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The interaction of waves with horizontal cylinders in two-layer fluids

Published online by Cambridge University Press:  26 April 2006

C. M. Linton  and
M. McIver
C. M. Linton
Affiliation:
Department of Mathematical Sciences, Loughborough University of Technology, Leicestershire LEU 3TU, UK
M. McIver
Affiliation:
Department of Mathematical Sciences, Loughborough University of Technology, Leicestershire LEU 3TU, UK
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Abstract

We consider two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise. These relations are systematically extended to the two-fluid case. It is shown that for symmetric bodies the solutions to scattering problems where the incident wave has wavenumber K and those where it has wavenumber k are related so that the solution to both can be found by just solving one of them. The particular problems of wave scattering by a horizontal circular cylinder in either the upper or lower layer are then solved using multipole expansions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 304 , 10 December 1995 , pp. 213 - 229
Copyright
© 1995 Cambridge University Press

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