y* -« 



\/4te/k/ 



(19) 



where I is the length of the jett y and E(x//4te/k) is again the error func- 

 tion complement of the argument x//4t£/k. The solution for various times is 

 shown in Figure 39. To describe the updrift beach behavior from t = to 

 t = °°, the solutions given by equations (17) and (19) must be matched at the 

 time when y = £; i.e., when y g = t, t = t' the shoreline from equation (17) 

 must be matched with a shoreline described by equation (19). For t > t' the 

 solution is given by equation (19) with t' = 0.62t substituted for the t in 

 the equation. 



Incident Wove Crests 



y 



I 





.^'~ 



f 



1 





Before Bypassing 



After Bypassing 



Figure 39. Shoreline evolution near a groin (after LeMehaute and 

 Soldate, 1980). 



The bypassing rate is given by the expression 



Q £ / 0.638 \ 

 q77 ~ V /(t/f) - 0.38/ 



(20) 



and is shown in Figure 40. The quantity Q^ is the longshore transport that 

 would occur along a straight beach and is the. transport rate to which Q^ is 

 asymptotic as t ■*■ °°. The coefficients 0.638 and 0.38 in equation (20) were 

 selected to match the solutions described by equations (17) and (19). 



1 



/ 



Asymptote 



All Sand | 

 Retained I 







_^_^_ 



^^Theoretical Bypassing Curve (eq. 20) 



i 



li 



III 



V°7o 



12 3 4 t/t 



Figure 40. Sand bypassing around a groin (after LeMehaute 

 and Soldate, 1980). 



58 



