Multi-mode approximations to wave scattering by an uneven bed

Chamberlain, P. G. and Porter, D. (2006) Multi-mode approximations to wave scattering by an uneven bed. Journal Of Fluid Mechanics, 556. pp. 421-441. ISSN 0022-1120

Abstract/Summary

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.