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.

[1]  A numerical solution of the Boussinesq equations in the inshore zone , 1990 .

[2]  P. Liu,et al.  Interactions of currents and weakly nonlinear water waves in shallow water , 1989, Journal of Fluid Mechanics.

[3]  Per A. Madsen,et al.  Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves , 1997 .

[4]  Rolf Deigaard,et al.  A Boussinesq model for waves breaking in shallow water , 1993 .

[5]  Per A. Madsen,et al.  Time Domain Modelling of Wave Breaking, Runup, and Surf Beats , 1995 .

[6]  B. P. Leonard,et al.  The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection , 1991 .

[7]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics , 1991 .

[8]  R. Dalrymple,et al.  A Numerical Model for Nearshore Circulation Including Convective Accelerations and Lateral Mixing. , 1979 .

[9]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry , 1992 .

[10]  Luc Hamm.  DIRECTIONAL NEARSHORE WAVE PROPAGATION OVER A RIP CHANNEL: AN EXPERIMENT , 1993 .

[11]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[12]  B. O'CONNOR,et al.  Intercomparison of wave-driven current models , 1997 .

[13]  H. Schaffer,et al.  A TWO-DIMENSIONAL SURF ZONE MODEL BASED ON THE BOUSSINESQ EQUATIONS , 1993 .

[14]  L. Hamm,et al.  Wave height, setup and currents around a detached breakwater submitted to regular or random wave forcing , 1997 .

[15]  Shinji Sato,et al.  Two-Dimensional Nonlinear Dispersive Wave-Current and Three-Dimensional Beach Deformation Model , 1993 .

[16]  C. Vreugdenhil,et al.  Numerical methods for advection-diffusion problems , 1993 .

[17]  BOUSSINESQ EQUATIONS WITH IMPROVED DOPPLER SHIFT AND DISPERSION FOR WAVE/CURRENT INTERACTION , 1997 .

[18]  J. Kirby,et al.  Surfzone currents, by D.R. Basco , 1984 .

[19]  Per A. Madsen,et al.  Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves , 1997 .

[20]  A. Watanabe,et al.  A NUMERICAL MODEL OF WAVE DEFORMATION IN SURF ZONE , 1988 .

[21]  H. Schäffer,et al.  Higher–order Boussinesq–type equations for surface gravity waves: derivation and analysis , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  WAVE BREAKING AND INDUCED NEARSHORE CIRCULATIONS , 1995 .