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On the excitation of edge waves on beaches

Published online by Cambridge University Press:  11 April 2006

A. A. Minzoni
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
G. B. Whitham
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena

Abstract

The excitation of standing edge waves of frequency ½ω by a normally incident wave train of frequency ω has been discussed previously (Guza & Davis 1974; Guza & Inman 1975; Guza & Bowen 1976) on the basis of shallow-water theory. Here the problem is formulated in the full water-wave theory without making the shallow-water approximation and solved for beach angles β = π/2N, where N is an integer. The work confirms the shallow-water results in the limit N [Gt ] 1, shows the effect of larger beach angles and allows a more complete discussion of some aspects of the problem.

Type
Research Article
Copyright
© 1977 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. 1965 Handbook of Mathematical Functions. Dover.
Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.
Friedrichs, K. O. 1948 Comm. Pure Appl. Math. 1, 109134.
Guza, R. T. & Bowen, A. J. 1975 J. Geophys. Res. 80, 45294534.
Guza, R. T. & Bowen, A. J. 1976 J. Mar. Res. 34, 269293.
Guza, R. T. & Davis, R. E. 1974 J. Geophys. Res. 79, 12851291.
Guza, R. T. & Inman, D. 1975 J. Geophys. Res. 80, 29973011.
Hanson, E. T. 1926 Proc. Roy. Soc. A 111, 491529.
Minzoni, A. A. 1976 J. Fluid Mech. 74, 369375.
Stoker, J. J. 1957 Water Waves. Interscience.
Whitham, G. B. 1976 J. Fluid Mech. 74, 353368.
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