Advertisement

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)

Abstract

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.

Keywords

Dispersion Relation Wave Height Internal Wave Short Wave Maximum Wave Height 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berkhoff, J.C.W., 1973. Proc. 13th Coastal Eng. Conf. Vancouver. 1: 471–490.Google Scholar
  2. Buchwald, V.T., and J.K. Adams, 1968. Proc. Roy. Soc. Ser.A. 305: 235–250.Google Scholar
  3. Gargett, A.E., and B.A. Hughes, 1972. J. Fluid Mech. 52: 179–191.Google Scholar
  4. Hughes, B.A. 1976. J. Fluid Mech. 74: 667–683.Google Scholar
  5. Longuet-Higgins, M.S., and R.W. Stewart, 1961. J. Fluid Mech. 10: 529–549.Google Scholar
  6. Ludwig, D., 1966. Comm. Pure Appl. Math. 19: 215–250.Google Scholar
  7. McKee, W.D., 1974. Proc. Camb. Phil. Soc. 75: 295–302.Google Scholar
  8. Pearcey, T., 1946. Phil. Mag. 37: 311–317.Google Scholar
  9. Peregrine, D.H., and R. Smith, 1975. Math. Proc. Camb. Phil. Soc. 77: 415–434.Google Scholar
  10. Smith, R., 1975. Math. Proc. Camb. Phil. Soc. 78: 517–525.Google Scholar
  11. Smith, R., and T. Sprinks, 1975. J. Fluid Mech. 72: 373–385.Google Scholar
  12. Stoker, J.J., 1957. Water Waves. Interscience, New York.Google Scholar
  13. Thom, R., 1975 Structural Stability and Morphogenesis. Benjamin, Reading, Massachusetts.Google Scholar
  14. Ursell, F., 1972. Proc. Camb. Phil. Soc. 72: 49–65.Google Scholar
  15. Whalin, R.W., 1973. Proc. 13th Coastal Eng. Conf. Vancouver. 1: 451–470.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

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

Personalised recommendations