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The low-frequency scattering of Kelvin waves by stepped topography

Published online by Cambridge University Press:  26 April 2006

E. R. Johnson
E. R. Johnson
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
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Abstract

A straightforward method that yields explicit transmission amplitudes is presented for Kelvin wave scattering by topography whose isobaths are parallel sufficiently far from the vertical, but not necessarily planar, wall supporting the incident wave. These results are obtained by first restricting attention to the low-frequency limit in which the flow splits naturally into three regions: an outer-x region containing the incident and transmitted Kelvin waves, an outer-y region containing outwardly propagating long topographic waves and an inner quasi-steady geostrophic region whose structure follows from earlier time-dependent analyses. The present analysis is further simplified by approximating general smooth features by stepped profiles with no restriction on the size, number or order of steps. Various qualitative results on the transmission amplitudes and flow fields are deduced from the explicit solutions and results are given on orthogonality, completeness and direction of propagation of the scattered long waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 215 , June 1990 , pp. 23 - 44
Copyright
© 1990 Cambridge University Press

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