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Wave scattering in a two-layer fluid of varying depth

Published online by Cambridge University Press:  09 February 2005

P. G. CHAMBERLAIN  and
D. PORTER
P. G. CHAMBERLAIN
Affiliation:
Department of Mathematics, University of Reading, P.O. Box 220, Whiteknights, Reading RG6 6AX, UK
D. PORTER
Affiliation:
Department of Mathematics, University of Reading, P.O. Box 220, Whiteknights, Reading RG6 6AX, UK
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Abstract

The scattering of waves in a two-layer fluid of varying mean depth is examined in a three-dimensional context using linear theory. A variational technique is used to construct a particular type of approximation which has the effect of removing the vertical coordinate and reducing the problem to two coupled partial differential equations in two independent variables. A transformation of this differential equation system leads to a particularly simple approximate representation of the scattering process. The theory is applied to two-dimensional scattering, for which a set of symmetry relations is derived. A selection of numerical results is presented to illustrate the principle interest in the problem, namely the energy transfer between surface and interfacial waves induced by bed undulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 524 , 10 February 2005 , pp. 207 - 228
Copyright
© 2005 Cambridge University Press

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