Hostname: page-component-76d6cb85b7-lcgwf Total loading time: 0 Render date: 2026-07-15T09:17:09.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Computations of overturning waves

Published online by Cambridge University Press:  20 April 2006

A. L. New ,
P. McIver  and
D. H. Peregrine
A. L. New
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, England Present address: Institute of Oceanographic Sciences, Crossway, Taunton, Somerset TA1 2DW, England.
P. McIver
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, England
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The numerical method of Longuet-Higgins & Cokelet (1976), for waves on deep water, is extended to account for a horizontal bottom contour, and used to investigate breaking waves in water of finite depth. It is demonstrated that a variety of overturning motions may be generated, ranging from the projection of a small-scale jet at the wave crest (of the type that might initiate a spilling breaker) to large-scale plunging breakers involving a significant portion of the wave. Although there seems to be a continuous transition between these wave types, a remarkable similarity is noticed in the overturning regions of many of the waves.

Three high-resolution computations are also discussed. The results are presented in the form of interrelated space-, velocity- and acceleration-plane plots which enable the time evolution of individual fluid particles to be followed. These computations should be found useful for the testing of analytical theories, and may also be applied, for example, to studies of slamming forces on shipping and coastal structures.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 150 , January 1985 , pp. 233 - 251
Copyright
© 1985 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.)

Article purchase

Temporarily unavailable

References

Baker G. R., Meiron, D. I. & Orszag S. A.1982 Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477–501.Google Scholar
Bowen A. J., Inman, D. L. & Simmons V. P.1968 Wave set-down and set-up. J. Geophys. Res. 73, 2569–2577.Google Scholar
Cokelet E. D.1977 Steep gravity waves in water of arbitrary uniform depth Phil. Trans. R. Soc. A 286, 183–230.Google Scholar
Cokelet E. D.1979 Breaking waves—the plunging jet and interior flow field. In Mechanics of Wave-Induced Forces on Cylinders (ed. T. L. Shaw), pp. 287–301. Pitman.
Galvin C. J.1968 Breaker type classification on three laboratory beaches. J. Geophys. Res. 73, 3651–3659Google Scholar
Greenhow M.1983 Free-surface flows related to breaking waves. J. Fluid Mech. 134, 259–275.Google Scholar
Isaacson M. De St Q.1982 Nonlinear-wave effects on fixed and floating bodies. J. Fluid Mech. 120, 267–281.Google Scholar
Longuet-Higgins M. S.1980 On the forming of sharp corners at a free surface Proc. R. Soc. Lond. A 371, 453–478.Google Scholar
Longuet-Higgins M. S.1982 Parametric solutions for breaking waves. J. Fluid Mech. 121, 403–424.Google Scholar
Longuet-Higgins, M. S. & Cokelet E. D.1976 The deformation of steep surface waves on water. I. A numerical method of computation Proc. R. Soc. Lond. A 350, 1–26.Google Scholar
Longuet-Higgins, M. S. & Cokelet E. D.1978 The deformation of steep surface waves on water. II. Growth of normal-mode instabilities Proc. R. Soc. Lond. A 364, 1–28.Google Scholar
Mciver, P. & Peregrine D. H.1981 Comparison of numerical and analytical results for waves that are starting to break. Proc. Intl Symp. on Hydrodynamics in Ocean Engineering, Trondheim, Norway, pp. 203–215.
New A. L.1983a On the breaking of water waves. Ph.D. thesis, University of Bristol.
New A. L.1983b A class of elliptical free-surface flows. J. Fluid Mech. 130, 219–239.Google Scholar
Peregrine D. H., Cokelet, E. D. & McIver P.1980 The fluid mechanics of waves approaching breaking. Proc. 17th Conf. Coastal Engineering, pp. 512–528. ASCE.
Riencker, M. M. & Fenton J. D.1981 A Fourier approximation method for steady water waves. J. Fluid Mech. 104, 119–137.Google Scholar
Vinje, T. & Brevig P.1981 Numerical calculations of forces from breaking waves. Proc. Intl Symp. on Hydrodynamics in Ocean Engineering, Trondheim, Norway, pp. 547–565.