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Water waves of finite amplitude on a sloping beach

Published online by Cambridge University Press:  28 March 2006

G. F. Carrier
Affiliation:
Pierce Hall, Harvard University
H. P. Greenspan
Affiliation:
Pierce Hall, Harvard University

Abstract

In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

Type
Research Article
Copyright
© Cambridge University Press

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References

Stoker, J. J. 1948 The formation of breakers and bores, Comm. Pure Appl. Math. 1, 1.
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions, 2nd Ed. Cambridge University Press.
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