y i = a sin (irrr) 



(39) 



k. = 



tan 



N - 1 



(40) 



The integer N is the number of corners in the polygon approximating the 

 semicircle. For example, if N = 3 then a triangular beach form is obtained. 

 The solution can be written with the previously defined quantities: 



N-l 



y(x,t) =| J < 



i=l 



I k.x. + y . - k.x] 



V i i ; i i / 



„ £ ill) . erf (iii: 



2v^t 



2/Tt 



+ 2k. 



1 > TT 



-(xJ-x)/4 E t _ -(x^x)/4 £ t 



(41) 



for t > -oo < x < 



»► X 



-a a 



Figure 16. Semicircular-shaped beach approximated by a polygon 



31 



