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An example of non-uniqueness in the two-dimensional linear water wave problem

Published online by Cambridge University Press:  26 April 2006

M. McIver
M. McIver
Affiliation:
Department of Mathematical Sciences, Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU, UK
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Abstract

An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 315 , 25 May 1996 , pp. 257 - 266
Copyright
© 1996 Cambridge University Press

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