**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30121

##### Turbulence Modeling and Wave-Current Interactions

**Authors:**
A.-C. Bennis,
F. Dumas,
F. Ardhuin,
B. Blanke

**Abstract:**

The mechanics of rip currents are complex, involving interactions between waves, currents, water levels and the bathymetry, that present particular challenges for numerical models. Here, the effects of a grid-spacing dependent horizontal mixing on the wave-current interactions are studied. Near the shore, wave rays diverge from channels towards bar crests because of refraction by topography and currents, in a way that depends on the rip current intensity which is itself modulated by the horizontal mixing. At low resolution with the grid-spacing dependent horizontal mixing, the wave motion is the same for both coupling modes because the wave deviation by the currents is weak. In high resolution case, however, classical results are found with the stabilizing effect of the flow by feedback of waves on currents. Lastly, wave-current interactions and the horizontal mixing strongly affect the intensity of the three-dimensional rip velocity.

**Keywords:**
Numerical modeling,
Rip currents,
Turbulence
modeling,
Wave-current interactions.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1099212

**References:**

[1] F. P. Shepard, “Undertow, rip tide or rip current,” Science, vol. 84, pp. 181–182, 1936.

[2] J. H. MacMahan, E. B. Thornton, and A. J. Reniers, “Rip current review,” Coastal Eng., vol. 53, pp. 191–208, 2006.

[3] L. Lasbeur and B. Thelot, “Epidemiological surveillance of drowning - the noyades 2012 survey. 1 june-30 september 2012,” Saint Maurice: Institut de veille vanitaire, Tech. Rep., 2013.

[4] F. P. Shepard, K. O. Emery, and E. C. L. Fond, “Rip currents: A process of geological importance,” Journal of Geology, vol. 49, pp. 337–369, 1941.

[5] P. H. Leblond and C. L. Tang, “On energy coupling between waves and rip currents,” J. Geophys. Res., vol. 79, pp. 811–816, 1974.

[6] A. Falques, A. Montoto, and D. Vila, “A note on hydrodynamic instabilities and horizontal circulation in the surf zone,” J. Geophys. Res., vol. 104, no. C9, pp. 20 605–20 615, 1999.

[7] J. Yu, “On the instability leading to rip currents due to wave-current interaction,” J. Fluid Mech., vol. 549, pp. 403–428, 2006.

[8] J. W. Long and H. T. Ozkan-Haller, “Offshore controls on nearshore rip currents,” J. Geophys. Res., vol. 110, p. C12007, 2005.

[9] K. A. Haas, I. A. Svendsen, and M. C. Haller, “Numerical modeling of nearshore circulations on a barred beach with rip channels, paper presented at the 26th conference on coastal engineering,” Am. Soc. of Civ. Eng., 1998.

[10] J. Yu and D. N. Slinn, “Effects of wave-current interaction on rip currents,” J. Geophys. Res., vol. 108, no. C3, p. 3088, 2003.

[11] B. Weir, Y. Uchiyama, E. M. Lane, J. M. Restrepo, and J. C. McWilliams, “A vortex force analysis of the interaction of rip currents and surface gravity waves,” J. Geophys. Res., vol. 116, p. C05001, 2011.

[12] F. Ardhuin, N. Rascle, and K. A. Belibassakis, “Explicit wave-averaged primitive equations using a generalized Lagrangian mean,” Ocean Modelling, vol. 20, pp. 35–60, 2008.

[13] A.-C. Bennis, F. Ardhuin, and F. Dumas, “On the coupling of wave and three-dimensional circulation models: Choice of theoretical framework, practical implementation and adiabatic tests,” Ocean Modelling, vol. 40, pp. 260–272, 2011.

[14] A.-C. Bennis, F. Dumas, F. Ardhuin, and B. Blanke, “Mixing parameterization: impacts on rip currents and wave set-up,” Ocean Engineering, vol. 42, pp. 213–227, 2014.

[15] P. Lazure and F. Dumas, “An external-internal mode coupling for a 3d hydrodynamical model for applications at regional scale (MARS),” Adv. Water Resources, vol. 31, pp. 233–250, 2008.

[16] H. L. Tolman, “User manual and system documentation of WAVEWATCH-IIITM version 3.14,” NOAA/NWS/NCEP/MMAB, Tech. Rep. 276, 2009.

[17] S. Buis, A. Piacentini, and D. D´eclat, “PALM: A computational framework for assembling high performance computing applications,” Concurrency Computat.: Pract. Exper., vol. 18, no. 2, pp. 247–262, 2008.

[18] F. Ardhuin, E. Rogers, A. Babanin, J.-F. Filipot, R. Magne, A. Roland, A. van der Westhuysen, P. Queffeulou, J.-M. Lefevre, L. Aouf, and F. Collard, “Semi-empirical dissipation source functions for wind-wave models: part i, definition, calibration and validation,” J. Phys. Oceanogr., vol. 40, pp. 1917–1941, 2010.

[19] A. Bourchtein and L. Bourchtein, “Modified time splitting scheme for shallow water equations,” Mathematics and Computers in Simulation, vol. 73, pp. 52–64, 2006.

[20] R. L. Soulsby, “Bed shear stresses due to combined waves and currents. In: Stive, M., Fredsøe, J., Hamm, L., Soulsby, R., Teisson, C., Winterwerp, J. (Eds),” Advances in Coastal Morphodynamics, Delft Hydraulics, Delft, The Netherlands, pp. 420–423, 1995.

[21] H. Burchard, “Simulating the wave-enhanced layer under breaking surface waves with two-equation turbulence models,” J. Phys. Oceanogr., vol. 31, pp. 3133–3145, 2001.

[22] J. C. McWilliams, J. M. Restrepo, and E. M. Lane, “An asymptotic theory for the interaction of waves and currents in coastal waters,” J. Fluid Mech., vol. 511, pp. 135–178, 2004.

[23] N. Kumar, G. Voulgaris, J. C. Warner, and M. Olabarrieta, “Implementation of the vortex force formalism in the coupled ocean-atmosphere-wave-sediment transport (COAWST) modeling system for inner shelf and surf zone applications,” Ocean Modelling, vol. 47, pp. 65–95, 2012.

[24] S. Moghimi, K. Klingbeil, U. Grawe, and H. Burchard, “A direct comparison of the depth-dependent radiation stress method and a vortex force formulation within a three-dimensional ocean model,” Ocean Modelling, pp. 1–38, 2012.

[25] Y. Uchiyama, J. C. McWilliams, and A. F. Shchepetkin, “Wave-current interaction in oceanic circulation model with a vortex-force formalism Application to the surf zone,” Ocean Modelling, vol. 34, pp. 16–35, 2010.

[26] D. J. R. Walstra, J. Roelvink, and J. Groeneweg, “Calculation of wave-driven currents in a 3D mean flow model,” in Proceedings of the 27th international conference on coastal engineering, Sydney, vol. 2. ASCE, 2000, pp. 1050–1063.

[27] J. A. Battjes, “Modelling of turbulence in surf zone,” in Symposium on Modelling Techniques, San Francisco. ASCE, 1975, pp. 1050–1061.

[28] J. Smagorinsky, “General circulations experiments with the primitive equations i. the basic experiment,” Monthly Weather Review, vol. 8, pp. 99–165, 1963.