where 



V = — and X = — (70) 



V X K 



o b 



v being the longshore current velocity at a distance x from the shoreline, 

 x. being the width of surf zone, and v Q being given by 



V o = 16 ™ V 5 "^^ ^1 S in 9 b cos 6 b (71) 



P, = - t + \\t + ±s (72) 



1 k yj 16 z? 



yj 16 + ?p 



P 2 = -f- ' : 



The coefficients in the solution are 



A = 1 - 1.5 P, (74) 



(P, - 1) A 



B l ■ p - P (75) 



1 1 2 



C- 5- (76) 



(1 + 0.375 y ) 



where tan 3 is the beach slope, P is the mixing parameter of Longuet- 



Higgins given by Equation 68, and y is the breaker index. Using the above 



velocity distribution and noting that the total sediment transport rate Q-^ 

 across the surf zone is given by 



X b 



Q n = C / v d dx (77) 



1 s ' 

 o 



in which C is the average sediment concentration (dimensionless) across the 

 surf zone, and d is the water depth, one may obtain the following result 

 after integration: 



48 



