in which y and y denote the transformed shoreline position corresponding 

 to the regions behind and outside the breakwater, respectively, and L is 

 half the length of the breakwater. Solving the system of equations subject to 

 the boundary conditions yields 



x q l X 



6a ol e l r . / x 



^r ^r + L 6 cosh ( q i x ) 



- sinh 



(v) 



6a 



tan a 



ol 



-q x L 



ol 



6 + 1 



q.s(6 sinh q^ + cosh q.L) 



-L < x < (C7) 



6a 



3S - - 



ol 



-q 9 x 



6+1 q,s 



6a 



tan a 



ol 



-q x L 



ol 



6 + 1 



-q x 



6e 



q 1 s(6 sinh q.L + cosh q.L) 



x > 



(C8) 



where 



6 "^o2 



q i = I7 



qo - 



(C9) 



2. The inverse transform of Equations C7 and C8 may be obtained by use 

 of the Fourier inversion theorem (Appendix A) or by expanding the denominator 

 in a Taylor series and finding the inverse transform of each term in the 

 series. The latter method will be used here. The denominator may be 

 rewritten as 



q x L 



q.s(6 sinh q^ + cosh q L) = - q s e (6 + 1) 



-(m) 



-2q 1 L 



(CIO) 



The last term in Equation CIO is expanded in a Taylor series according to 



-2q.L 



-1 



n -2q nL 



1 - \ttt) e = Z {T-n) e 



(Cll) 



n=0 



C2 



