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Multi-mode approximations to wave scattering by an uneven bed

Published online by Cambridge University Press:  24 May 2006

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

Abstract

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode ‘mild-slope’ approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

Type
Papers
Copyright
© 2006 Cambridge University Press

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