(Equation 9) does not provide a complete description of the shoreline evolu- 

 tion if diffraction is significant. 



68. Bypassing may occur immediately after construction of a groin and 

 not start just at the time when the groin is completely filled. If the by- 

 passing sand transport rate grows exponentially to a limiting value Q the 

 boundary condition at the groin will be 



1Z= a -J-H _ e" Yt> ) 

 3x o 2 Q V 1 e / 



x = 



(69) 



69. In Appendix B a derivation is given. The quantity y is a rate 

 coefficient describing the speed at which the bypassing sand discharge grows 



toward the limiting value Q 



The solution downdrift of a groin may be 



written (for an initially straight beach) as 



- „-jQ^ 



t -x /4et 



erf c 



\2/Ft" 



-i^J 



r 2 2 // r 2 

 Y? -x /4e5 



d£ 



(70) 



for t > and x > . 



2 

 Employing the two dimensionless parameters, Q^/Q and yL '/e , the solution 



B o 



is illustrated in Figure 30. 



2 

 70. The parameter yL /e describes the rate at which the sand bypassing 



increases in comparison to the size of the coastal constant (e) . In Equa- 

 tion 70 the second term is a transient which decays with elapsed time. Ac- 

 cordingly, after sufficient elapsed time, Equation 70 will be identical to the 

 solution given by Equation 64 with a modified incident breaking wave angle 



at x = (tan ot ss a ) . Equation 70 may be used also to describe shoreline 

 o o 



change updrift of a groin (with reversed sign) if bypassing occurs immediately 

 after construction of the groin. If, in Equation 70, CL/Q = 2ot , the 



50 



