Surf zone dynamics simulated by a Boussinesq type model. III. Wave-induced horizontal nearshore circulations

This is the third of three papers on the modelling of various types of surf zone phenomena by the use of a time-domain Boussinesq type model, which is extended to the surf zone and swash zone by including a simple description of wave breaking and a moving boundary at the shoreline. In the first paper [Madsen, P.A., Sorensen, O.R., Schaffer, H.A., 1997. Surf zone dynamics simulated by a Boussinesq type model: Part 1. Model description and cross-shore motion of regular waves. Coastal Eng. 32, 255-288.], the numerical model was described and it was applied to study cross-shore motion of regular waves in the surf zone including shoaling, breaking and runup. The first paper also included a discussion of time-averaged quantities derived from the time-domain solutions. The second paper [Madsen, P.A., Sorensen, O.R., Schaffer, H.A., 1997. Surf zone dynamics simulated by a Boussinesq type model: Part 2. Surf beat and swash oscillations for wave groups and irregular waves. Coastal Eng. 32, 289-320.] treated the cross-shore motion of wave groups and irregular waves with emphasis on the resulting shoreline motion and surf beat. The present paper concentrates on wave breaking and wave-induced currents in the horizontal plane. This is done without the traditional splitting of the phenomenon into a wave problem and a current problem. Mutual interaction between short waves and long waves and wave-induced (depth-averaged) currents is inherent in the model. Two situations are studied with waves normally incident on a plane sloping beach, but with some alongshore non-uniformity. In the first example, a rip channel is present and the other concerns a detached breakwater parallel to the shoreline. In both situations, wave-driven currents are generated and circulation cells appear. In turn, the currents appear to affect the waves. Results are presented for the case of unidirectional waves as well as for directionally spread waves. The resulting current patterns and wave height distributions are shown to be in good agreement with laboratory measurements from the literature. (C) 1998 Elsevier Science B.V.