Initially Filled Groin System 



72. Dean (1984) presents an analytical solution for shoreline evolution 

 between two identical groins which define a compartment initially filled with 

 sand. The distance between the groins is denoted by W , and the groin length 

 is L . At time t = , the shoreline is exposed to the action of waves 

 breaking with angle a . The solution is 



y(x , t) = L . W (l - |) tan a Q + ^^ ][ I [ ^ ^ 



n=0 (^ 



-e(2n+l 



)Vt/4W 2 r(2n+l)TTx"| I 



COS |_ 2W J f (71) 



for t > and < x < W 



The boundary conditions for this configuration are no sand transport at x = 

 (8y/9x = tan a ) and a constant shoreline position of y = L at x = W . 

 Consequently, bypassing occurs at the boundary x = W , whereas no sand enters 

 the system at x = . This occurrence means that the solution is unsuitable 

 for application to a groin system of more than one compartment. Otherwise, 

 bypassing must be accounted for in the boundary conditions at the updrift 

 groin (left) in each compartment leading to a coupled problem. The last term 

 in Equation 71 approaches zero as t ■> °° and causes a shoreline parallel to 

 the wave crests to be created between the groins. In Figure 33 the analytical 

 solution is presented in dimensionless form. All distances have been nor- 

 malized with the compartment width W . 



73. The final percentage loss of sand from the groin compartment is 



■x 7- tan a (72) 



L L O 



53 



