A RANS model for spilling breaking waves is developed, which can be implemented with ship hydrodynamics RANS CFD codes. The model is based on the Cointe & Tulin theory of steady breakers. The breaker cross section is assumed triangular with maximum height determined by the theoretical/experimental linear relationship with following wave height. Pressure and velocity boundary conditions are imposed on the dividing streamline between the breaker and underlying flow based on the hydrostatic and mixing layer models. An iterative solution procedure provides a unique solution for specified breaking criteria and simulation conditions. The model is implemented using CFDSHIP-IOWA and validated using spilling breaking wave benchmark data for two-dimensional submerged hydrofoils. As with other current RANS codes, wave elevations are under-predicted. However, for the first time in literature, the breaking wave wake is predicted. Results for total head, mean velocities, and Reynolds stresses are in agreement with available spilling breaking wave benchmark data.

1.
Baba
,
E.
,
1969
, “
A New Component of Viscous Resistance
,”
J. of Soc. Naval Archi. Japan
,
125
, pp.
23
34
.
2.
Longuet-Higgins, M. S., 1996, “Progress toward Understanding How Waves Break,” Proc. 21st Sympo. on Naval Hydro., Trondheim, Norway.
3.
Tulin, M. P., and Landrini, M., 2000, “Breaking Waves in the Ocean and around Ships,” Proc. 23rd Sympo. on Naval Hydro., Val de Reuil, France.
4.
Cointe
,
R.
, and
Tulin
,
M. P.
,
1994
, “
A Theory of Steady Breakers
,”
J. Fluid Mech.
,
276
, pp.
1
20
.
5.
Duncan
,
J. H.
,
1983
, “
The Breaking and Non-breaking Wave Resistance of a Two-dimensional Hydrofoil
,”
J. Fluid Mech.
,
126
, pp.
507
520
.
6.
Mori
,
K.-H.
,
1986
, “
Sub-breaking Waves and Critical Condition for Their Appearance
,”
J. of Soc. Naval Archi. Japan
,
159
(
23
), pp.
1
8
.
7.
Duncan
,
J. H.
,
1981
, “
An Experimental Investigation of Breaking Waves Produced by a Towed Hydrofoil
,”
Proc. R. Soc. London, Ser. A
,
377
, pp.
331
348
.
8.
Battjes
,
J. A.
, and
Sakai
,
T.
,
1981
, “
Velocity Field in a Steady Breaker
,”
J. Fluid Mech.
,
111
, pp.
421
437
.
9.
Duncan
,
J. H.
,
Philomin
,
V.
,
Behres
,
M.
, and
Kimmel
,
J.
,
1994
, “
The Formation of Spilling Breaking Water Waves
,”
Phys. Fluids
,
6
, pp.
2558
2560
.
10.
Longuet-Higgins
,
M. S.
,
1994
, “
Shear Instability in Spilling Breakers
,”
Proc. R. Soc. London, Ser. A
,
446
, pp.
399
409
.
11.
Lin
,
J. C.
, and
Rockwell
,
D.
,
1995
, “
Evolution of a Quasi-steady Breaking Wave
,”
J. Fluid Mech.
,
302
, pp.
29
44
.
12.
Miller, M., Nennstiel, T., Fiaklowski, L., Pro¨stler, S., Duncan, J., and Dimas, A., 1998, “Incipient Breaking of Steady Waves,” Proc. 22nd Sympo. on Naval Hydro., Washington, D.C.
13.
Iafrati, A., Olivieri, F., Pistani, E., and Campana, E., 2000, “Numerical and Experimental Study of the Wave Breaking Generated by a Submerged Hydrofoil,” Proc. 23rd Sympo. on Naval Hydro., Val de Reuil, France.
14.
Coakley, D. B., 1997, Surface Shape of Laboratory Generated Steady Breaking Waves, Ph.D. thesis, University of Maryland, College Park, MD.
15.
Chang
,
K.-A.
, and
Liu
,
P. L.-F.
,
1998
, “
Velocity, Acceleration and Vorticity under a Breaking Wave
,”
Phys. Fluids
,
10
, pp.
327
329
.
16.
Walker
,
D. T.
,
Lyzenga
,
D. R.
,
Ericson
,
E. A.
, and
Lund
,
D. E.
,
1996
, “
Radar Backscatter and Surface Roughness Measurements for Stationary Breaking Waves
,”
Proc. R. Soc. London, Ser. A
,
452
, pp.
1953
1984
.
17.
Coakley
,
D. B.
,
Haldeman
,
P. M.
,
Morgan
,
D. G.
,
Nicolas
,
K. R.
,
Penndorf
,
D. R.
,
Wetzel
,
L. B.
, and
Weller
,
C. S.
,
2001
, “
Electromagnetic Scattering from Large Steady Breaking Waves
,”
Exp. Fluids
,
30
(
5
), pp.
479
487
.
18.
Coleman, R. M., 1986, “Nonlinear Calculation of Breaking and Non-breaking Waves behind a Two-dimensional Hydrofoil,” Proc. 16th Sympo. on Naval Hydro., Berkeley, CA.
19.
Sadovnikov, D., and Trincas, G., 1998, “Nonlinear Simulation of Breaking Waves with Spilling Breakers by a Boundary Integral Method,” Proc. 22nd Sympo. on Naval Hydro., Washington, D.C.
20.
Longuet-Higgins
,
M. S.
, and
Cokelet
,
E. D.
,
1976
, “
The Deformation of Steep Surface Waves on Water. I. A Numerical Method for Computation
,”
Proc. R. Soc. London, Ser. A
,
358
, pp.
1
26
.
21.
Liou, B., Martinelli, L., Baker, T., and Jameson, A., 1998, “Calculation of Plunging Breakers with a Fully-implicit Adaptive-grid method,” 29th AIAA Fluid Dynamics Conf., AIAA-98-2968.
22.
Mori, K.-H., and Shin, M.-S., 1988, “Sub-breaking Wave: Its Characteristics, Appearing Condition and Numerical Simulation,” Proc. 17th Sympo. on Naval Hydro., The Hague, The Netherlands.
23.
Lungu, A., Raad, P. E., and Mori, K.-H., 1997, “Turbulent Early-stage Breaking Wave Simulation,” ASME FED Summer Meeting, ASME FEDSM97-3404.
24.
Lemos, C.M., 1992, Wave Breaking: A Numerical Study, Springer-Verlag.
25.
Lin
,
P.
, and
Liu
,
P. L.-F.
,
1998
, “
A Numerical Study of Breaking Waves in the Surf Zone
,”
J. Fluid Mech.
,
359
, pp.
239
264
.
26.
Chen
,
G.
,
Kharif
,
C.
,
Zaleski
,
S.
, and
Li
,
J.
,
1999
, “
Two-dimensional Navier-Stokes Simulation of Breaking Waves
,”
Phys. Fluids
,
11
, pp.
121
133
.
27.
Azcueta, R., Muzaferija, S., Peric, M., and Yoo, S.-D. 1999, “Computation of Flows around Hydrofoils under the Free Surface,” Proc. 7th Int. Conf. on Num. Ship Hydro., Nantes, France.
28.
Vogt, M., and Larsson, L., 1999 “Level Set Methods for Predicting Viscous Free Surface Flows,” Proc. 7th Int. Conf. on Num. Ship Hydro., Nantes, France.
29.
Miyata
,
H.
,
Kanai
,
A.
,
Kawamura
,
T.
, and
Park
,
J.-C.
,
1996
, “
Numerical Simulation of Three-dimensional Breaking Waves
,”
J. of Marine Sci. and Tech.
,
1
, pp.
183
197
.
30.
Celik
,
I.
, and
Rodi
,
W.
,
1984
, “
Simulation of Free-Surface Effects in Turbulent Channel Flows
,”
Physicochemical Hydrodynamics
,
5
, pp.
217
226
.
31.
Walker, D. T., 2000, “Reynolds-Averaged Models of High Froude Number Free-Surface Jets,” Proc. 23rd Sympo. on Naval Hydro., Val de Reuil, France.
32.
Sreedhar
,
M. K.
, and
Stern
,
F.
,
1998
, “
Non-linear Eddy-viscosity Turbulence Model for Solid/Free-surface Juncture Boundary Layer and Wake
,”
ASME J. Fluids Eng.
,
120
, pp.
354
362
.
33.
Craig
,
P. D.
, and
Banner
,
M. L.
,
1994
, “
Modeling Wave-enhanced Turbulence in the Ocean Surface Layer
,”
J. of Physical Oceanography
,
24
, pp.
2546
2559
.
34.
Melville, W. K., Veron, F., and White, C. J., 2001, “The velocity field under breaking waves: coherent structures and turbulence,” J. Fluid Mech., in press.
35.
Banner
,
M. L.
, and
Peregrine
,
D. H.
,
1993
, “
Wave Breaking in Deep Water
,”
Annu. Rev. Fluid Mech.
,
25
, pp.
373
397
.
36.
Melville
,
W. K.
,
1996
, “
The Role of Surface-wave Breaking in Air-sea Interaction
,”
Annu. Rev. Fluid Mech.
,
28
, pp.
279
321
.
37.
Stern
,
F.
,
Hwang
,
W. S.
, and
Jaw
,
S. Y.
,
1989
, “
Effects of Waves on the Boundary Layer of a Surface-Piercing Flat Plate: Experiment and Theory
,”
J. of Ship Research
,
33
(
1
), Mar, pp.
63
80
.
38.
Nadaoka, K., Ono, O., and Kurihara, H., 1997, “Analysis of Near-crest Pressure Gradient of Irregular Water Waves,” Proc. 7th Int. Offshore and Polar Eng. Conf., Honolulu, HI.
39.
Paterson, E. G., Wilson, R. V., and Stern, F., 1998, “Verification/Validation of Steady Flow RANS CFD for Naval Combatant,” Proc. 1st Marine CFD Applications Symposium, Washington, D.C.
40.
Wilson, R. V., Paterson, E. G., and Stern, F., 1998 “Unsteady RANS CFD Method for Naval Combatants in Waves,” Proc. 22nd Sympo. On Naval Hydro., Washington, DC.
41.
Wilson, R. V., Paterson, E. G., and Stern, F., 2000, “Verification and Validation for RANS Simulation of a Naval Combatant,” Proc. Gothenburg 2000: A Workshop on Numerical Ship Hydrodynamics, Gothenburg, Sweden.
42.
Iowa Institute of Hydraulic Research, 2001, “http://www.iihr.uiowa.edu/∼cfdship/cfdship-iowa.htm.”
43.
Larsson, L., Stern, F., and Bertram, V., ed., 2000, Proc. Gothenburg 2000: A Workshop on Numerical Ship Hydrodynamics, Chalmers Univ. of Technology, Gothenburg, Sweden.
44.
Menter
,
F. R.
,
1994
, “
Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications
,”
AIAA J.
,
32
, pp.
1598
1605
.
45.
Hino
,
T.
,
1988
, “
Numerical Computation of a Free Surface Flow around a Submerged Hydrofoil by the Euler/Navier-Stokes Equations
,”
J. of Soc. Naval Archi. Japan
,
164
, pp.
17
25
.
46.
Hino, T., 1997, “An Unstructured Grid Method fo Incompressible Viscous Flows with a Free Surface,” 35th Aerospace Sci. Meeting and Exhibit, AIAA-97-0862.
47.
Carrica
,
P. M.
,
Bonetto
,
F. J.
,
Drew
,
D. A.
, and
Lahey
, Jr.,
R. T.
,
1998
, “
The Interaction of Background Ocean Air Bubbles with a Surface Ship
,”
Int. J. Numer. Methods Fluids
,
28
, pp.
571
600
.
You do not currently have access to this content.