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On the forced surface waves due to a vertical wave-maker 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

The classical wave-maker problem to determine the forced two-dimensional wave motion with outgoing surface waves at infinity generated by a harmonically oscillating vertical plane wave-maker immersed in water was solved long ago by Sir Thomas Havelock. In this paper we reinvestigate the problem, making allowance for the presence of surface tension which was excluded before, and obtain a solution of the boundary-value problem for the velocity potential which is made unique by prescribing the free surface slope at the wave-maker. The cases of both infinite and finite constant depth are treated, and it is essential to employ a method which is new to this problem since the theory of Havelock cannot be extended in the latter case of finite depth. The solution of the corresponding problem concerning the axisymmetric wave motion due to a vertical cylindrical wave-maker is deduced in conclusion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 323 - 337
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Evans, D. V.The influence of surface tension on the reflection of water waves by a plane vertical barrier. Proc. Cambridge Philos. Soc. 64 (1968), 795–810.CrossRefGoogle Scholar
(2)Evans, D. V.The effect of surface tension on the waves produced by a heaving circular cylinder. Proc. Cambridge Philos. Soc. 64 (1968), 833–847.CrossRefGoogle Scholar
(3)Havelock, T. H.Forced surface waves on water. Philos. Mag. 8 (1929), 569–576.CrossRefGoogle Scholar
(4)Rhodes-Robinson, P. F.Fundamental singularities in the theory of water waves with surface tension. Bull. Austral. Math. Soc. 2 (1970), 317–333.CrossRefGoogle Scholar
(5)Titchmarsh, E. C.The theory of functions, 2nd ed. (Oxford, 1939).Google Scholar