In the limit N + °° the polygon coincides with a semicircle. The solution 

 (N = 101) is illustrated in Figure 17 which shows the shoreline evolution as a 

 function of time for an initially semicircular-shaped beach. 



t 1 = o 



0.5 1 1.5 2 



ALONGSHORE DISTANCE (x/a) 



Figure 17. Shoreline evolution of an initially semicircular 



beach 



49. If the beach is formed as a circular segment, the solution may be 

 derived by superimposing Equation 41 with the appropriate summation limits and 

 Equation 16 with reversed sign. In Figure 18 a definition sketch is shown. 

 If the pitch height is denoted by p , then the width of the circle segment 

 becomes 2v'p(2a - p) . Furthermore, the height of the rectangular fill is 

 a - p , and the angle a (see Figure 18) is arc sin (1 - p/a) . Conse- 

 quently, the summation of the solutions for the polygon stretches should start 

 at angle a in the semicircle and end at angle it - a . The solution is 



32 



