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Wave-source expansions for water of infinite depth in the presence of surface tension

Part of: Incompressible inviscid fluids

Published online by Cambridge University Press:  26 February 2010

P. F. Rhodes-Robinson
P. F. Rhodes-Robinson
Affiliation:
Department of Mathematics, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand.
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Abstract

In this paper two expansions are obtained by contour integration methods for the velocity potential describing two-dimensional time-harmonic surface waves due to a free-surface wave source on water of infinite depth in the presence of surface tension. First the series expansion at r = 0 is found and then the asymptotic expansion as Kr®¥, where K is the wave number for progressive waves and r the radial distance from the source. The corresponding expansions for the more important submerged wave source in terms of the radial distance from the image source in the free surface may then easily be deduced. The latter are required in a number of surface wave problems, particularly those of a short-wave asymptotic nature, and are also relevant in obtaining expansions for finite constant depth.

MSC classification

Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 67 - 76
Copyright
Copyright © University College London 1991

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References

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