in which a is the incident breaking wave angle at the ietty, and a„ is 

 v H 



the angle in the illuminated region. The mathematical description for this 

 case is almost the same as for a river mouth of finite length which discharges 

 sand but with a modified source term. This is a coupled problem containing 

 two solution areas but with a boundary condition at the jetty given by 



9x 



= tan a 



(102) 



The analytical solution to this problem is (see Appendix F) 



YjCx.t) = 



(a H - a v )et 



„.2 / B - x \ , .2 / B + x ■ 



2i erf c I + 2 1 erf c ( | - 1 



2/et 



2/et 



- tan a 



\ir ' 



-x"/4et 



- x erfc 



2 /Ft 



(103) 



for t > and ^ x ^ B 



y 2 ( x .t) 



(a R - a v )et 



o- 2 e / x + B \ „ .2 . /x - B 

 2i erfc ( ) - 2 i erfc 



2/et 



2/et 



- tan a 



\? ( 



-x /4et 



- x erfc 



2/et 



(104) 



for t > and x > B . 



The quantity B is the geometric length of the shadow zone as before. In 



Figure 43, the dimensionless shoreline evolution is presented for the specific 



case of a = -0.1 rad and a„ = 0.4 rad . Shoreline position has been 

 v H K 



normalized by the length of the shadow region. 



90. Another case that allows a fairly easy analytical solution is ob- 

 tained by assuming that the incident breaking wave angle varies exponentially 

 with distance from the jetty according to 



68 



