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Wave interaction with two-dimensional bodies floating in a two-layer fluid: uniqueness and trapped modes

Published online by Cambridge University Press:  19 August 2003

N. KUZNETSOV ,
M. MCIVER  and
P. MCIVER
N. KUZNETSOV
Affiliation:
Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St Petersburg 199178, Russia
M. MCIVER
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK
P. MCIVER
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leics LE11 3TU, UK
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Abstract

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Existing results on the linearized water-wave problem for a homogeneous fluid are extended to the case of a two-layer fluid. In particular, the appropriate form of Maz'ya's identity is presented and used to obtain results on the uniqueness of the solutions to forcing problems for a structure in a two-layer fluid. Further, examples of geometries are constructed for which trapped modes occur; such modes are finite-energy solutions of the unforced problem and provide examples of non-uniqueness.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 490 , 10 September 2003 , pp. 321 - 331
Copyright
© 2003 Cambridge University Press