a = a (l - e " Yx ) 



o m\ / 



(105) 



Here, the quantity Y is a coefficient describing the rate at which the 

 breaking wave angle approaches the undisturbed value a along the x-axis. 



-0.1- 



^-^^^ t ' = . <*^-^^^ 







3» 









O -0.2- 

 M 



en 

 o 

 a. 



u 



2 -0.3- 



_] 

 u 



K 



O 



x 

 en 



V^ 0.8^-^ y/ 



1 .2^^ ./ 



B 2 





1.6^-^ / 





-0.4^ 



2.0^ / 







-0.5 H 









RLONGSHORE DISTANCE (x/B) 



Figure 43. Shoreline evolution behind a jetty with linear 



variation in breaking wave angle in the shadow zone 



(a = -0.1 rad , a = 0.4 rad) 

 V H 



The derivation of the analytical solution is presented in Appendix G. The 



solution is 



a y 

 y(x,t) = -j- 



,/eT -x 2 /4et , . x g / x \ 



, 1 -Yx + etY e I x / — \ 

 + -=■ e erfc ( Y^et I 



Y 2 \2/it / 



1 Yx + £tY 



erfc 



2 /it 



+ Y^et 



a / 2 \ 

 + -= e" YX (l - e~ Y £t ) 



(106) 



for t > and x ^ 



69 



