-1 -0.5 0.5 



ALONGSHORE DISTANCE (x/B) 



Figure 42. Shoreline evolution in the vicinity of a groin 

 for variable sand transport rate conditions (two solution 

 areas; 6 = 0.5 



a , = -0.1 rad 

 ol 



a _ = -0.4 rad) 

 oz 



x , is easier to treat analytically and provides interesting solutions, 

 these circumstances, Equation 11 will take the following form: 



Under 



a 2 i a da 



o y _ 1_ oy o 



. 2 " e 3t dx 



dX 



(100) 



in which a is a function of x only. This is formally the same equation 

 as that describing heat conduction in a solid containing a finite source. 

 Consequently, if a grows linearly with x (a = x<* /B) the situation will 

 be identical to the one describing a river mouth of finite length which dis- 

 charges sand at a constant rate. Equations 55 and 56 are the solutions to 



this case, with reversed sign and q_. replaced by a /B . The solution is 



R m 



presented in Figure 26 in dimensionless form. 



89. If a is different from zero at the jetty, but still grows lin- 

 early along the x-axis in the shadow zone, the variation in breaking wave 

 angle will be 



a = a + /a - a \ — 

 o v ^ H vj B 



(101) 



67 



