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Scattering and near-trapping of water waves by axisymmetric topography

Published online by Cambridge University Press:  10 June 1999

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 scattering of plane surface water waves by both surface-piercing and submerged axisymmetric bed formations has been investigated by a number of authors. We extend previous contributions in two ways: we employ the recently derived modified mild-slope equation to approximate the fluid motion and we consider arbitrary axisymmetric topography, subject only to the restriction imposed by the mild-slope approximation. We thereby derive a robust method for calculating the scattered wave field for the small seabed slopes typical of most real situations and make a contribution to the phenomena of near-resonance and near-trapping over submerged axisymmetric shoals, which have previously been detected for only one idealized bedform.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 388 , 10 June 1999 , pp. 335 - 354
Copyright
© 1999 Cambridge University Press

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