Pierre Lubin, Stéphane Glockner, Olivier Kimmoun, Hubert Branger


Numerical simulation of spilling breaking waves is still a very challenging aim to achieve since small interface
deformations, air entrainment and vorticity generation are involved during the early stage of the breaking of the wave.
High mesh grid resolutions and appropriate numerical methods are required to capture accurately the length scales of
the complex mechanisms responsible for the start of the breaking (small plunging jet, white foam, etc.). Numerical
works usually showed better agreements when simulating plunging breaking waves than the spilling case compared
with available experimental data. Kimmoun and Branger (2007) recently experimented surf-zone breaking waves.
Detailed pictures showed a short spilling event occurred at the crest of the waves, before degenerating into strong
plunging breaker. This work is devoted to the qualitative comparison of our numerical results with the experimental
observations, as we will focus on capturing and describing the spilling phase experimented.


breaking waves; Navier-Stokes; numerical simulations; Large Eddy Simulation

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Battjes, A. 1988. Surf-zone dynamics. Ann. Rev. Fluid Mech., 20, 257-293.

Bonmarin, P. 1989. Geometric properties of deep-water breaking waves, J. Fluid Mech., 209, 405-433.

Christensen, E. D., D. J. Walstra, and N. Emarat. 2002. Vertical variation of the flow across the surf zone, Coastal Engineering, 45, 169-198.

Christensen, E. D. 2006. Large eddy simulation of spilling and plunging breakers, Coastal Engineering, 53, 463- 485.

Deane, G. B., and M. D. Stokes. 2002. Scale dependence of bubble creation mechanisms in breaking waves, Nature, 418, 839-844.

Duncan, J. H., 2001. Spilling breakers, Annu. Rev. Fluid Mech., 33, 519-547.

Fenton, J. D. 1985. A fifth-order Stokes theory for steady waves. Journal of Waterway, Port, Coastal and Ocean Engineering, 111, 216-234.

Helluy, P., F. Gollay, S. T. Grilli, N. Seguin, P. Lubin, J.-P. Caltagirone, S. Vincent, D. Drevard, and R.

Marcer. 2005. Numerical simulations of wave breaking. Mathematical Modelling and Numerical Analysis Mathematical Modelling and Numerical Analysis, 39 (3), 591-608.

Kimmoun O., H. Branger, and B. Zucchini. 2004. Laboratory PIV measurements of wave breaking on a beach. Proceedings of 14th International Offshore and Polar Engineering Conference, 3, 293-298.

Kimmoun K. and H. Branger. 2007. A PIV investigation on laboratory surf-zone breaking waves over a sloping beach, J. Fluid Mech, 588, 353-397.

LeVeque, R. J. 1992. Numerical methods for conservation laws, Lectures in Mathematics, Birkhauser, Zurich.

Lin, P., and P. L.-F. Liu. 1999a. Free surface tracking methods and their applications to wave hydrodynamics, Vol. 5 of Advances in Coastal and Ocean Eng., World Scientific, 213-240.

Lin, P., and P. L.-F. Liu. 1999b. Internal wave-maker for Navier-Stokes equations models, Journal of Waterway, Port, Coastal and Ocean Engineering, 125, 322-330.

Lubin, P. 2004. Large eddy simulation of plunging breaking waves, PhD thesis (in English), University of Bordeaux.

Lubin, P., H. Branger, and O. Kimmoun. 2006a. Large eddy simulation of regular waves breaking over a sloping beach, Proceedings of 30th International Conference on Coastal Engineering, ASCE, 238-250.

Lubin, P., S. Vincent, S. Abadie and J.-P. Caltagirone. 2006b. Three-dimensional Large Eddy Simulation of air entrainment under plunging breaking waves, Coastal Engineering, 53, 631-655.

Lubin, P., S. Glockner, and H. Chanson. 2010a. Numerical simulation of a weak breaking tidal bore, Mechanics Research Communications, 37, 119-121.

Lubin, P., H. Chanson, and S. Glockner. 2010b. Large Eddy Simulation of turbulence generated by a weak breaking tidal bore, Environmental Fluid Mechanics, 10, 587-602.

Lubin, P., and J.-P. Caltagirone. 2010. Large eddy simulation of the hydrodynamics generated by breaking waves, in: Q. Ma (Ed.), Advances in numerical simulation of nonlinear water waves, Vol. 11 of Advances in Coastal and Ocean Engineering, World Scientific Publishing Company, Ch. 16, 575–604.

Miller, R. L. 1976. Role of vortices in surf zone prediction: sedimentation and wave forces, Soc. Econ. Paleontol. Mineral. Spec. Publ., 24, Ed. R. A. Davis, R. L. Ethington, 92-114.

Peregrine, D. H. 1983. Breaking waves on beaches, Ann. Rev. Fluid Mech., 15, 149-178.

Rudman, M. 1998. A volume-tracking method for incompressible multifluid flows with large density variations, Int. J. Numer. Meth. Fluids, 28, 357–378.<357::AID-FLD750>3.0.CO;2-D

Sagaut, P. 1998. Large eddy simulation for Incompressible Flows, Springer, Verlag.

Sakaï, T., T. Mizutani, H. Tanaka and Y. Tada. 1986. Vortex formation in plunging breaker, Proceedings of 20th International Conference on Coastal Engineering, ASCE, 711-723.

Vincent, S., J.-P. Caltagirone, P. Lubin and T. N. Randrianarivelo. 2003. An adaptative augmented Lagrangian method for three-dimensional multi-material flows, Computers and Fluids, 33, 1273-1289.

Watanabe, Y., H. Saeki and R. J. Hosking. 2005. Three-dimensional vortex structures under breaking waves, J. Fluid Mech., 545, 291-328.