y (x, t) ■ ■=■ y erfc 



2 /Ft 



(29) 



for t > and -<*> < x < °o . 



The solution is antisymmetric about the y-axis , taking the constant value 



v /2 at x = . If the shape of the shoreline for x > is approximated 

 o 



by a triangle having height y /2 so as to conserve mass, the speed of prop- 

 agation of the triangle's front is inversely proportional to the square root 

 of elapsed time. This relationship is also valid for Equation 26. Figure 10 

 illustrates the solution of Equation 29. The right side of Equation 29 for 

 x > equals half the solution of Equation 26. 



o 0.6- 



RLONGSHORE DISTANCE lx/y ) 



Figure 10. Shoreline evolution of an initially semi-infinite 

 rectangular beach 



Rectangular Cut in a Beach 



39. The initial conditions for rectangular cut in a beach are formu- 

 lated as 



24 



