APPENDIX B: SHORELINE EVOLUTION DOWNDRIFT OF A GROIN WITH 

 BYPASSING REPRESENTED BY AN EXPONENTIAL FUNCTION 



1. Sand is transported past the groin according to the following 

 relationship: 



Q = Q B (1 - e" Yt ) (Bl) 



Here Q denotes the maximum bypassing sand transport rate which occurs at 

 the groin, and y is a rate coefficient describing the rate at which the 

 limiting value Q is approached in time. Using Equation 8, the boundary 

 condition at the groin is written: 



jx u o 2 Q 



^ = a_ - "^ (1 - e"^) x = (B2) 



Consequently, the mathematical statement of this case is, together with the 

 above boundary condition: 



2 



2 at (B3) 



3x 



y(x,t) =0 x + ex, (B4) 



y(x,0) = (B5) 



2. By using the Laplace transform technique, an ordinary linear differ- 

 ential equation is obtained: 



,2- 



d y s — _ 



y = (B6) 



dx' 



2 e 



where y denotes the transformed function of y . The transformed boundary 

 condition is 



Bl 



