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A harbour theory for wind-generated waves based on ray methods

Published online by Cambridge University Press:  12 April 2006

Jesper Larsen
Jesper Larsen
Affiliation:
Laboratory of Applied Mathematical Physics, Technical University of Denmark, Copenhagen Present address: The Institute of Mathematical Technology, Sommervej 7, DK 2920 Charlottenlund, Denmark.
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Abstract

In the paper we consider harbour oscillations excited by wind-generated gravity waves. The analysis is based on the fact that waves propagate along rays (wave orthogonals). In this way the elliptic boundary-value problem is turned into an initial-value problem along each ray. When a ray strikes the boundary (the harbour walls), reflected rays are produced in accordance with the law of reflexion. When a ray strikes an edge point of the boundary (e.g. the tip of a breakwater) diffracted rays are produced and emitted in all directions into the harbour. Algorithms for the tracing of incident, multiply reflected and singly diffracted rays as well as the computation of the field on each ray are presented. Attenuation mechanisms (e.g. partial reflexion), which limit the number of rays needed to compute the field, are included. Numerical examples for a rectangular and an actual harbour are given. A comparison between the results obtained by ray methods and finite difference methods is included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 1 , 12 July 1978 , pp. 143 - 158
Copyright
© 1978 Cambridge University Press

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