N-m-1 



'(x.t) = \ £ 



i=m+l 



y\ + k ± (xj - x) 



+ 2k. J^ 

 i > t\ 



-( x i- x )7 4et -( x r x )/ 4 



et 



2 ( a " P) 



for t > and -°° < x < 



. £ / /p(2a - p) - x \ + erf / /p(2a - p) + 

 \ 2/eT / \ 2 /it 



(42) 



, 



1 











Vp(2a - p) 









i 



^Tl 



p 







l/^a 









-a a 



Figure 18. Definition sketch for a circular segment-shaped beach 



The quantity N is, as before, the number of corners in the polygon, and m 

 represents the number of corners minus one contained in the angle a . Fig- 

 ure 19 illustrates the transformation of an initially circular segment-shaped 

 shoreline. 



50. Since the tangent of the shoreline orientation (see Equation 5) is 

 infinite at the corners of the semicircle (x = ±a) , the condition of small 



33 



