Triple roots and cusped caustics for surface gravity waves

  • Ronald Smith
Part IV — Waves and Currents
Part of the Lecture Notes in Physics book series (LNP, volume 64)


For short waves which are travelling obliquely to a non-uniform current U(x) there is a critical frequency (or transverse wavenumber) such that at one line across the current there is a coalescence of three wavenumbers. The triple root is the one-dimensional counterpart of the group velocity paths' having an almost exact focus (or cusped caustic). Thus locally the wave amplitude is exceptionally large. Here an extension of a method due to Ludwig (1966) is used to obtain a uniformly valid solution for waves on an irrotational current when there is a cusped caustic. For triple roots a crucial role is played by terms not present in Ludwig's work. Detailed numerical results are presented for a situation which would appear to be amenable to laboratory experiments.


Dispersion Relation Wave Height Internal Wave Short Wave Maximum Wave Height 
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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Ronald Smith
    • 1
  1. 1.University of CambridgeEngland

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