Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier–Stokes equation. The numerical modeling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account such as a nonisotropic stress tensor concentrated near the interface. Results concerning the time evolution of liquid–gas interface and velocity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Breaking processes including overturning, splash-up and gas entrainment, and breaking induced vortex-like motion beneath the surface and energy dissipation, are presented and discussed. It is found that strong vorticities are generated during the breaking process, and that more than of the total pre-breaking wave energy is dissipated within three wave periods. The numerical results are compared with some laboratory measurements, and a favorable agreement is found.
REFERENCES
1.
W. K.
Melville
, “The role of surface-wave breaking in air-sea interaction
,” Annu. Rev. Fluid Mech.
28
, 279
(1996
).2.
M. L.
Banner
and W. K.
Melville
, “On the separation of air flow over water waves
,” J. Fluid Mech.
77
, 825
(1976
).3.
J. H.
Duncan
, “An experimental investigation of breaking waves produced by a towed hydrofoil
,” Proc. R. Soc. London, Ser. A
377
, 331
(1981
).4.
P.
Bonmarin
, “Geometric properties of deep-water breaking waves
,” J. Fluid Mech.
209
, 405
(1989
).5.
R. J.
Rapp
and W. K.
Melville
, “Laboratory measurements of deep-water breaking waves
,” Philos. Trans. R. Soc. London, Ser. A
331
, 735
(1990
).6.
M. S.
Longuet-Higgins
and E. D.
Cokelet
, “The deformation of steep surface waves on water. I. A numerical method for computation
,” Proc. R. Soc. London, Ser. A
358
, 1
(1976
).7.
M. S.
Longuet-Higgins
and E. D.
Cokelet
, “The deformation of steep surface waves on water. II. Growth of normal-mode instabilities
,” Proc. R. Soc. London, Ser. A
364
, 1
(1978
).8.
W. J.
Jillians
, “The superharmonic instability of Stokes waves in deep water
,” J. Fluid Mech.
204
, 563
(1989
).9.
D. H.
Peregrine
, “Breaking waves on beaches
,” Annu. Rev. Fluid Mech.
15
, 149
(1983
).10.
M. L.
Banner
and D. H.
Peregrine
, “Wave breaking in deep water
,” Annu. Rev. Fluid Mech.
25
, 373
(1993
).11.
D. G.
Dommermuth
, D. K. P.
Yue
, W. M.
Lin
, R. J.
Rapp
, E. S.
Chan
, and W. K.
Melville
, “Deep-water plunging breakers: A comparison between potential theory and experiments
,” J. Fluid Mech.
189
, 432
(1988
).12.
D.
Skyner
, “A comparison of numerical predictions and experimental measurements of the internal kinematics of a deep-water plunging wave
,” J. Fluid Mech.
315
, 51
(1996
).13.
M.
Perlin
, J-H.
He
, and L. P.
Bernal
, “An experimental study of deep water plunging breakers
,” Phys. Fluids
8
, 2365
(1996
).14.
J. J.
Monaghan
, P. J.
Bicknell
, and R. J.
Humble
, “Volcanos, tsunamis and the demise of the minoans
,” Physica D
77
, 217
(1994
).15.
C. W.
Hirt
and B. D.
Nichols
, “Volume of Fluid (VOF) method for the dynamics of free boundaries
,” J. Comput. Phys.
39
, 201
(1981
).16.
D. L. Youngs, “Time dependent multimaterial flow with large fluid distortion,” in Numerical Methods for Fluid Dynamics, edited by K. M. Morton and M. J. Baines (Academic, New York, 1982), p. 27.
17.
J. M.
Hyman
, “Numerical methods for tracking interfaces
,” Physica D
12
, 396
(1984
).18.
J. M.
Floryan
and H.
Rasmussen
, “Numerical methods for viscous flows with moving boundaries
,” Appl. Mech. Rev.
42
, 323
(1989
).19.
N.
Ashgriz
and J. Y.
Poo
, “FLAIR: Flux line-segment model for advection and interface reconstruction
,” J. Comput. Phys.
93
, 449
(1991
).20.
E. G.
Puckett
and J. S.
Saltzman
, “A 3d adaptive mesh refinement algorithm for interfacial gas dynamics
,” Physica D
60
, 84
(1992
).21.
B.
Lafaurie
, C.
Nardone
, R.
Scardovelli
, S.
Zaleski
, and G.
Zanetti
, “Modelling merging and fragmentation in multiphase flows with SURFER
,” J. Comput. Phys.
113
, 134
(1994
).22.
J.
Li
, “Calcul d’interface affine par morceaux (piecewise linear interface calculation)
,” C. R. Acad. Sci. Paris, Ser. IIb: Mec., Phys., Chim., Astron.
320
, 391
(1995
).23.
A. J.
Chorin
, “Numerical solution of the Navier–Stokes equation
,” Math. Comput.
22
, 745
(1968
).24.
W. H. Press and S. A. Teukolsky, “Multigrid methods for boundary value problems,” Comput. Phys. Sep/Oct, 514 (1991).
25.
H. Lamb, Hydrodynamics, 6th ed. (Cambridge University Press, Cambridge, 1932).
26.
D. H. Peregrine, E. D. Cokelet, and P. McIver, “The fluid mechanics of waves approaching breaking” Proceedings of the 17th Coastal Engineering Conference, Sidney, Australia, 1980, Vol. 1, p. 512.
27.
T.
Vinje
and P.
Brevig
, “Numerical simulation of breaking waves
,” Adv. Water Resour.
4
, 77
(1981
).28.
G. R.
Baker
, D. I.
Meiron
, and S. A.
Orszag
, “Generalized vortex methods for free-surface flow problems
,” J. Fluid Mech.
123
, 477
(1982
).29.
A. L.
New
, P.
McIver
, and D. H.
Peregrine
, “Computations of overturning waves
,” J. Fluid Mech.
150
, 233
(1985
).30.
M. Perlin (private communication, 1997).
31.
M. S.
Longuet-Higgins
, “Parametric solutions for breaking waves
,” J. Fluid Mech.
121
, 403
(1982
).32.
A. L.
New
, “A class of elliptical free-surface flows
,” J. Fluid Mech.
130
, 219
(1983
).33.
M.
Greenhow
, “Free-surface flows related to breaking waves
,” J. Fluid Mech.
134
, 259
(1983
).34.
F.
Dias
and E. O.
Tuck
, “A steady breaking wave
,” Phys. Fluids A
5
, 277
(1993
).35.
A. D.
Jenkins
, “A stationary potential-flow approximation for a breaking-wave crest
,” J. Fluid Mech.
280
, 335
(1994
).36.
T. S.
Lundgren
and N. N.
Mansour
, “Oscillations of drops in zero gravity with weak viscous effects
,” J. Fluid Mech.
194
, 479
(1988
).37.
M. S.
Longuet-Higgins
, “Theory of weakly damped Stokes waves: a new formulation and its physical interpretation
,” J. Fluid Mech.
235
, 319
(1992
).38.
E.
Lamarre
and W. K.
Melville
, “Air entrainment and dissipation in breaking waves
,” Nature (London)
351
, 469
(1991
).39.
H. Yeh, “Vorticity generation at a fluid interface,” Proceedings of the IUTAM Symposium on Breaking Waves, edited by M. L. Banner and R. H. J. Grimshaw (Springer-Verlag, Berlin, 1991), p. 257.
40.
M. S.
Longuet-Higgins
, “Capillary rollers and bores
,” J. Fluid Mech.
240
, 659
(1992
).41.
W. K.
Melville
and R. J.
Rapp
, “Momentum flux in breaking waves
,” Nature (London)
317
, 514
(1985
).
This content is only available via PDF.
© 1999 American Institute of Physics.
1999
American Institute of Physics
You do not currently have access to this content.
