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The generation of surface waves over a sloping beach by an oscillating line-source. I. The general solution

Published online by Cambridge University Press:  24 October 2008

Clare A. N. Morris
Clare A. N. Morris
Affiliation:
(Department of Mathematics and Statistics, City of London Polytechnic)
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Abstract

The problem of wave generation by a line source of sinusoidally varying strength situated in water above a beach of arbitrary angle α(0 < α ≤ π) is solved by the use of a Laplace-integral representation of the solution. It is shown that a solution can be constructed which is regular at the shoreline and gives an outgoing wave-train at infinity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 3 , November 1974 , pp. 545 - 554
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Peters, A. S.Comm. Pure Appl. Math. 3 (1950), 310–354.CrossRefGoogle Scholar
(2)Stoker, J. J.Quart. Appl. Math. 5 (1947), 1–54.CrossRefGoogle Scholar
(3)Lewy, H.Bull. Amer. Math. Soc. 52 (1946), 737–775.CrossRefGoogle Scholar
(4)Sretenskii, L. N.Prikl. Mat. Meh. 27 (1963), 1012–1025.Google Scholar
(5)Shen, M. C. New York University, Courant Institute of Mathematical Sciences, report no. IMM 342, (1965).Google Scholar
(6)Morris, C. A. N.Proc. Cambridge Philos. Soc. 76 (1974), 555–562.CrossRefGoogle Scholar
(7)Titchmarsh, E. C.The theory of functions (Oxford, 1932).Google Scholar
(8)Muskhelishvili, N. I.Singular integral equations, Noordhoff (Groningen, 1953).Google Scholar