Antonino Viviano, Rosaria Ester Musumeci, Enrico Foti


A 2DH highly nonlinear Boussinesq-type of model for breaking waves has been developed in order to investigate surf zone hydrodynamics, also in the presence of complex bathymetries. The set of equations includes continuity and rotational momentum equations, coupled with the vorticity transport equation. An appropriate spatial definition of the 3D roller concept, along with an algorithm for accurately tracking the roller position, have been on purposely developed. Several numerical simulations have been carried out for the case of a submerged elliptic shoal. The results have been compared with both experimental data and with the results of other numerical models available in the literature. Finally, the vorticity dynamics under a breaking wave has been analyzed both in time and space, showing that a fairly correct interpretation of the wake effect in the rear part of the wave crest is obtained.


vorticity; roller; breaking; Boussinesq; 2DH; numerical model; rotational motion

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Bingham, H.B., Madsen, P.A., and Fuhrman, D.R. 2009. Velocity potential formulations of highly accurate Boussinesq-type models. Coastal Engng, 56, 467-478. http://dx.doi.org/10.1016/j.coastaleng.2008.10.012

Boussinesq, J. 1872. Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. Journal de Mathématique Pures et Appliquées, Deuxième Série, 17, 55-108.

Briganti, R., Musumeci, R. E., Bellotti, G., Brocchini, M., and Foti, E. 2004. Boussinesq modeling of breaking waves: Description of turbulence. J. Geophys. Res., 109.

Chen, Q., Kirby, J. T., Dalrymple, R. A., Kennedy, A. B., and Chawla, A. 2000. Boussinesq modeling of wave transformation, breaking, and runup. ii: 2D. J.Wat., Port, Coast. Oc. Engng., 126, 48-56.

Choi, J., Chae, H. L., Jong, I. L., and Sung, B. Y. 2009. Evolution of waves and currents over a submerged laboratory shoal. Coastal Engng., 56, 297-312.http://dx.doi.org/10.1016/j.coastaleng.2008.09.002

Cox, D. T., Kobayashi, N., and Okaiasu, A. 1995. Experimental and numerical modeling of surf zone hydrodynamics. Research report CACR–95–07, Center For Applied Coastal Research, University of Delaware.

Gobbi, M.F., and Kirby,J.T. 1999. Wave evolution over submerged sills:tests of a high order Boussinesq model. Coastal Engng., 37, 57–96. http://dx.doi.org/10.1016/S0378-3839(99)00015-0

Lynett, P. and Liu, P.L.F. 2004. A two-layer approach to wave modelling. Proc. R. Soc. Lond. A, 460, 2637-2669. http://dx.doi.org/10.1098/rspa.2004.1305

Kennedy, A.B., Chen, Q., Kirby, J.T. and Dalrymple, R.A. 2000. Boussinesq modeling of wave transformation, breaking and run-up. I: 1D. J.Waterway, Port, Coast. and Oc. Engng., 126, 39-47.

Madsen, P.A., Fuhrman, D.R., and Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coastal Engineering, 53, 487-504.http://dx.doi.org/10.1016/j.coastaleng.2005.11.002

Madsen, P.A., and R. Sørensen, O.R. 1992. A new form of the Boussinesq equations with improved linear dispersion characteristic. Part 2. A slowly-varying bathymetry. Coast. Eng,18, 183-204. http://dx.doi.org/10.1016/0378-3839(92)90019-Q

Madsen, P. A., Sørensen, O. R., and Schäffer, H. A. 1997. Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves. Coastal Engng., 32, 255-287. http://dx.doi.org/10.1016/S0378-3839(97)00028-8

Musumeci, R.E., Svendsen, I.A., and Veeramony, J. 2005. The flow in the surf zone: a fully nonlinear Boussinesq-type of approach. Coastal Engineering, 52, 565-598. http://dx.doi.org/10.1016/j.coastaleng.2005.02.007

Sørensen, O. R., Schäffer, H. A., and Madsen, P. A. 1998. Surf zone dynamics simulated by a Boussinesq type model. part iii. wave-induced horizontal nearshore circulation. Coastal Engineering, 33, 155-176. http://dx.doi.org/10.1016/S0378-3839(98)00007-6

Svendsen, I. A. 1984. Wave heights and set-up in a surf zone. Coastal Engineering, 8, 303-329. http://dx.doi.org/10.1016/0378-3839(84)90028-0

Svendsen, I. A., Veeramony, J., Bakunin, J., and Kirby, J. 2000. The flow in weak turbulent hydraulic jump. J. Fluid Mech, 418, 25-57.http://dx.doi.org/10.1017/S0022112000008867

van Dongeren, A. R. and Svendsen, I.A. 1997. Absorbing-generating boundary condition for shallow water models. J. of Waterway, Port, Coast. And Oc. Engnrg, 123(6), 303-313.,

Veeramony, J. and Svendsen, I. A. 2000. The flow in the surf-zone waves. Coastal Engng, 39:93-122.

Vincent, C.L., and Briggs, M.J. 1989. Refraction-diffraction of irregular waves over a mound. J. of Waterway, Port, Coastal and Ocean Engng.,115 (2), 269-284.

Wei, G., Kirby, J.T., Grilli, S.T., and Subramanya, R. 1995. A fully nonlinear Boussinesq model for surface waves: I. Highly nonlinear unsteady waves. J. Fluid Mech., 294, 71-92.

Yoon, S.B., Cho, Y.-S., and Lee, C. 2004. Effects of breaking-induced currents on refraction-diffraction of irregular waves over submerged shoal. Ocean. Eng., 31, 633652.

Zelt, J.A. 1991. The run-up of nonbreaking and breaking solitary waves. Coastal Engng., 15, 205-246.

DOI: https://doi.org/10.9753/icce.v32.currents.50