

0.3- 



\ t' = 



t' = 



et 



a 2 













o 



3] 



0.2- 



N^p, i o \ 







O 



H 



c7) 



o 



Q_ 



LJ 



Z 



_J 

 (il 



0.1- 



^0.20 \^ \ 



0.40 ^nV 



. 60~~~~~~-~~-^V\,!v 







o 



1 .00 \ . 





(/) 



0.0- 









0.5 1 1.5 2 



ALONGSHORE DISTRNCE (x/a) 



Figure 19. Shoreline evolution of an initially circular 

 segment-shaped beach (a = 45 deg) 



angles is violated. This condition implies, as previously discussed, that the 

 sand transport is overestimated, leading to a faster dispersion process of the 

 shoreline toward the stable condition (a beach parallel to the wave crests) . 

 An analytical solution for a circular segment-shaped beach, however, will show 

 better agreement with the numerical solution of the original sand transport 

 formula if the angle of shoreline orientation is small at the edges. A com- 

 parison between an analytical and a numerical solution for a circular segment 

 beach is illustrated in Figure 20. In this case the linearization approxi- 

 mates the transport equation well; thus, the solution is accurate. 



Semicircular Cut in a Beach 



51. The situation of a semicircular cut in a beach is the antisymmetric 

 analog of the case described in the previous section. A solution is obtained 

 by superimposing Equation 41 with opposite sign for a beach of width a . The 

 solution is displayed in Figure 21. 



34 



