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Note on the reflexion of water waves at a wall in the presence of surface tension

Published online by Cambridge University Press:  24 October 2008

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

In this note we examine the influence of surface tension on surface waves incident against a fixed vertical plane wall. The motion is time harmonic and is determined by making the initial assumption that the free-surface slope at the wall is prescribed. From the unique solution obtained for the velocity potential, the parameter involved in this specification can be determined, for small laboratory-scale waves at least, using some longstanding experimental results on meniscus behaviour at a moving contact line. The effect of surface tension is to produce a motion wherein reflexion from the wall is not complete and there is a local disturbance, in contrast to the classical standing-wave motion in the absence of surface tension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 2 , September 1982 , pp. 369 - 374
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Ablett, R.An investigation of the angle of contact between paraffin wax and water. Philos. Mag. 46 (1923), 244–256.Google Scholar
(2)Allwood, D. A.Capillary-gravity waves over a sloping beach. Proc. Cambridge Philos. Soc. 74 (1973), 539–547.CrossRefGoogle Scholar
(3)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.Google Scholar
(4)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.Google Scholar
(5)Packham, B. A.Capillary-gravity waves against a vertical cliff. Proc. Cambridge Philos. Soc. 64 (1968), 827–832.Google Scholar
(6)Rhodes-Robinson, P. F.Fundamental singularities in the theory of water waves with surface tension. Butt. Austral. Math. Soc. 2 (1970), 317–333.CrossRefGoogle Scholar
(7)Rhodes-Robinson, P. F.On the forced surface waves due to a vertical wave-maker in the presence of surface tension. Proc. Cambridge Philos. Soc. 70 (1971), 323–337.CrossRefGoogle Scholar