s 

 0. 



_ 



Q. '■ 



y i " 



y- 



i 



1 





i ; 



h ~ 



y 



L 



* 







y i 



- 



y s i 



Q- 1 



- 



(J. 









1+1 





i+ 



1 h 



■ 



h 



(6a) 

 (6b) 



The logic behind Equation 6 is perhaps more clearly understood by rearranging 

 terms, to give, for example, 



Q Q* 



(7) 



y^ ~ Ji y± ~ i 



from which it is seen that, whereas Q- causes the shoreline to move from y, 

 to y! , the corrected transport rate Q. moves the shoreline from y. to 

 ys^ (as required) . 



54. By substitution of Equation 6 into Equation 5, with Q^ and 

 Q i 1 replaced by Q. and Q. , respectively, it is verified that the 

 corrected shoreline position is 



Y i = ys i (8) 



Since the adjustment was made through use of the continuity equation, the pro- 

 cedure conserved sand volume. 



Correction at a 



regular cell (Figure 7b) 



55. With corrections at the minus cell completed, adjustments continue 

 for cells on both sides, following the direction of transport. The transport 

 rate at an updrift face will have previously been corrected and should not be 

 corrected again. Assuming for the purpose of explanation that the transport 

 rate through a particular cell is in the positive x-direction, the adjusted 

 downdrift transport rate Q is obtained by setting the new position y! 

 equal to ys. in Equation 5, to give 



ys. =y. + 2B(Q. -Q* +1 ) (9) 



The corrected transport rate is then 



» y s i - Yi 



*i + 1 - Q i - ^2B-^ (10) 



23 



