Arjen Luijendijk, Johan Henrotte, Dirk Jan Walstra, Maarten van Ormondt


A quasi-three-dimensional model (quasi-3D) has been developed through the implementation of an analytical 1DV flow model in existing depth-averaged shallow water equations. The model includes the effects of waves and wind on the vertical distribution of the horizontal velocities. Comparisons with data from both physical and field cases show that the quasi-3D approach is able to combine the effect of vertical structures with the efficiency of depth-averaged simulations.
Inter-comparisons with three-dimensional simulations show that the quasi-3D approach can represent similar velocity profiles in the surf zone. Quasi-3D morphodynamic simulations show that the bed dynamics in the surf zone represent the
relevant 3D effects in the surf zone much more than the depth-averaged computations. It was shown that the quasi-3D approach is computationally efficient as it only adds about 15-20% to the runtimes of a 2DH simulation which is minor compared to a run time increase of 250-800% when switching to a 3D simulation.


quasi-3d modelling; surf zone; coastal modelling; nearshore morphodynamics

Full Text:



Arcilla, A.S., J.A. Roelvink, B.A O'Connor, A.J.H.M. Reniers, and J.A. Jimenez. 1994. The Delta Flume'93 experiments, Proc. Coastal Dynamics '94, Barcelona, Spain, ASCE, New York (1994), pp. 488–502.

De Vriend, H.J. and M.J.F. Stive. 1987. Quasi-3D modelling of nearshore currents. Coastal Engineering, 11, pp. 565-601.http://dx.doi.org/10.1016/0378-3839(87)90027-5

Gallappatti, R. 1993. A depth integrated model for suspended transport, Delft Univ. Rep. 83-7, Department of Civil Engineering, Delft University of Technology, Delft, The Netherlands.

Lesser, G.R., J.A. Roelvink, J.A.T.M. van Kester, and G.S. Stelling, 2004. Development and validation of a three-dimensional morphological model. Coastal Engineering 51, pp. 883 – 915.http://dx.doi.org/10.1016/j.coastaleng.2004.07.014

Ranasinghe, R., C. Pattiaratchi, G. Masselink. 1999. A morphodynamic model to simulate the seasonal closure of tidal inlets, Coastal Engineering, 37, Issue 1.

Reniers, A.J.H.M., E.B. Thornton, T.P. Stanton, and J.A. Roelvink. 2004. Vertical flow structure during Sandy Duck: observations and modeling. Coastal Engineering, 51, pp. 237-260. http://dx.doi.org/10.1016/j.coastaleng.2004.02.001

Roelvink, J.A., and I. Broker. 1993. Cross-shore profile models. Coastal Engineering 21, 193– 224. http://dx.doi.org/10.1016/0378-3839(93)90049-E

Roelvink, J.A., and A.J.H.M. Reniers. 1994. Upgrading of a quasi-3D hydrodynamic model, Abstractsin-depth, MAST G8-M overall workshop, Gregynog.

Ruessink B.G., Y. Kuriyama, A.J.H.M. Reniers, J.A. Roelvink and D.J.R. Walstra, 2007. Modeling cross-shore sandbar behavior on the time scale of weeks. Journal of Geophysical Research, 112

Ruggiero, P., D.J.R. Walstra, G. Gelfenbaum, and M. van Ormondt. 2009. Seasonal-scale nearshore morphological evolution: Field observations and numerical modelling Coastal Engineering, 56, Issues 11-12.

Stive, M.J.F. and H.G. Wind. 1986. Cross-shore mean flow in the surf zone. Coastal Engineering 10, 325–340. http://dx.doi.org/10.1016/0378-3839(86)90019-0

Svendsen, I.A. and R.S. Lorenz, 1989. Velocities in combined undertow and longshore currents. Coastal Engineering, 13, pp 55-79http://dx.doi.org/10.1016/0378-3839(89)90032-X

van Dongeren, A.R. and A. Svendsen. 1997. Quasi-3D modelling of nearshore hydrodynamics. Research Report No. CACR-97-04.

van Rijn, L.C., 2007. Unified View of Sediment Transport by Currents and Waves. I: Initiation of Motion, Bed Roughness, and Bed-Load Transport." Journal of Hydraulic Engineering, 133

DOI: https://doi.org/10.9753/icce.v32.currents.52