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    Mok, K. M. and Yeh, Harry 1999. Mass Transport of Progressive Edge Waves : A Comparison between the Full and Shallow-Water Wave Theories. p. 443.
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    Yeh, Harry H. 1992. Shoreline Profile of Stokes‐Mode Edge Waves. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 118, Issue. 1, p. 112.
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Nonlinear effects in edge waves

  • G. B. Whitham (a1)
Abstract

Nonlinear corrections to Stokes's linear edge-wave solution are obtained by means of perturbation expansions in the amplitude. The shallow-water formulation is considered first, but even for small beach angles β the behaviour in the deep water offshore becomes important and this formulation is limited. In the full formulation, amplitude dependence is required in the dispersion relation and in the exponents for the exponential decay away from the shore. There is a non-uniformity in the results as β → ½π, which is corrected by a special perturbation expansion.

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© 1976 Cambridge University Press
References
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Guza, R. T. & Davis, R. E. 1974 J. Geophys. Res. 79, 1285–810.
Hanson, E. T. 1926 Proc. Roy. Soc A 111, 491–529.
Munk, W., Snodgrass, F. & Carrier, G. F. 1956 Science, 123, 127–810.
Ostrowskii, L. A. 1967 Sov. Phys., J. Exp. Theor. Phys. 24, 797–810.
Ostrowskii, L. A. 1968 U.R.S.I. Symp. on Electromagnetic Waves VI, Stresa, Italy.
Stoker, J. J. 1957 Water Waves. Interscience.
Stokes, G. G. 1846 Report on recent researches in hydrodynamics. Brit. Ass. Rep. (See also Papers, vol. 1, p. 167. Cambridge University Press.)
Ursell, F. 1952 Proc. Roy. Soc A 214, 79–97.
Whitham, G. B. 1974 Linear and Nonlinear Waves. Interscience.
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Journal of Fluid Mechanics
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