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    Shillington, F. A. and Brundrit, G. B. 1986. Energy flux of edge waves travelling along a continental shelf. Geophysical & Astrophysical Fluid Dynamics, Vol. 37, Issue. 3, p. 219.

    Yeh, Harry H. 1985. Nonlinear progressive edge waves: their instability and evolution. Journal of Fluid Mechanics, Vol. 152, Issue. -1, p. 479.

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Nonlinear effects in edge waves

  • G. B. Whitham (a1)
  • DOI:
  • Published online: 01 March 2006

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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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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