with wave height. This increase in width increases the cross section of the 

 surf zone. 



If the surf zone cross section is approximated by a triangle, then an 

 increase in height increases the area (and thus the volume of the flow) as the 

 square of the height, which nearly offsets the increase in energy flux (which 

 increases as the 5/2 power of height). Thus, the height is important in 

 determining the width and volume rate of longshore current flow in the surf 

 zone (Galvin, 1972b). 



Longshore current velocity varies both across the surf zone (Longuet- 

 Higgins, 1970b) and in the longshore direction (Galvin and Eagleson, 1965). 

 Where an obstacle to the flow, such as a groin, extends through the surf zone, 

 the longshore current speed downdrift of the obstacle is low, but it increases 

 with distance downdrift. Laboratory data suggest that the current takes a 

 longshore distance of about 10 surf widths to become fully developed. These 

 same experiments (Galvin and Eagleson, 1965) suggest that the velocity profile 

 varies more across the surf zone at the start of the flow than it does 

 downdrift where the flow has fully developed. The ratio of longshore current 

 speed at the breaker position to longshore current speed averaged across the 

 surf zone varied from about 0.4 where the flow started to about 0.8 or 1.0 

 where the flow was fully developed. 



b. Velocity Prediction . The variation in longshore current velocity 

 across the surf zone and along the shore, and the uncertainties in variables 

 such as the surf zone hydrography, make prediction of longshore current 

 velocity uncertain. There are three equations of possible use in predicting 

 longshore currents: Longuet-Higgins (1970b), an adaptation from Bruun (1963), 

 and Galvin (1963). All three equations require coefficients identified by 

 comparing measured and computed velocities, and all three show about the same 

 degree of agreement with data. Two sets of data (Putnam, Munk, and Traylor, 

 1949, field data; Galvin and Eagleson, 1965, laboratory data) appear to be the 

 most appropriate for checking predictions. 



The radiation stress theory of Longuet-Higgins (1970a, eq. 62), as 

 modified by fitting it to the data is the one recommended for use based on its 

 theoretical foundation: 



Vj^ = Ml m (gH^)^^^ sin 2aj^ (4-20) 



where 



and 



m = beach slope 



g = acceleration of gravity 



Hi^ = breaker height 



a, = angle between breaker crest and shoreline 



M = 0'^^^ r(2e)-^/^ (,_2i) 



^ f 



4-54 



