40. Since the present situation is the inverse problem of the rectangu- 

 lar beach fill, Figure 8 can be used to evaluate the rate of infilling of a 

 certain volumetric percentage of sand. 



Triangular-Shaped Beach 



41. The triangular-shaped solution is also mentioned by Walton and Chiu 

 (1979). The original beach has the shape of a triangle according to the 

 initial conditions as follows: 



y(x,0) = 



< x < a 



-a < x < 

 |x| > a 



(32) 



In this case the solution takes the following form: 



y(x,t) = Yg \ ( a - x ) erf 



/*^JE\ + (a + x) erf / ^f\ - 2x erf /-£--\ 

 \2/ e t ) \2/ e t / \2/ e t/ 



+ *4¥l-- 



(x+a) 2 /4 e t . -(x-a) 2 /4 e t . -x 2 /4 e t 

 + e - ze 



1} 



(33) 



for t > and -<» < x < » . 



A nondimensional illustration of the shoreline evolution from an initially 

 triangular beach is shown in Figure 12. 



42. Depending upon the height-to-width ratio of the triangle, lineari- 

 zation of the transport equation may reduce accuracy of the analytical solu- 

 tion. However, even though the assumptions forming the basis for the lineari- 

 zation procedure appear to be extremely limiting (particularly in requiring 

 small wave angles) , in practice the analytical solution is found to be appli- 

 cable for angles as large as about 45 deg between the shoreline and the break- 

 ing waves. In order to estimate the effect of the linearization, a comparison 



26 



