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On the breaking of water waves of finite amplitude on a sloping beach

Published online by Cambridge University Press:  28 March 2006

H. P. Greenspan
H. P. Greenspan
Affiliation:
Pierce Hall, Harvard University
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Abstract

In a recent paper Carrier & Greenspan (1958) showed that, within the framework of the non-linear shallow-water theory, there exist waves which do not break as they climb a sloping beach. The formation of a shock or bore is dependent on a variety of factors (wave shape, particle velocity, etc.) and, as yet, no general criteria for breaking have been found. In this paper, we consider waves which propagate shoreward into quiescent water; it is shown that any compressive wave (a wave of positive amplitude) which has a non-zero slope at the wave-front eventually breaks before reaching the coastline. In fact, an explicit relation is obtained between the initial conditions and the position where breaking occurs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 4 , Issue 3 , July 1958 , pp. 330 - 334
Copyright
© Cambridge University Press

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References

Carrier, G. F. & Greenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach, J. Fluid Mech. 4, 97.Google Scholar
Stoker, J. J. 1948 The formation of breakers and bores, Comm. Pure Appl. Math. 1, 9.Google Scholar