Time Domain Modelling of Wave Breaking, Runup, and Surf Beats

In this paper we study wave breaking and runup of regular and irregular waves, and the generation of surf beats. These phenomena are investigated numerically by using a time-domain primary-wave resolving model based on Boussinesq type equations. As compared with the classical Boussinesq equations the ones adopted here allow for improved linear dispersion characteristics, and wave breaking is incorporated by using a roller concept for spilling breakers. The swash zone is represented by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. The model results presented include wave height decay, mean water setup, depth-averaged undertow, shoreline oscillations and the generation and release of low frequency waves.

[1]  J. A. Battjes,et al.  Energy loss and set-up due to breaking random waves , 1978 .

[2]  J. Buhr Hansen,et al.  A Theoretical and Experimental Study of Undertow , 1984 .

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

[4]  I. A. Svendsen.  Wave Heights and Set-up in a Surf Zone , 1983 .

[5]  J. A. Roelvink.  Surf beat and its effect on cross-shore profiles , 1993 .

[6]  J. A. Battjes,et al.  ENERGY LOSS AND SET-UP DUE TO BREAKING OF RANDOM WAVES , 1978 .

[7]  Per A. Madsen,et al.  Bound waves and triad interactions in shallow water , 1993 .

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

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

[10]  Hemming A. Schäffer,et al.  Infragravity waves induced by short-wave groups , 1993, Journal of Fluid Mechanics.

[11]  H. P. Greenspan,et al.  Water waves of finite amplitude on a sloping beach , 1958, Journal of Fluid Mechanics.

[12]  Nobuhisa Kobayashi,et al.  Wave transformation and swash oscillation on gentle and steep slopes , 1989 .

[13]  D. Howell Peregrine,et al.  Low frequency waves in the surf zone , 1993 .

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

[15]  M. Stive.  VELOCITY AND PRESSURE FIELD OF SPILLING BREAKERS , 1980 .

[16]  D. Huntley,et al.  Long Wave Generation by a Time-Varying Breakpoint , 1982 .

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

[18]  J. K. Kostense,et al.  MEASUREMENTS OF SURF BEAT AND SET-DOWN BENEATH WAVE GROUPS , 1984 .