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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  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

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
Information
Journal of Fluid Mechanics , Volume 556 , 10 June 2006 , pp. 421 - 441
Copyright
© 2006 Cambridge University Press

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