The symbol erf denotes the error function which is defined as 



z 



if 



-e 



erf z = — / e * d£ (17) 



At 



The error function is tabulated in standard mathematical reference books 

 (e.g., Abramowitz and Stegun 1965). It is convenient to introduce the fol- 

 lowing dimensionless quantities: 



y' = 2- (18) 



y„ 



(19) 



. _ et 



(20) 



The quantity used to normalize the time variable expresses half the time 

 elapsed before a square beach fill of length a would completely erode at the 

 constant transport rate Q . If the solution is expressed in dimensionless 

 quantities, the resultant shoreline evolution can be displayed in compact 

 form. Figure 7 illustrates how a rectangular fill spreads or diminishes with 

 time according to Equation 16. It should be noted that the vertical scale of 

 this and the following figures has been distorted for the sake of clarity. 



34. Dean (1984) discusses how the sand from two different beach nour- 

 ishment projects spreads with time. The time t „ for a certain percentage 

 P to be lost from the original rectangular beach fill is compared with the 

 corresponding time t for different conditions: 



H 2 - Hi (?)' I 



35. This formula is obtained by noting that the same percentage of 

 beach volume is lost during the same dimensionless time. Consequently, a 



20 



