Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-21T19:33:53.923Z Has data issue: false hasContentIssue false
  • English
  • Français

Deep-water plunging breakers: a comparison between potential theory and experiments

Published online by Cambridge University Press:  21 April 2006

Douglas G. Dommermuth ,
Dick K. P. Yue ,
W. M. Lin ,
R. J. Rapp ,
E. S. Chan  and
W. K. Melville
Douglas G. Dommermuth
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K. P. Yue
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
W. M. Lin
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
R. J. Rapp
Affiliation:
Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
E. S. Chan
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
W. K. Melville
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The primary objective of this paper is to provide a detailed confirmation of the validity of potential-flow theory for describing steep gravity waves produced in an experimental tank. Very high-resolution computations are carried out which use a refined mixed Eulerian-Lagrangian solution scheme under the assumptions of potential flow. The numerical results for a plunging breaker produced by a programmed piston-type wavemaker are found to be in excellent agreement with tank measurements up to and including overturning. The calculated free-surface elevations are almost indistinguishable from measured profiles, even close to where the wave plunges. The horizontal and vertical water-particle velocities measured with a laser anemometer throughout the water depth at two longitudinal stations are also well predicted by the theory. In contrast to the fully nonlinear theory, predictions based on linearized theory become poorer as the wave packet moves down the tank. To allow other investigators to evaluate the computations and experiments, the Fourier amplitudes and phases which completely specify the time history of the wavemaker's velocity are given in Appendix B.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 189 , April 1988 , pp. 423 - 442
Copyright
© 1988 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

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
Chan, E. S. 1985 Deep water breaking wave forces on structures. Sc.D. dissertation, MIT, Dept. of Civil Engineering.
Dommermuth, D. G. & Yue, D. K. P. 1987 Numerical simulations of nonlinear axisymmetric flows with a free surface. J. Fluid Mech. 178, 195–219.Google Scholar
Fink, P. T. & Soh, W. K. 1974 Calculation of vortex sheets in unsteady flow and applications in ship hydrodynamics. In Proc. 10th Symp. Naval Hydro., Cambridge, MA (ed. R. D. Cooper & S. W. Doroff), pp. 463–491. Washington: Government Printing Office.
Greenhow, M. 1983 Free-surface flows related to breaking waves. J. Fluid Mech. 134, 259–275.Google Scholar
Greenhow, M., Vinje, T., Brevig, P. & Taylor, J. 1982 A theoretical and experimental study of the capsize of Salter's duck in extreme waves. J. Fluid Mech. 118, 221–239.Google Scholar
Kennard, E. H. 1949 Generation of surface waves by a moving partition. Q. Appl. Maths 7, 303–312.Google Scholar
Lin, W. M. 1984 Nonlinear motion of the free surface near a moving body. Ph.D. thesis, MIT, Dept. of Ocean Engineering.
Lin, W. M., Newman, J. N. & Yue, D. K. P. 1984 Nonlinear forced motions of floating bodies. In Proc. 15th Symp. on Naval Hydro., Hamburg, pp. 33–49. Washington: National Academy Press.
Longuet-Higgins, M. S. 1974 Breaking waves in deep or shallow water. In Proc. 10th Symp. Naval Hydro., Cambridge, MA (ed. R. D. Cooper & S. W. Doroff), pp. 597–605. Washington: Government Printing Office.
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
Melville, W. K. & Rapp, R. J. 1985 Momentum flux in breaking waves. Nature 317, 514–516.Google Scholar
New, A. 1983 A class of elliptical free-surface flows. J. Fluid Mech. 130, 219–239.Google Scholar
New, A. L., McIver, P. & Peregrine, D. H. 1985 Computations of overturning waves. J. Fluid Mech. 150, 233–251.Google Scholar
Rapp, R. J. 1986 Laboratory measurements of deep water breaking waves. Ph.D. thesis, MIT, Dept. of Ocean Engineering.
Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes' expansion for gravity waves. J. Fluid Mech. 62, 553–578.Google Scholar
Ursell, F., Dean, R. G. & Yu, Y. S. 1959 Forced small-amplitude water waves: a comparison of theory and experiment. J. Fluid Mech. 7, 33–52.Google Scholar
Vinje, T. & Brevig, P. 1981 Nonlinear ship motions. In Proc. 3rd Intl Conf. Num. Ship Hydro., Paris, pp. 257–268. Bassin d'Essais des Carénes, France.