Rozita Jalali Farahani, Robert A. Dalrymple, Alexis Hérault, Giuseppe Bilotta


A Lagrangian numerical model called Smoothed Particle Hydrodynamics is used to analyze rip current system generated by a single bar and a rip channel. The pattern of the wave-induced circulation cell over the bar, the oppositely-rotating circulation cell on-shore and a strong seaward-directed current in the rip channel is modeled numerically. The mean horizontal variations of rip current system as well as three-dimensional circulations are studied. The results in three-dimensional space reveal the wave-current interaction and flow patterns in different parts of rip channel, bar, and the trough located near shore. For comparison to experimental data, Eulerian nodes are introduced to the numerical model and SPH interpolation over neighboring Lagrangian particles is implemented to find fluid parameters at those specific nodes. This methodology leads to a better understanding of depth-integrated flows and a more accurate comparison of numerical results with experimental results. Model predictions are compared to laboratory measurements of Drønen et al. (2002) and show good agreement, including mean velocity profiles, mean surface elevation and three-dimensional velocity components.


rip current system; Smoothed Particle Hydrodynamics; near-shore circulations

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Arthur, R. S., 1962, A note on the dynamics of rip currents, Journal of Geophysical Research, Vol. 67, No. 7, P. 2777-2779.http://dx.doi.org/10.1029/JZ067i007p02777

Bowen A., D. Inman, 1969, Rip currents 1. Theoretical investigation, Journal of Geophysical Research, Vol. 74, No. 23, P. 5467-5478.http://dx.doi.org/10.1029/JC074i023p05467

Bowen A., Inman D., Rip currents 2. Laboratory and field observations, 1969, Journal of Geophysical research, Vol. 74, No. 23, P. 5479-5490.http://dx.doi.org/10.1029/JC074i023p05479

Chen Q., R. A. Dalrymple, J. Kirby, A. Kennedy, M. Haller, 1999, Boussinesq modeling of a rip current system, Journal of Geophysical Research, Vol. 104, No. C9, P. 20617-20637.http://dx.doi.org/10.1029/1999JC900154

Colagrosi A., M. Landrini, 2003, Numerical simulation of interfacial flows by smoothed particle hydrodynamics, Journal of Computational Physics, Vol.191, P. 448-475.http://dx.doi.org/10.1016/S0021-9991(03)00324-3

Dalrymple, R. A., Knio, O, Cox, D.T., Gómez-Gesteira, M., and Zou, 2002, Using a Lagrangian particle method for deck overtopping, Proceedings of Waves, ASCE. 1082-1091

Dalrymple R. A., B. Rogers, 2006, Numerical modeling of water waves with SPH method, Coastal Engineering, Vol.53, P.141-147.http://dx.doi.org/10.1016/j.coastaleng.2005.10.004

Dalrymple R. A., J. MacMahan, A. Reniers, V. Nelko, 2011, Rip currents, Annual Review of Fluid Mechanics, Vol.43, P. 551-581.http://dx.doi.org/10.1146/annurev-fluid-122109-160733

Drønen N., H. Karunarathna, J. Fredsoe, B. Sumer, R. Deiggard, 2002, An experimental study of rip channel flow, Coastal Engineering, Vol. 45, P. 223-238.http://dx.doi.org/10.1016/S0378-3839(02)00035-2

Feldman J., J. Bonet, 2007, Dynamic refinement and boundary contact forces in SPH with applications in fluid flow problems, Journal of Numerical Methods in Engineering, Vol. 27, P. 295-324.http://dx.doi.org/10.1002/nme.2010

Haller M., R. A. Dalrymple, I. Svendsen, 1997, Rip channels and nearshore circulation: experiments, ASCE, P. 594-603.

Haas K. A., A. Svendsen, 2002, Laboratory measurements of the vertical structure of rip currents, Journal of Geophysical Research, Vol. 107, NO. C5, P. 15-1, 15-19.

Haas K. A., A. Svendsen, M. C. Haller, Q. Zhao, 2003, Quasi-three-dimensional modeling of rip current systems, Journal of Geophysical Research, Vol. 108, NO. C7, P. 10-1, 15-21.http://dx.doi.org/10.1029/2002JC001355

Hérault A., G. Bilotta, R. A. Dalrymple, 2010, SPH on GPU with CUDA, Journal of Hydraulic Research, Vol.48, P. 74-79.http://dx.doi.org/10.1080/00221686.2010.9641247

Marrone S., A. Colagrossi, D. Le Touze, G. Graziani, 2010, Fast free-surface detection and level-set function definition in SPH solvers, Journal of Computational Physics, Vol.229, P. 3652-3663.http://dx.doi.org/10.1016/j.jcp.2010.01.019

Mei, C. C., and U. Ünlüata, 1972, Harmonic generation in shallow water waves. Waves on Beaches and Resulting Sediment Transport, P. 181-202.

Monaghan J., 1994, Simulating free surface flows with SPH, Computational Physics, Vol. 110, P. 399-406.http://dx.doi.org/10.1006/jcph.1994.1034

Monaghan J., A. Kos, 1999, Solitary waves on a certain beach, Journal of Waterway, Port, Coastal and Ocean Engineering, P.145-154.http://dx.doi.org/10.1061/(ASCE)0733-950X(1999)125:3(145)

Monaghan J.,J. Kajtar, 2009, SPH particle boundary forces for arbitrary boundaries, Computer Physics Communications, Vol.180, P. 1811-1820.

Mckenzie P., 1958, Rip current systems, The Journal of Geology, Vol.66, P. 103-113.http://dx.doi.org/10.1086/626489

Wright L. D., A. D. Short, 1984, Morphodynamic variability of surf zones and beaches: a synthesis, Marine Geology, Vol. 56, P. 93-118.http://dx.doi.org/10.1016/0025-3227(84)90008-2

Panizzo, A., R. A. Dalrymple, 2004, SPH modeling of under-water landslide generated waves. Proc. ICCE, ASCE.

Shepard F. P., K. O. Emery, E. C. La Fond, 1941, Rip currents: A process of geological importance, The Journal of Geology, Vol.49, P. 337-369.http://dx.doi.org/10.1086/624971

De Vriend, H.J., J. Zyserman, J. Nicholson, J.A. Roelvink, P. Pechon, and H.N. Southgate. 1993. Medium-term 2DH coastal area modeling, Coastal Engineering, 21, 193-224.http://dx.doi.org/10.1016/0378-3839(93)90050-I

Wiegel, R.L. 1965. Oceanographical Engineering, Prentice-Hall, Englewood Cliffs, New Jersey, 531.

DOI: http://dx.doi.org/10.9753/icce.v33.currents.37