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The effect of surface tension on the waves produced by a heaving circular cylinder

Published online by Cambridge University Press:  24 October 2008

D. V. Evans
D. V. Evans
Affiliation:
University of Manchester
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Abstract

In this paper the effect of surface tension on water waves is considered. The usual assumptions of the linearized theory are made. A uniqueness theorem is derived for the waves at infinity for a general class of bounded two-dimensional obstacles in a free surface by means of an energy argument. It is shown how the wave amplitude at infinity depends on the prescribed angle at which the free surface meets the normal to the obstacle. The particular case of a heaving half-immersed circular cylinder is considered in detail, and an expression obtained for the velocity potential in terms of a convergent infinite series, the coefficients of which may be computed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 833 - 847
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Benjamin, T. B. and Ursell, F.The stability of the plane free surface of a liquid in a vertical periodic motion. Proc. Roy. Soc. Ser. A 225 (1954), 505–515.Google Scholar
(2)John, F.Waves in the presence of an inclined barrier. Comm. Pure Appl. Math. 1 (1948), 149–200.CrossRefGoogle Scholar
(3)John, F.On the motion of floating bodies. II. Comm. Pure Appl. Math. 3 (1950), 45–101.CrossRefGoogle Scholar
(4)Lamb, H.Hydrodynamics, 6th ed. (Cambridge University Press, 1932).Google Scholar
(5)Riesz, F.Leçons sur les systèmes d'équationa linéaires à une infinité d'inconnues (Paris, 1913).Google Scholar
(6)Sparenberg, J. A.The influence of surface tension on the surface waves induced by the rolling of a thin strip. Nederl. Acad. Wetensch. Proc. Ser. B 63 (1960).Google Scholar
(7)Stoker, J. J.Water waves (Interscience Publishers, New York and London, 1957).Google Scholar
(8)Ursell, F.On the heaving motion of a circular cylinder on the surface of a fluid. Quart. J. Mech. Appl. Math. 2 (1949), 218–231.CrossRefGoogle Scholar
(9)Ursell, F. Unpublished notes on water waves.Google Scholar
(10)Ursell, F.Surface waves on deep water in the presence of a submerged circular cylinder, II. Proc. Cambridge Philos. Soc. 46 (1950), 153–158.CrossRefGoogle Scholar
(11)Wehausen, J. V. and Laitone, E. V.Surface waves (Handbuch der Physik, Springer Verlag, 1960).CrossRefGoogle Scholar