Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-07T09:45:54.614Z Has data issue: false hasContentIssue false
  • English
  • Français

Parametric solutions for breaking waves

Published online by Cambridge University Press:  20 April 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, England, and Institute of Oceanographic Sciences, Wormley, Surrey
Get access Rights & Permissions [Opens in a new window]

Abstract

Time-dependent flows such as occur in breaking surface waves are often most con- veniently described in parametric form, with the coordinate z and velocity potential χ each expressed in terms of a third complex variable ω and the time t.

In this paper we discuss some interesting flows given in terms of elementary functions of ω and t. Included are the Stokes 120° corner flow, the 45° rotor or rotating wedge, and a decelerated upwelling flow, with an exactly plane surface.

Lastly it is shown that a class of cubic flows, which are related to the plane upwelling flow just mentioned, has a free surface that corresponds with remarkable accuracy to the forward face of an overturning, or plunging, breaker.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 403 - 424
Copyright
© 1982 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

John, F. 1953 Two-dimensional potential flows with a free boundary. Communs Pure Appl. Math. 6, 497–503.Google Scholar
Longuet-Higgins, M. S. 1976 Self-similar, time-dependent flows with a free surface. J. Fluid Mech. 73, 603–620.Google Scholar
Longuet-Higgins, M. S. 1980a (Paper I) A technique for time-dependent, free-surface flows. Proc. R. Soc. Lond. A 371, 441–451.Google Scholar
Longuet-Higgins, M. S. 1980b (Paper III) On the forming of sharp corners at a free surface. Proc. R. Soc. Lond. A 371, 453–478.Google Scholar
Longuet-Higgins, M. S. 1981 (Paper III) On the overturning of gravity waves. Proc. R. Soc. Lond. A 376, 377–400.Google Scholar
Miller, R. L. 1957 Role of vortices in surf zone prediction, sedimentation and wave forces. In Beach and Nearshore Sedimentation (ed. R. A. Davis & R. L. Ethington), pp. 92–114. Tulsa, Oklahoma: Soc. of Economic Palaeontologists and Mineralogists.
New, A. L. 1981 Breaking waves in water of finite depth. British Theor. Mech. Colloq., Bradford, 6–9 April 1981 (abstract only).
Stokes, G. G. 1880 On the theory of oscillatory waves. Appendix B: Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Mathematical Physical Papers, vol. 1, pp. 225–228. Cambridge University Press.
Vinje, T. & Brevig, P. 1981 Breaking waves on finite water depths: a numerical study. Ship Res. Inst. of Norway, Rep. R-111.81.Google Scholar