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On the scattering of short surface waves by a finite dock

Published online by Cambridge University Press:  24 October 2008

F. G. Leppington
F. G. Leppington
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

A sinusoidal travelling wave-train is at normal incidence upon a two-dimensional finite dock fixed on the surface of a body of water of great depth, and the problem investigated herein is that of finding the limiting form of the induced velocity potential for short waves. Of particular interest are the amplitudes of the wave-trains reflected and transmitted towards infinity by such an obstacle. The potential is expressed as a sum of coupled semi-infinite dock potentials, whence results a pair of weakly coupled integral equations for the solution. This formulation of the problem is shown to be amenable to an approximate solution for large wave-numbers, and the first few terms are derived in formal expansions for the reflection and transmission coefficients.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1109 - 1129
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Erdélyi, A.Asymptotic expansions (Dover, 1956).Google Scholar
(2)Friedrichs, K. O. and Lewy, H.Comm. Pure Appl. Math. 1 (1948), 135.CrossRefGoogle Scholar
(3)Holford, R. L.Proc. Cambridge Philos. Soc. 60 (1964), 957.CrossRefGoogle Scholar
(4)Holford, R. L.Proc. Cambridge Philos. Soc. 60 (1964), 985.Google Scholar
(5)Keller, J. B., Lewis, R. M. and Seckler, B. D.Comm. Pure Appl. Math. 9 (1956), 207.CrossRefGoogle Scholar
(6)Kendall, M. G. and Stuart, A.Advanced theory of statistics, 2nd (3 vol.) Ed., vol. 1 (Griffin, London, 1963).Google Scholar
(7)Stoker, J. J.Water waves (Interscience, New York, 1957).Google Scholar
(8)Ursell, F.Proc. Roy. Soc. Ser. A 220 (1953), 90.Google Scholar
(9)Ursell, F.Proc. Cambridge Philos. Soc. 53 (1957), 115.Google Scholar
(10)Ursell, F.Proc. Cambridge Philos. Soc. 57 (1961), 638.Google Scholar
(11)Ursell, F.Proc. Cambridge Philos. Soc. 62 (1966), 227.Google Scholar
(12)Watson, G. N.Theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar
(13)Erdélyi, A. et al. Tables of integral transforms, vol. 1, Bateman Manuscript Project (McGraw-Hill, 1954).Google Scholar