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    Ionescu-Kruse, Delia 2015. An Exact Solution for Geophysical Edge Waves in the $${\beta}$$ β -Plane Approximation. Journal of Mathematical Fluid Mechanics, Vol. 17, Issue. 4, p. 699.


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    Ionescu-Kruse, Delia 2014. Instability of edge waves along a sloping beach. Journal of Differential Equations, Vol. 256, Issue. 12, p. 3999.


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    Ehrnström, Mats Escher, Joachim and Matioc, Bogdan-Vasile 2009. Two-dimensional steady edge waves. Part I: Periodic waves. Wave Motion, Vol. 46, Issue. 6, p. 363.


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Nonlinear effects in edge waves

  • G. B. Whitham (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112076001833
  • Published online: 01 March 2006
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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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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