Articles | Volume 8, issue 4
https://doi.org/10.5194/os-8-657-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/os-8-657-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
17 Aug 2012
Research article |
| 17 Aug 2012
Three-dimensional modelling of wave-induced current from the surf zone to the inner shelf
H. Michaud
Géosciences Montpellier, UMR5243, CNRS – Université Montpellier 2 Sciences et Techniques, place E Bataillon, 34095 Montpellier cedex 5, France
Laboratoire d'Aérologie,UMR5560, CNRS – Université de Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France
P. Marsaleix
Laboratoire d'Aérologie,UMR5560, CNRS – Université de Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France
Y. Leredde
Géosciences Montpellier, UMR5243, CNRS – Université Montpellier 2 Sciences et Techniques, place E Bataillon, 34095 Montpellier cedex 5, France
C. Estournel
Laboratoire d'Aérologie,UMR5560, CNRS – Université de Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France
F. Bourrin
Centre de Formation et de Recherche sur l'Environnement Marin, UMR5110, CNRS – Université de Perpignan Via Domitia, 52 avenue de Villeneuve, 66860 Perpignan cedex, France
F. Lyard
Laboratoire d'Etudes en Géophysique et Océanographie Spatiales (CNRS/CNES/IRD/UPS), 14 avenue Edouard Belin, 31400 Toulouse, France
C. Mayet
Laboratoire d'Etudes en Géophysique et Océanographie Spatiales (CNRS/CNES/IRD/UPS), 14 avenue Edouard Belin, 31400 Toulouse, France
F. Ardhuin
IFREMER, Centre de Brest, Laboratoire d'Océanographie Spatiale, 29280 Plouzané, France
Related subject area
Approach: Numerical Models | Depth range: Surface | Geographical range: Mediterranean Sea | Phenomena: Current Field
Use of a hydrodynamic model for the management of water renovation in a coastal system
Numerical simulation and decomposition of kinetic energy in the Central Mediterranean: insight on mesoscale circulation and energy conversion
Pablo Cerralbo, Marta F.-Pedrera Balsells, Marc Mestres, Margarita Fernandez, Manuel Espino, Manel Grifoll, and Agustin Sanchez-Arcilla
Ocean Sci., 15, 215–226, https://doi.org/10.5194/os-15-215-2019, https://doi.org/10.5194/os-15-215-2019, 2019
Short summary
Short summary
In this contribution we investigate the hydrodynamic response in Alfacs Bay (Delta Ebro, NW Mediterranean Sea) to freshwater flows and inner bay to open sea connections. The numerical model ROMS is applied nested to Copernicus models and validated with in situ data. Considering the results, only the modification of freshwater flows is recommended due to its lower impact on the environment and associated economic costs. None of the proposed solutions solve the problem related to warm waters.
R. Sorgente, A. Olita, P. Oddo, L. Fazioli, and A. Ribotti
Ocean Sci., 7, 503–519, https://doi.org/10.5194/os-7-503-2011, https://doi.org/10.5194/os-7-503-2011, 2011
Cited articles
Agrawal, Y. C., Terray, E. A., Donelan, M. A., Hwang, M. A., Williams III, A. J., Drennan, W. M., Kahma, K. K., and Kitaigorodskii, K. K.: Enhanced dissipation of kinetic energy beneath surface waves, Nature, 359, 219–233, 1992.
Aleman, N., Robin, N., Certain, R., Vanroye, C., Barusseau, J., and Bouchette, F.: Typology of nearshore bars in the Gulf of Lions (FRANCE) using LIDAR technology, J. Coastal Res., 64, 721–725, 2011.
Andrews, D. and McIntyre, M.: An exact theory of non-linear waves on a Lagrangian mean flow, J. Fluid Mech., 89, 609–646, 1978.
Anguenot, F. and Monaco, A.: Etude des transits sédimentaires sur le littoral du Roussillon par la méthode des traceurs radioactifs, Cahiers Océanographiques, 19, 579–589, 1967.
Ardhuin, F., Chapron, B., and Elfouhaily, T.: Waves and the Air{\textendash}Sea Momentum Budget: Implications for Ocean Circulation Modeling, J. Phys. Oceanogr., 34, 1741–1755, 2004.
Ardhuin, F., Collard, F., Chapron, B., Queffeulou, P., Filipot, J.-F., and Hamon, M.: Spectral wave dissipation based on observations: a global validation, in: Proceedings of the chinese-german joint symposium on hydraulic and ocean engineering, edited by Zanke, U and Roland, A and Saenger, N and Wiesemann, JU and Dahlem, G, pp. 391–400, Chinese-German Joint Symposium on Hydraulic and Ocean Engineering, Darmstadt, Germany, 24–30 August 2008, {2008}a.
Ardhuin, F., Jenkins, A. D., and Belibassakis, K. A.: Comments on \textquotedblleft}The {Three-Dimensional} Current and Surface Wave Equations{\textquotedblright, J. Physical Oceanogr., 38, 1340–1350, https://doi.org/10.1175/2007JPO3670.1, 2008b.
Ardhuin, F., Rascle, N., and Belibassakis, K.: Explicit wave-averaged primitive equations using a generalized Lagrangian mean, Ocean Modelling, 20, 35–60, https://doi.org/10.1016/j.ocemod.2007.07.001, 2008c.
Ardhuin, F., Marie, L., Rascle, N., Forget, P., and Roland, A.: Observation and estimation of Lagrangian Stokes and Eulerian currents induced by wind at the sea surface, J. Phys. Oceanogr., 39, 2820–2838, 2009.
Ardhuin, F., Rogers, E., Babanin, A. V., Filipot, J., Magne, R., Roland, A., van der Westhuysen, A., Queffeulou, P., Lefevre, J., Aouf, L., and Collard, F.: Semiempirical Dissipation Source Functions for Ocean Waves. Part I: Definition, Calibration, and Validation, J. Phys. Oceanogr., 40, 1917–1941, https://doi.org/10.1175/2010JPO4324.1, 2010.
Bennis, A. and Ardhuin, F.: Comments on "The {Depth-Dependent} current and Wave Interaction Equations: A Revision", J. Phys. Oceanogr., 41, 2008–2012, 2011.
Bennis, A., Ardhuin, F., and Dumas, F.: On the coupling of wave and three-dimensional circulation models: Choice of theoretical framework, pratical implementation and adiabatic tests, Ocean Model., 40, 260–272, 2011.
Berné, S., Satra, C., Alosi, J., Baztan, J., Dennielou, B., Droz, L., Reis, A. D., Lofi, J., Méar, Y., and Rabineau, M.: Carte morpho-bathymétrique du Golfe du Lion, notice explicative. Institut français de recherche pour l'éléxploitation de la mer (IFREMER), Brest, France, 2002.
Blumberg, A. and Mellor, G.: A description of a three-dimensional coastal ocean circulation model, Three-dimensional Coastal Ocean Models, Coastal and Estuarine Sciences, American Geophysical Union, 4, 1–16, 1987.
Booij, N., Ris, R., and Holthuijsen, L.: A third generation wave model for coastal regions, part1: model descritpion and validation, J. Geophys. Res., 104, 7649–7666, 1999.
Bourrin, F., Friend, P., Amos, C., Manca, E., Ulses, C., Palanques, A., de Madron, X. D., and Thompson, C.: Sediment dispersal from a typical Mediterranean flood: The Têt River, Gulf of Lions, Cont. Shelf Res., 28, 1895–1910, https://doi.org/10.1016/j.csr.2008.06.005, 2008.
Bowen, A.: Rip currents: 1.Theoretical investigations, J. Geophys. Res., 74, 5467–5478, 1969.
Bruneau, N.: Modélisation morphodynamique des plages sableuses, Ph.D. thesis, Université Bordeaux I, 2009.
Burchard, H. and Bolding, K.: Comparative analysis of four second-moment turbulence closure models for the oceanic mixed layer, J. Phys. Oceanogr., 31, 1943–1968, 2001.
Certain, R.: Morphodynamique d'une côte sableuse microtidale à barres : le Golfe du Lion (Languedoc-Roussillon), Ph.D. thesis, Université de Perpignan, 2002.
Chawla, A. and Kirby, J.: Monochromatic and random wave breaking at blocking points, J. Geophys. Res., 107, C7, https://doi.org/10.1029/2001JC001042, 2002.
Chen, Q., Kirby, J. T., Dalrymple, R. A., Fengyan, S., and Thornton, E. B.: Boussinesq modeling of longshore currents, J. Geophys. Res. Oceans, 108, 1–24, 2003.
Clark, D., Feddersen, F., and Guza, R.: Boussinesq modeling of surfzone tracer plumes, part 2: Tracer plumes and cross-shore dispersion, J. Geophys. Res., 116, C11028, https://doi.org/10.1029/2011JC007211, 2011.
Craig, P. D. and Banner, M. L.: Modeling Wave-Enhanced Turbulence in the Ocean Surface Layer, J. Phys. Oceanogr., 24, 2546–2559, 1994.
Davies, A. and Jones, J.: Sensitivity of tidal bed stress distributions, near bed currents, overtides and tidal residuals to frictional effect in the eastern Irish Sea, J. Phys. Oceanogr., 26, 2553–2575, 1996.
Delpey, M. T., Ardhuin, F., Collard, F., and Chapron, B.: Space-time structure of long ocean swell fields, J. Geophys. Res.-Oceans, 115, C12037, https://doi.org/10.1029/2009JC005885, 2010.
Delpont, G. and Motti, E.: Monitoring by remote sensing of the geomorphological evolution of a part of the Roussillon coastal layout (France), Oceanis 94 Osates, pp. 44–47, 1994.
Donelan, M., Dobson, F., and Smith, S.: On the dependance of sea surface roughness on wave development, J. Phys. Oceanogr., 23, 2143–2149, 1993.
Dufois, F.: Modélisation du transport particulaire dans le Golfe du Lion en vue d'une application au devenir des traceurs radioactifs issus du Rhône, Ph.D. thesis, Université du Sud Toulon-Var, 2008.
Estournel, C. and Guedalia, D.: A new parameterization of eddy diffusivities for nocturnal boundary-layer modelling, Bound.-Lay. Meteorol., 39, 191–203, 1987.
Estournel, C., Broche, P., Marsaleix, P., Devenon, J., Auclair, F., and Vehil, R.: The Rhone river plume in unsteady conditions: Numerical and experimental results, Estuarine Coast. Shelf Sci., 53, 25–38, 2001.
Estournel, C., Durrieu de Madron, X., Marsaleix, P., Auclair, F., Julliand, C., and Vehil, R.: Observation and modeling of the winter coastal oceanic circulation in the Gulf of Lion under wind conditions influenced by the continental orography (FETCH experiment), J. Geophys. Res.-Oceans, 108, 8059, https://doi.org/10.1029/2001JC000825, 2003.
Estournel, C., Zervakis, V., Marsaleix, P., Papadopoulos, A., Auclair, F., Perivoliotis, L., and Tragou, E.: Dense water formation and cascading in the Gulf of Thermaikos (North Aegean), from observations and modelling, Cont. Shelf Res., 25, 2366–2386, https://doi.org/10.1016/j.csr.2005.08.014, 2005.
Estournel, C., Auclair, F., Lux, M., Nguyen, C., and Marsaleix, P.: "Scale oriented" embedded modeling of the North-Western Mediterranean in the frame of MFSTEP, Ocean Sci., 5, 73–90, https://doi.org/10.5194/os-5-73-2009, 2009.
Flather, R.: A tidal model of the northwest european continental shelf, Mémoires, Société Royale des Sciences de Liege 6, 10, 141–164, 1976.
Galperin, B., Kantha, L., Hassid, S., and Rosati, A.: A quasi-equilibrium turbulent energy model for geophysical flows, J. Atmos. Sci., 45, 55–62, 1988.
Garrett, C.: Generation of Langmuir circulations by surface waves - a feedback mechanism, J. Mar. Res., 34, 117–130, 1976.
Guillén, J., Bourrin, F., Palanques, A., de Madron, X. D., Puig, P., and Buscail, R.: Sediment dynamics during wet and dry storm events on the Têt inner shelf (SW Gulf of Lions), Marine Geology, 234, 129–142, 2006.
Guizien, K.: Spatial variability of wave conditions in the Gulf of Lions (NW Mediterranean Sea), Vie et milieu, 59, 261–270, 2009.
Haas, K. A. and Svendsen, I. A.: Laboratory measurements of the vertical structure of rip currents, J. Geophys. Res., 107, C5, https://doi.org/10.1029/2001JC000911, 2002.
Haas, K. A. and Warner, J. C.: Comparing a quasi-3D to a full 3D nearshore circulation model: SHORECIRC and ROMS, Ocean Model., 26, 91–103, 2009.
Haas, K. A., Svendsen, I. A., Haller, M., and Zhao, Q.: Quasi-three-dimensional modeling of rip current systems, J. Geophys. Res., 108, 3217, https://doi.org/10.1029/2002JC001355, 2003.
Haller, M., Dalrymple, R., and Svendsen, I. A.: Experimental study of nearshore dynamics on a barred beach with rip channels, J. Geophys. Res., 107, C6, https://doi.org/10.1029/2001JC000955, 2002.
Jenkins, A. D.: The use of a wave prediction model for driving a near-surface current model, Deut. Hydrogr. Z, 42, 133–149, 1989.
Jordà, G., Bolaños, R., Espino, M., and Sánchez-Arcilla, A.: Assessment of the importance of the current-wave coupling in the shelf ocean forecasts, Ocean Sci., 3, 345–362, https://doi.org/10.5194/os-3-345-2007, 2007.
Kantha, L. and Clayson, C.: An improved mixed layer model for geophysical applications, J. Geophys. Res., 99, 25235–25266, 1994.
Komar, P., Neudeck, R., and Kulm, L.: Shelf Sediment Transport, chap. Observations and significance of deep-water oscillatory ripple marks on the Oregon continental shelf, Hutchinson and Ross, Stroudsburg, Pa, 1972.
Kumar, N., Voulgaris, G., and Warner, J.: Implementation and modification of a three-dimensional radiation stress formulation for surf zone and rip-current applications, Coastal Engineering, 58, 1097–1117, 2011.
Lazure, P. and Dumas, F.: An external-internal mode coupling for 3D hydrodynamical model for applications at regional scale (MARS), Adv. Water Resour., 31, 233–250, 2008.
Lentz, S. J., Guza, R. T., Elgar, S., Feddersen, F., and Herbers, T. H. C.: Momentum balances on the North Carolina inner shelf, J. Geophys. Res., 104, 18205–18226, 1999.
Lentz, S. J., Fewings, M., Howd, P., Fredericks, J., and Hathaway, K.: Observations and a Model of Undertow over the Inner Continental Shelf, J. Phys. Oceanogr., 38, 2341–2357, 2008.
Leredde, Y. and Michaud, H.: Hydrodynamique sédimentaire sur le plateau continental du Golfe du Lion, in: Xèmes Journées Nationales Génie Cotier-Génie Civil, 14-16 octobre 2008, Sophia-Antipolis, pp. 111–123, 2008.
Longuet-Higgins, M. and Stewart, R.: Radiation stress and mass transport in gravity waves with application to surf beat, J. Fluid Mech., 13, 481–504, 1962.
MacMahan, J., Thornton, E., Stanton, T., and Reniers, A.: RIPEX: Observations of a rip current system, Mar. Geol., 218, 113–134, 2005.
Madec, G.: NEMO ocean engine, Note du Pole de modelisation, Institut Pierre-Simon Laplace (IPSL), France, no 27, 2008.
Marsaleix, P., Auclair, F., and Estournel, C.: Considerations on open boundary conditions for regional and coastal ocean models., J. Atmos. Oceanic Technol., 23, 1604–1613, https://doi.org/10.1175/JTECH1930.1, 2006.
Marsaleix, P., Auclair, F., Floor, J. W., Herrmann, M. J., Estournel, C., Pairaud, I., and Ulses, C.: Energy conservation issues in sigma-coordinate free-surface ocean models, Ocean Model., 20, 61–89, https://doi.org/10.1016/j.ocemod.2007.07.005, 2008.
Marsaleix, P., Auclair, F., and Estournel, C.: Low-order pressure gradient schemes in sigma coordinate models: The seamount test revisited, Ocean Modelling, 30, 169–177, 2009{a}.
Marsaleix, P., Ulses, C., Pairaud, I., Herrmann, M. J., Floor, J. W., Estournel, C., and Auclair, F.: Open boundary conditions for internal gravity wave modelling using polarization relations, Ocean Model., 29, 27–42, 2009{b}.
Mastenbroek, C., Burgers, G., and Janssen, P.: The dynamical coupling of a wave model and a storm surge model through the atmospheric boundary layer, J. Phys. Oceanogr., 23, 1856–1866, 1993.
McWilliams, J. C., Restrepo, J. M., and Lane, E. M.: An asymptotic theory for the interaction of waves and currents in coastal waters, J. Fluid Mech., 511, 135–178, https://doi.org/10.1017/S0022112004009358, 2004.
Mellor, G.: The Three-Dimensional current and surface wave equations, J. Phys. Oceanogr., 33, 1978–1989, 2003.
Michaud, H., Leredde, Y., Estournel, C., Berthebaud, E., and Marsaleix, P.: Hydrodynamics during a typical winter storm in the Gulf of Aigues-Mortes (NW Mediterranean Sea): In-situ measurements and numerical modelling, Comptes Rendus Geoscience, submitted, 2012.
Myrhaug, D., Holmedal, L. E., Simons, R. R., and MacIver, R. D.: Bottom friction in random waves plus current flow, Coastal Engineering, 43, 75–92, 2001.
Newberger, P. and Allen, J.: Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 1. Formulation, J. Geophys. Res., 112, C08018, https://doi.org/10.1029/2006JC003472, 2007.
Palanques, A., Puig, P., Guillén, J., Durrieu de Madron, X., Latasa, M., Scharek, R., and Martin, J.: Effects of storm events on the shelf-to-basin sediment transport in the southwestern end of the Gulf of Lions (Northwestern Mediterranean), Nat. Hazards Earth Syst. Sci., 11, 843–850, https://doi.org/10.5194/nhess-11-843-2011, 2011.
Phillips, O.: The dynamics of the upper ocean, Cambridge University Press, London, 1977.
Rascle, N.: Impact des vagues sur la circulation océanique, Ph.D. thesis, Université de Bretagne Occidentale, 2007.
Rascle, N. and Ardhuin, F.: Drift and mixing under the ocean surface revisited: Stratified conditions and model-data comparisons, J. Geophys. Res., 114, C02016, https://doi.org/10.1029/2007JC004466, 2009.
Rascle, N., Ardhuin, F., and Terray, E. A.: Drift and mixing under the ocean surface: A coherent one-dimensional description with application to unstratified conditions, J. Geophys. Res., 111, C03016, https://doi.org/10.1029/2005JC003004, 2006.
Rascle, N., Ardhuin, F., Queffeulou, P., and Croizé-Fillon, D.: A global wave parameter database for geophysical applications. Part I: Wave-current-turbulence interaction parameters for the open ocean based on traditional parameterizations, Ocean Model., 25, 154–171, 2008.
Reniers, A., Symonds, G., and Thornton, E.: Modelling of rip currents during rdex, in: Coastal Dynamics '01: Proceedings, edited by Hanson, H and Larson, M, pp. 493–499, Amer Soc Civil Engineers, Coasts, Oceans, Ports & Rivers Inst, 4th International Conference on Coastal Dynamics, Lund, Sweden, 11–15 June 2001, 2001.
Reniers, A., Roelvink, J., and Thornton, E.: Morphodynamic modeling of an embayed beach under wave group forcing, J. Geophys. Res., 109, C01030, https://doi.org/10.1029/2002JC001586, 2004.
Rusu, E. and Soares, C. G.: Numerical modelling to estimate the spatial distribution of the wave energy in the Portuguese nearshore, Renewable Energy, 34, 1501–1516, 2009.
Serrat, P., Ludwig, W., Navarro, B., and Blazi, J.: Variabilité spatio-temporelle des flux de maières en suspension d'un fleuve côtier méditerranéen: la Têt (France), Comptes Rendus de l'Académie des Sciences, D333, 389–397, 2001.
Shchepetkin, A. and McWilliams, J.: The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model, Ocean Model., 9, 347–404, https://doi.org/10.1016/j.ocemod.2004.08.002, 2005.
Smith, J. A.: Wave–current interactions in finite-depth, J. Phys. Oceanogr., 36, 1403–1419, 2006.
Smith, R.: Reflection of short gravity waves on a non-uniform current, Math. Proc. Cambridge Philos. Soc., 78, 517–525, 1975.
Soulsby, R., Stive, M., de Vriend, H., Fredsoe, J., Hamm, L., Teisson, C., and Winterwerp, J.: Bed shear stresses due to combined waves and current, Adv. Coastal Morphodynamics, 4–20, 4–23, 1995.
Stokes, G.: On the theory of oscillatory waves, Transactions of the Cambridge Philosophical Society, 8, 441–455, 1847.
Svendsen, I. A., Haas, K., and Zhao, Q.: Shorecirc – the quasi-3d nearshore circulation model., Tech. Rep. Technical report CACR-02-01, University of Delaware, Center for Applied Coastal Research, 2002.
Taylor, G.: Standing waves on a contracting or expanding current, J. Fluid Mech., 13, 182–194, 1962.
Terray, E. A., Donelan, M., Agrawal, Y., Drennan, W., Kahma, K., Williams, A., Hwang, P., and Kitaigorodskii, S.: Estimates of kinetic energy dissipation under breaking waves, J. Physical Oceanogr., 26, 792–807, 1996.
Terray, E. A., Drennan, W., and Donelan, M.: The vertical structure of shear and dissipation in the ocean surface layer, Proc. Symp. on Air-Sea Interaction, pp. 239–245, 2000.
Tolman, H.: A mosaic approach to wind wave modeling, Ocean Model., 25, 35–47, https://doi.org/10.1016/j.ocemod.2008.06.005, 2008.
Tolman, H.: User Manual and system documentation of WAVEWATCH-III version 3.14. Technical Report, Tech. Rep. 276, NOAA/NWS/NCEP/MMAB, 2009.
Tonani, M., Pinardi, N., Dobricic, S., Pujol, I., and Fratianni, C.: A high-resolution free-surface model of the Mediterranean Sea, Ocean Sci., 4, 1–14, https://doi.org/10.5194/os-4-1-2008, 2008.
Trampenau, T., Oumeraci, H., and Dette, H.: Hydraulic functioning of permeable pile groins, J. Coastal Res., 33, 160–187, 2004.
Uchiyama, Y., McWilliams, J. C., and Shchepetkin, A. F.: Wave{\textendash}current interaction in an oceanic circulation model with a vortex-force formalism: Application to the surf zone, Ocean Model., 34, 16–35, https://doi.org/10.1016/j.ocemod.2010.04.002, 2010.
Ulses, C.: Dynamique océanique et transport de la matière particulaire dans le Golfe du Lion: Crue, tempête et période hivernale, Ph.D. thesis, Université Paul Sabatier Toulouse, 2005.
Ulses, C., Estournel, C., Bonnin, J., Durrieu de Madron, X., and Marsaleix, P.: Impact of storms and dense water cascading on shelf-slope exchanges in the Gulf of Lion (NW Mediterranean), J. Geophys. Res., 113, C02010, https://doi.org/10.1029/2006JC003795, 2008{a}.
Ulses, C., Estournel, C., Durrieu de Madron, X., and Palanques, A.: Suspended sediment transport in the Gulf of Lions (NW Mediterranean): Impact of extreme storms and floods, Cont. Shelf Res., 28, 2048–2070, https://doi.org/10.1016/j.csr.2008.01.015, 2008{b}.
Ulses, C., Estournel, C., Puig, P., Durrieu de Madron, X. D., and Marsaleix, P.: Dense shelf water cascading in the northwestern Mediterranean during the cold winter 2005: Quantification of the export through the Gulf of Lion and the Catalan margin, Geophys. Res. Lett., 35, L07610, https://doi.org/10.1029/2008GL033257, 2008{c}.
Warner, J., Sherwood, C., Arango, H., and Signell, R. P.: Performance of four turbulence closure models implemented using a generic length scale method, Ocean Model., 8, 81–113, 2005.
Weaver, P., Canals, M., and Trincardi, F.: EUROSTRATAFORM Special Issue of Marine Geology, Marine Geology, 234, 1–2, https://doi.org/10.1016/j.margeo.2006.09.001, 2006.
Weir, B., Uchiyama, Y., Lane, E. M., Restrepo, J. M., and Williams, J. M.: A vortex force analysis of the interaction of rip currents and surface gravity waves, J. Geophys. Res., 116, C05001, https://doi.org/10.1029/2010JC006232, 2011.
Whitham, G.: Mass, momentum and energy flux in water waves, J. Fluid Mech., 12, 135–147, 1962.
Xu, Z. and Bowen, A.: Wave- and wind-driven flow in water of finite depth, J. Phys. Oceanogr., 24, 1850–1866, 1994.
Yu, J. and Slinn, D.: Effects of wave–current interaction on rip currents, J. Geophys. Res., 108, 3088, https://doi.org/10.1029/2001JC001105, 2003.
