APPENDIX G: SHORELINE EVOLUTION BEHIND A JETTY FOR EXPONENTIALLY 

 VARYING BREAKING WAVE ANGLE 



1. The breaking wave angle varies exponentially with the distance be- 

 hind the jetty from zero at the jetty to the undisturbed value a far from 



m 



the jetty. The mathematical formulation of the boundary condition at the 

 jetty is expressed by Equation 105 (main text). A varying breaking wave angle 

 along the x-axis is described in terms of the diffusion equation by a distrib- 

 uted sink with a decaying strength with distance. The transformed equation 

 and boundary conditions are 



,2- a y 

 d y s_ — m 



.2 e y " s 

 dx 



iz = 



x > (Gl) 



dx ° x " ° < G2 > 



y = x ■* - (G3) 



The solution to Equation Gl is 



2 -qx -yx 



aye a ye 



y = " — T2 2\ + "J! 2\ (G4) 



qs(j - q J s(j - q ) 



Equation G4 may be written as partial fractions: 



-qx 

 a Y e 



Vq - Y q + y/ Y \ s _ y \ a) 



y = —2&- ^^^ ~ ^^> ~ "^— 1—^^ " rl (65) 



In Equation G5, the last term may be inverse transformed to yield 



6 - ^) 



-yx 



Ct 6 



y 2 = JL ir V 



Gl 



