APPENDIX D 

 LONGSHORE CURRENT PROFILE THEORY EQUATIONS 



The equations for the longshore current profile theory of Kraus and 

 Sasaki (1979) are found by expanding v in a power series and determining 

 the unknown coefficients by the boundary conditions. Namely, v and dv/dx 

 must be continuous at the breaker line at v finite at the limits X-^0 and 

 infinity. Introducing dimensionless variables V and X defined by 



V = ^^ . X = 



^b 



where 



\ 



tan 3 



^^""^(1+3/728) '^"^ ^f 



/gh^ -—^ (D-1) 



and essentially equivalent to the modified reference velocity with correction 



for wave setup without the cosa, term (eq. 72). 



Expressed in dimensionless variables the general solution of equation 

 (42) is 



E (A X+B X^)X^ , < X < 1 



n n ' 

 n=0 



V ={ ^ (D-2) 



E C X'^"'^ , 1 < X < - 



n=0 



where 



n = 



l-(5/2)P 

 A={ ._^2^_^ (D-3a) 



n = 1,2,.. . 



n-1 



l-(n+l)(n+5/2)P 





1 



, 



n=0 



a 

 n 



"^ l(2n+5)(2n-3)! 



5 „n , 

 2 n! 



!^2n ^ 



n=l,2, 



ith, b 



= sina, 

 b 







(D-3b) 



242 



