0.5 1 1.5 2 



ALONGSHORE DISTANCE (x/a) 

 Figure 12. Shoreline evolution of an initially triangular beach 



was made between the analytical solution and a numerical solution with the 

 original sand transport equation (Equation 7). Figure 13 shows the result as 

 a function of the height-to-width ratio and elapsed time. 



43. It is quite clear that the analytical solution produces a higher 

 rate of shoreline change by overestimating the longshore sand transport rate 

 (since a > sin a). Thus, if the analytical solution is used to estimate the 

 time scale involved in beach nourishment problems, a higher rate of attenua- 

 tion of the fill will always be obtained than is expected to actually occur. 



Trapezoidal-Shaped Beach 



44. A trapezoidal beach form is described by the following initial 

 conditions: 



y(x,0) = 



y-i - yi 



X + 



y l X 2 " X l y 2 



(34) 



X < X, , X > x r 



27 



