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Nonlinear effects in edge waves

Published online by Cambridge University Press:  29 March 2006

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


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.

Research Article
© 1976 Cambridge University Press

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