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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:69028", author = "A.-C. Bennis and F. Dumas and F. Ardhuin and B. Blanke", title = "Turbulence Modeling and Wave-Current Interactions", 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.", volume = "9", number = "1", pages = "111-7", }
