Figure 15. Shoreline of arbitrary shape approximated by N 

 straight lines 



46. The shoreline position can be written, accordingly: 



(x,t) -I £ 



i=l 



- erf 



i+1 



x + 



y i x i+l " X i y i+1 



'i+1 



i+1 



2/et 



i+1 



'i+1 



- y.i 



erf 



2 J — 



'4et 



2 /it 



Et 



for t > and -°° < x < 



(36) 



Semicircular-Shaped Beach 



47. In order to find an analytical solution for a beach formed in a 

 half circle between -a < x < a , the circle is approximated by a polygon with 

 a finite number of corners (Figure 16) . 



48. The solution can be obtained using Equation 36 with proper expres- 

 sions for the line segments. The following quantities are defined: 



R l "(i - Oi l 



. = a cos |__ __ j 



x i = a cos (f5t) 



(37) 

 (38) 



30 



