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On forced three-dimensional surface waves in a channel in the presence of surface tension

Published online by Cambridge University Press:  24 October 2008

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

In this paper wave-maker theory including the effect of surface tension is determined for three-dimensional motion of water in a semi-infinite rectangular channel with outgoing surface wave modes allowed for at infinity; the motion is generated by a harmonically oscillating vertical plane wave-maker at the end of the channel and the cases of both infinite and finite constant depth are treated. The solution of the boundary-value problem for the velocity potential is more complicated in the presence of surface tension due mainly to the additional effect of the channel walls at which the normal free surface slopes are prescribed—as also is the slope at the wave-maker—to ensure uniqueness. The simpler three-dimensional solution for a semi-infinite region—obtained long ago by Sir Thomas Havelock in the absence of surface tension for the case of infinite depth—is also noted.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 3 , May 1974 , pp. 405 - 426
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

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