Here y. and y~ denote shoreline positions corresponding to the longshore 



locations x and x„ . The solution is 



y(x,t) = 



1 / y 2 " y l . y l X 2 - X l y 2 



2 \ x 2 - x L 



x + 



k 2 A l 



X„ - X \ fx. - J 



erf I — - erf ' 



2/et 



2/et 



yo - y, 



1\ let 



r (x r x) 2 /A e t_ -(x 2 -x) 2 /4, 



(35) 



for t > and 



0.5 1 



ALONGSHORE DISTANCE (x/a) 



Figure 13. Comparison between analytical solution with the 

 linearized transport equation and numerical solution with 

 the original transport equation for a triangular beach fill 

 (for height-to-width ratios 1.0 and 0.5) 



The solution for the triangular beach form (Equation 33) can be obtained by 

 superimposing two trapezoidal beach shapes which reduce to triangles. In the 

 same way, in principle, the analytical solution for any arbitrary shoreline 

 shape may be obtained by approximating the shoreline with a series of straight 

 lines. Even though the sand transport at each boundary of the trapezoids in 



28 



