with a finer grid ( Ax = Ay = 30 ft) and a time-step of 0.25 sec. Figure 16 

 shows a comparison between the numerical model calculations for longshore 

 current and the analytical solution of Longuet-Higgins (1970). As the cell 

 size and time-step are reduced, the numerical solution approaches the 

 analytical solution of Longuet-Higgins. The grid cell size and time-step 

 would have to approach zero for the solutions to agree identically, since the 

 Longuet-Higgins analytical solution has an infinite gradient at the breaker 

 line that only can be resolved with infinitely small grid cells. Of course, 

 when lateral mixing is considered, the infinite gradient disappears. Figure 

 17 shows the effect of lateral mixing on the numerical solution for longshore 

 velocity distribution. The mixing parameter P was defined by Longuet- 

 Higgins (1970) as 



p=1 N_tan_e 

 Y c 



where tan 6 is the bottom slope of the plane beach and N is an empirical 

 coefficient which varies between and 0.016. P = corresponds to no 

 lateral mixing. Figure 17 presents the numerical solution for P between 

 0.01 and 0.4. For completeness, the analytical solution of Longuet-Higgins 

 for P = is also shown in the figure. Based upon laboratory data, Longuet- 

 Higgins suggested that P varies generally in the range of 0.1 to 0.4. 

 Increasing values of P (therefore increasing lateral mixing) reduce the 

 magnitude of the peak velocity, move the location of the peak velocity closer 

 to the shoreline, and increase the velocities offshore of the breaker line. 

 Figure 17 demonstrates that the numerical solution does indeed exhibit the 

 proper behavior. 



47. To demonstrate an application of the wave- induced current and setup 

 model to Oregon Inlet, a particular wave condition that occurred during the 

 1962 Ash Wednesday storm was selected. From the WESWIS, a wave with a height 

 of 11.39 ft, period of 8.0 sec, and an angle 9 of 51.1 deg in 60-ft depth 

 was selected. This particular wave condition was selected since the angle of 

 incidence is large, and thus it is a good test of the stability of the model 

 for large angles of incidence and complex bathymetry. The wave propagation 

 numerical model was used to calculate the wave height, direction of propaga- 

 tion, and wave number at every grid cell. 



39 



