Journal of Fluid Mechanics



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Multi-mode approximations to wave scattering by an uneven bed


P. G. CHAMBERLAIN a1 and D. PORTER a1
a1 Department of Mathematics, The University of Reading, PO Box 220, Whiteknights, Reading, RG6 6AX, UK

Article author query
chamberlain pg   [Google Scholar] 
porter d   [Google Scholar] 
 

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.

(Published Online May 24 2006)
(Received September 6 2005)
(Revised November 22 2005)



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