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The Quarterly Journal of Mechanics and Applied Mathematics 1997 50(2):165-178; doi:10.1093/qjmam/50.2.165
© 1997 by Oxford University Press
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TRAPPED MODES IN AN AXISYMMETRIC WATER-WAVE PROBLEM

P. MCIVER and M. MCIVER

( Department of Mathematical Sciences, Loughborough University Loughborough LE11 3TU )

Trapped-mode solutions, that is, examples of non-uniqueness, are given for a class of axisymmetric problems in the linearized theory of the interaction of water waves with structures. The solutions are constructed by placing an axisymmetric ring source in the free surface with the radius of the ring chosen to eliminate radial circular waves. The ring-source potential then corresponds to a localized standing wave. Suitable structural surfaces are obtained by looking for stream surfaces of the flow.


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R. Harter, I. D. Abrahams, and M. J Simon
The effect of surface tension on trapped modes in water-wave problems
Proc R Soc A, December 8, 2007; 463(2088): 3131 - 3149.
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