Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-19T17:11:39.082Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear gravity–capillary surface waves in a slowly varying current

Published online by Cambridge University Press:  29 March 2006

Dennis Holliday
Dennis Holliday
Affiliation:
R & D Associates, P.O. Box 3580, Santa Monica, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation of nonlinear gravity–capillary surface waves in a deep slowly varying current is investigated using the conservation equations in the eikonal approximation. Graphical comparisons are made between solutions of the wave- slope and wavenumber equations for infinitesimal waves and finite amplitude waves. Finite amplitude effects are shown to be weaker for small amplitude capillary waves than for gravity waves. The ‘wave barrier’ noted by Gargett & Hughes (1972) for infinitesimal gravity waves on a slowly varying current is seen to be removed by finite amplitude effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 4 , 6 March 1973 , pp. 797 - 802
Copyright
© 1973 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Crapper, G. D. 1972 J. Fluid Mech. 52, 713.
Defant, A. 1960 Physical Oceanography, vol. 11. Pergamon.
Gargett, A. E. & Hughes, B. A. 1972 J. Fluid Mech. 52, 179.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Landau, L. D. & Lifschitz, E. M. 1959 Fluid Mechanics. Pergamon.
Lighthill, M. J. 1967 Proc. Roy. Soc. A 299, 28.
Longuet-Higgins, M. S. & Stewart, R. W. 1961 J. Fluid Mech. 10, 529.
Rayleigh, Lord 1877 Proc. Lond. Math. Soc. 9, 21.
Reynolds, O. 1877 Nature, 16, 343.
Wehausen, J. W. & Laitone, E. V. 1960 Surface waves. Handbuch der Physik, vol. 9, Fluid Mechanics, 111. Springer.
Whitham, G. B. 1962 J. Fluid Mech. 12, 135.
Whitham, G. B. 1965a Proc. Roy. Soc. A 283, 238.
Whitham, G. B. 1965b J. Fluid Mech. 22, 273.