- X 



Figure 41. Definition sketch for shoreline evolution 

 downdrift of a jetty for which a finite number of 

 solution areas is used to model diffraction 



For the first and last solution areas, other conditions prevail on the outer 



boundaries, such as no sand transport at the jetty, and y = as x -*■ +°° . 



86. Extremely complex algebraic manipulations are associated with the 



analytical solution of coupled systems with several solution areas. In Fig- 



ure 42 the solution is presented for two areas, with a , = -0.1 rad , 



ol 



a ~ = -0.-4 rad , and 6 =0.5 . 

 o2 



87. The solution for an arbitrary number of distinct areas is outlined 

 in Appendix E. In Figure 42 are plotted shoreline positions normalized with 

 the length of the shadow region. The length of the geometric shadow region is 

 B = L tan (a ) , where L is the jetty length and a is the incident 

 breaking wave angle in the illuminated region. 



88. If the amplitude of the longshore sand transport rate is considered 

 to be a continuous function of x in the shadow zone, Equation 11 is appli- 

 cable. However, this equation is quite complex, and it is difficult to find 

 analytical solutions even if very simple functions are employed. The related 

 case, in which the incident breaking wave angle is a continuous function of 



66 



