Comptes Rendus
Fully three-dimensional direct numerical simulation of a plunging breaker
Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 495-501.

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier–Stokes equations in air and water. The interface tracking is achieved by a Lax–Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed.

Une étude du déferlement tridimensionelle est présentée sur la base de résultats obtenus par simulation numérique directe des équations de Navier–Stokes diphasiques. Le suivi de l'interface est réalisé par l'utilisation du schéma TVD Lax–Wendroff (Total Variation Diminishing) qui permet de gérer les reconnexions de l'interface. Le déferlement est obtenu à partir de l'initialisation dans un domaine semi-périodique d'une onde sinusoidale instable. Après présentation des équations et des méthodes numériques employées, une comparaison est effectuée entre deux simulations tridimensionelles et une discussion est menée quant à la nécessité d'utiliser une perturbation afin de destabiliser la symétrie du calcul. Les résultats obtenus sont alors commentés.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-0721(03)00108-6
Keywords: Fluid mechanics, Navier–Stokes, Plunging breaker, Numerical simulation
Mot clés : Mécanique des fluides, Navier–Stokes, Déferlement plongeant, Simulation numérique

Pierre Lubin 1; Stéphane Vincent 1; Jean-Paul Caltagirone 1; Stéphane Abadie 2

1 Modélisation avancée des systèmes thermiques et écoulements réels (MASTER), ENSCPB – Université Bordeaux 1, 16, avenue Pey-Berland, 33607 Pessac cedex, France
2 Laboratoire des sciences appliquées au génie civil (LaSAGeC), ISA du BTP – Université de Pau et des Pays de l'Adour, 1, allée du Parc Montaury, 64600 Anglet, France
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Pierre Lubin; Stéphane Vincent; Jean-Paul Caltagirone; Stéphane Abadie. Fully three-dimensional direct numerical simulation of a plunging breaker. Comptes Rendus. Mécanique, Volume 331 (2003) no. 7, pp. 495-501. doi : 10.1016/S1631-0721(03)00108-6. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(03)00108-6/

[1] D.H. Peregrine Breaking waves on beaches, Ann. Rev. Fluid Mech., Volume 15 (1983), pp. 149-178

[2] E.D. Christensen; D.J. Walstra; N. Emarat Vertical variation of the flow across the surf zone, Coastal Eng., Volume 45 (2002), pp. 169-198

[3] S. Vincent; J.P. Caltagirone Efficient solving method for unsteady incompressible interfacial flow problems, Int. J. Numer. Meth. Fluids, Volume 30 (1999), pp. 795-811

[4] S. Vincent; J.P. Caltagirone A one cell local multigrid method for solving unsteady incompressible multi-phase flows, J. Comput. Phys., Volume 163 (2000), pp. 172-215

[5] J.U. Brackbill; B.D. Kothe; C. Zemach A continuum method for modeling surface tension, J. Comput. Phys., Volume 100 (1992), pp. 335-354

[6] S. Abadie; J.-P. Caltagirone; P. Watremez Mécanisme de génération du jet secondaire ascendant dans un déferlement plongeant, C. R. Acad. Sci. Paris, Sér. IIb, Volume 326 (1998), pp. 553-559

[7] P. Lubin, S. Vincent, J.-P. Caltagirone, S. Abadie, Fully three-dimensional direct numerical simulation of plunging breaking waves, in: Coastal Engineering 2003, 6th International Conference on Computer Modelling and Experimental Measurements of Seas and Coastal Regions, Cadiz, Spain, 2003, accepted

[8] T. Vinje; P. Brevig Numerical simulation of breaking waves, J. Adv. Water Resource, Volume 4 (1981), pp. 77-82

[9] G. Chen; C. Kharif; S. Zaleski; J. Li Two-dimensional Navier–Stokes simulation of breaking waves, Phys. Fluid, Volume 11 (1999), pp. 121-133

[10] S. Abadie Numerical modelling of the flow generated by plunging breakers, Proceedings Coastal Dynamics, Lund, Sweden, 2001, pp. 202-211

[11] P. Bonmarin Geometric propertries or deep-water breaking waves, J. Fluid Mech., Volume 209 (1989), pp. 405-433

[12] R.L. Miller Role of vortices in surf zone prediction: sedimentation and wave forces, Soc. Econ. Paleontol. Mineral. Spec. Publ., Volume 24 (1976), pp. 92-114

[13] T. Sakai; T. Mizutani; H. Tanaka; Y. Tada Vortex formation in plunging breaker, Proc. of the 20th ICCE, 1986, pp. 711-723

[14] Y. Watanabe; H. Saeki Three-dimensional large eddy simulation of breaking waves, Coastal Eng. J. Japan, Volume 3–4 (1999), pp. 281-301

[15] E.D. Christensen; R. Deigaard Large eddy simulation of breaking waves, Coastal Eng., Volume 42 (2001), pp. 53-86

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