Journal of Fluid Mechanics

Nonlinear effects in edge waves

G. B.  Whitham a1
a1 Applied Mathematics, California Institute of Technology, Pasadena

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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 [rightward arrow] [fraction one-half]π, which is corrected by a special perturbation expansion.

(Published Online March 29 2006)
(Received September 2 1975)