occurred without the seawall (dashed line). The incident waves then swing 

 in direction and arrive obliquely from the left for 138 hr, as seen in Fig- 

 ure 10c. Sand is transported past the center of the seawall to form a wide 

 beach adjacent to the right headland. The beach planform in (c) is not a mir- 

 ror image of (b) because, although the waves were mirror images, the initial 

 shoreline conditions were different. 



83. In Figure 10c, the seawall is protecting approximately half of the 

 shore, and much of the eroded sector is still located on the right side. In- 

 tuition might have suggested more erosion on the leftmost side since the more 

 recent waves were from the left. However, the interaction between waves and 

 shoreline is nonlinear (Equation 2, the sine dependence), and the calculated 

 change is different than might be expected. Finally, almost normally incident 

 waves arrive to the coast for 72 hr, to give the result shown in Figure 10d. 

 The beach has essentially returned to its initial planform, Figure 10a. A 

 beach again exists all along the front of the seawall. 



84. In this example, the seawall protected the beach under episodes of 

 oblique wave incidence, preventing excessive landward retreat of the shore- 

 line. The seawall therefore worked to promote recovery of the beach (compare 

 solid and dashed lines in Figure 10d). It should be cautioned that this re- 

 sult is partially an artifact of the assumption of an equilibrium (constant) 

 profile. In nature, the beach profile in an eroded area would probably become 

 steeper than the average beach profile; it then might take a longer duration 

 of the normally incident waves to cause the beach to recover. 



Comparison of Accuracy and Efficiency of the Explicit 

 Scheme and the Implicit Scheme 



85. The configuration of Example 2 was used to compare the numerical 

 accuracy and efficiency of the explicit and implicit numerical solution 

 schemes when operating under the seawall constraint. Although the results are 

 necessarily site-dependent, experience has shown the trends to be representa- 

 tive and the conclusions qualitatively correct. Kraus and Harikai (1983) gave 

 a similar comparison of explicit and implicit numerical schemes for shoreline 

 models without the seawall constraint. 



86. The results of the comparison are shown in Table 1. The wave input 

 used was that in Figure 10b and run for 120 hr. The values of key parameters 

 were the same as in the previous examples: maximum wave height H max = 3 m , 



36 



