varying crest amplitude, and finally for the diffraction of waves into a channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 192 , July 1988 , pp. 33 - 50
Copyright
© 1988 Cambridge University Press

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