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Finite amplitude effects in free and forced edge waves

Published online by Cambridge University Press:  24 October 2008

Nicole Rockliff
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Extract

The effect of non-linearity on standing edge waves is studied on the basis of shallow water theory. Four problems are considered: the decay of free edge waves and the forcing of edge waves by an incident wave of double the frequency, a synchronous incident wave and by a side-wall wavemaker. Hysteresis effects are predicted for all types of forcing.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Abramowitz, M. and Stegun, I.Handbook of mathematical functions (New York: Dover, 1965).Google Scholar
(2)Bowen, A. J.Rip currents, 1. Theoretical investigations. J. Geophys. Res. 74 (1969), 54675478.CrossRefGoogle Scholar
(3)Bowen, A. J. and Inman, D. L.Rip currents, 2. Laboratory and field observations. J. Oeophys. Res. 74 (1969), 54795490.CrossRefGoogle Scholar
(4)Bowen, A. J. and Inman, D. L.Edge waves and crescentic bars. J. Oeophys. Res. 76 (1971), 86628671.CrossRefGoogle Scholar
(5)Cole, J. D.Perturbation methods in applied mathematics (Waltham, Mass.: Blaisdell, 1968).Google Scholar
(6)Eckart, C.Surface waves on water of variable depth. Wave Rep. 100 (Scripps Inst. of Oceanography, University of California, La Jolla, 1951).Google Scholar
(7)Galvin, C. J.Resonant edge waves on laboratory beaches. Eos Trans. AGU 46 (1965), 122.Google Scholar
(8)Greenspan, H.The generation of edge waves by moving pressure distributions. J. Fluid Mech. 1 (1956), 574592.CrossRefGoogle Scholar
(9)Guza, R. T. & Bowen, A. J.Finite amplitude edge waves. J. Mar. Res. 34 (1976), 269293.Google Scholar
(10)Guza, R. T. & Davis, R. E.Excitation of edge waves by waves incident on a beach. J. Geophys. Res. 79 (1974), 12851291.CrossRefGoogle Scholar
(11)Guza, R. T. and Inman, D. L.Edge waves and beach cusps. J. Geophys. Res. 80 (1975), 29973011.CrossRefGoogle Scholar
(12)Lamb, H.Hydrodynamics, 6th edition (Cambridge: Cambridge University Press, 1932).Google Scholar
(13)Minzoni, A. A. and Whitham, G. B.On the excitation of edge waves on beaches. J. Fluid Mech. 79 (1977), 273287.CrossRefGoogle Scholar
(14)Munk, W., Snodgrass, F. and Carrier, G. F.Edge waves on the continental shelf. Science 123 (1956), 127132.CrossRefGoogle ScholarPubMed
(15)Nayfeh, A. H.Perturbation methods (New York: Wiley, 1973).Google Scholar
(16)Reid, R. O.Effect of Coriolis force on edge waves, (i) Investigation of the normal modes. J. Mar. Res. 16 (1958), 109144.Google Scholar
(17)Stokes, G. G.Report on recent researches in hydrodynamics. Rep. Brit.Assoc. (1846), 120.Google Scholar
(18)Ursell, F.Trapping modes in the theory of surface waves. Proc. Cambridge Philos. Soc. 47 (1951), 347358.CrossRefGoogle Scholar
(19)Ursell, F.Edge waves on a sloping beach. Proc. Roy. Soc. A 214 (1952), 7997.Google Scholar