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Topographic waves in open domains. Part 2. Bay modes and resonances

Published online by Cambridge University Press:  26 April 2006

Thomas F. Stocker  and
E. R. Johnson
Thomas F. Stocker
Affiliation:
Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zürich, Switzerland.
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

The topographic wave equation is solved in a domain consisting of a channel with a terminating bay zone. For exponential depth profiles the problem reduces to an algebraic eigenvalue problem. In a flat channel adjacent to a shelf–like bay zone the solutions form a countably infinite set of orthogonal bay modes: the spectrum of eigenfrequencies is purely discrete. A channel with transverse topography allows wave propagation towards and away from the bay: the spectrum has a continuous part below the cutoff frequency of free channel waves. Above this cutoff frequency a finite number (possibly zero) of bay-trapped solutions occur. Bounds for this number are given. At particular frequencies below the cutoff the system is in resonance with the incident wave. These resonances are shown to be associated with bay modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 200 , March 1989 , pp. 77 - 93
Copyright
© 1989 Cambridge University Press

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