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Trapping of water waves by submerged plates using hypersingular integral equations

Published online by Cambridge University Press:  26 April 2006

Neil F. Parsons  and
P. A. Martin
Neil F. Parsons
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
P. A. Martin
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
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Abstract

The trapping of surface water waves by a thin plate in deep water is reduced to finding non-trivial solutions of a homogeneous, hypersingular integral equation for the discontinuity in velocity potential across the plate. The integral equation is discretized using an expansion-collocation method, involving Chebyshev polynomials of the second kind. A non-trivial solution to the problem is given by the vanishing of the determinant inherent in such a method. Results are given for inclined flat plates, and for curved plates that are symmetric with respect to a line drawn vertically through their centre. Comparisons with published results for horizontal flat plates (in water of finite depth) and for circular cylinders are made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 284 , 10 February 1995 , pp. 359 - 375
Copyright
© 1995 Cambridge University Press

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