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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(2):193-208; doi:10.1093/qjmam/44.2.193
© 1991 by Oxford University Press
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TRAPPING OF SURFACE WATER WAVES BY FIXED BODIES IN A CHANNEL

P. McIVER{dagger}

( Department of Mathematics and Statistics, Brunel University Uxbridge, Middlesex UB3 3PH )

{dagger} Present address: Department of Mathematical Sciences, Loughborough University of Technology, Loughborough, Leicestershire LE11 3TU.

Solutions are constructed by the method of matched asymptotic expansions for surface water waves trapped by fixed bodies in a deep channel with vertical walls. In particular, approximate relations between the frequency of trapped waves and the channel width are obtained in terms of simple properties of the bodies. A number of geometries are considered. First, the result of Ursell for a submerged, horizontal, circular cylinder spanning the channel is generalized to cylinders symmetric about a vertical plane perpendicular to the channel walls, but of otherwise arbitrary cross-section. Secondly, both submerged and surface-piercing compact, three-dimensional bodies with appropriate symmetries are considered. Finally, a solution is given for a vertical cylinder extending throughout the channel depth which is equivalent to a two-dimensional problem in acoustics.


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