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Capillary-gravity waves over a sloping beach

Published online by Cambridge University Press:  24 October 2008

D. A. Allwood
D. A. Allwood
Affiliation:
Institute of Applied Mathematics, University of British Columbia
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Abstract

It is shown how the solution for the velocity potential may be determined when the effect of surface tension is included in the linearized theory of surface waves over a sloping beach. In particular, two independent standing wave solutions are found, both of which have finite amplitude at the shoreline. The results agree with those of previous writers when the surface tension force tends to zero.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 539 - 547
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Brillouet, G.Publ. Sci. Tech. Ministre de l'air (Paris), 329 (1957).Google Scholar
(2)Lewy, H.Bull. Amer. Math. Soc. 52 (1946), 737–775.CrossRefGoogle Scholar
(3)Mondal, M. M. Surface tension effects in the theory of gravity waves. Ph.D. Thesis, University of Surrey (1969).Google Scholar
(4)Packham, B. A.Proc. Cambridge Philos. Soc. 64 (1968), 827–832.CrossRefGoogle Scholar
(5)Peters, A. S.Comm. Pure Appl. Math. 5 (1952), 87–108.CrossRefGoogle Scholar
(6)Roseau, M.Comm. Pure Appl. Math. 11 (1958), 433–493.CrossRefGoogle Scholar
(7)Stoker, J. J.Quart. Appl. Math. 5 (1947), 1–54.CrossRefGoogle Scholar
(8)Williams, W. E.Proc. Roy. Soc. A252 (1959), 376–393.Google Scholar
(9)Williams, W. E.Proc. Cambridge Philos. Soc. 57 (1961), 160–165.CrossRefGoogle Scholar
(10)Wehausen, J. V. and Laitone, E. V.Surface waves. Handbuch der Physik 9 (1960).Google Scholar