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Approximations to wave trapping by topography

Published online by Cambridge University Press:  26 April 2006

P. G. Chamberlain  and
D. Porter
P. G. Chamberlain
Affiliation:
Department of Mathematics, The University of Reading, PO Box 220, Whiteknights, Reading RG6 6AX, UK
D. Porter
Affiliation:
Department of Mathematics, The University of Reading, PO Box 220, Whiteknights, Reading RG6 6AX, UK
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Abstract

The trapping of linear water waves over two-dimensional topography is investigated by using the mild-slope approximation. Two types of bed profile are considered: a local irregularity in a horizontal bed and a shelf joining two horizontal bed sections at different depths. A number of results are derived concerning the existence of trapped modes and their multiplicity. It is found, for example, that the maximum number of modes which can exist depends only on the gross properties of the topography and not on its precise shape. A range of problems is solved numerically, to inform and illustrate the analysis, using both the mild-slope equation and the recently derived modified mild-slope equation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 357 - 376
Copyright
© 1996 Cambridge University Press

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