in which £ = tan£/(H /L ) 1/2 is the surf similarity parameter, H b is the 

 breaking wave height, h b is the depth at breaking, tan/9 is the average 

 bottom slope evaluated over a distance of one third the wavelength seaward of 

 the break point, H /L is the wave steepness, and H and L are the 

 deepwater wave height and wavelength. On the basis of laboratory measurements 

 (Mimura, Otsuka, and Watanabe , 1986) and recent model tests and comparisons to 

 field data (Larson, Kraus, and Sunamura, 1988), significant wave height should 

 be used in the breaking wave (Equation 2) and sand transport (Equations 4-6) 

 calculations , whereas mean wave height should be used to predict the net sand 

 transport direction (Equation 3). 



Wave height and mean water level, including setdown, setup, and runup, are 

 calculated at each time step by using the profile shape determined from the 

 profile change model at the previous step. In this quasi -stationary solution 

 approach, changes in representative incident waves and bathymetry are assumed 

 to occur on a long time scale compared to the wave period. 



Profile Change Model 



Transport direction 



Larson (1988) examined several criteria for distinguishing bar and berm 

 formation. Net direction of cross -shore sand transport was found to be 

 closely related to profile type, with onshore transport predominant on 

 profiles exhibiting berm growth and offshore transport predominant if a 

 notable bar appeared near the break point. The criterion for distinguishing 

 profile type shown in Figure 1 was developed and is used in the model to 

 determine net transport direction: 



H 



3 



— < C (H /wT) , erosion 

 L o 



3 

 — > C (H /wT) , accretion 

 L o 



(3) 



in which C = 0.00070 is an empirical coefficient, w is the sand fall 

 speed, and T is the wave period. The parameter H /wT is called the dimen- 



93 



