4.442 Velocity Prediction . The variation in longshore current velocity 

 across the surf zone and along the shore, and the uncertainties in vari- 

 ables 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 (1970); an adaptation 

 from Bruun (1963); and Galvin (1963). All three equations require co- 

 efficients identified by comparing measured and computed velocities, and 

 all three show about the same degree of agreement with data. Two sets of 

 data (Putnam, et al., 1949, field data; Galvin and Eagleson, 1965, labora- 

 tory data) appear to be the most appropriate for checking predictions. 



The radiation stress theory of Longuet-Higgins (1970a, Equation 62), 

 as modified by fitting it to the data, is the one recommended for use 

 based on its theoretical foundation. The other two semiempirical equa- 

 tions may provide a check on the Longuet-Higgins prediction. Written 

 in common symbols (m is beach slope; g is acceleration of gravity; H^ 

 is breaker height; T is wave period; and a^j is angle between breaker 

 crest and shoreline), these equations are: 



a. Longuet-Higgins . 



vj, = M, m(gHj,)*/^ sin2aj, , (4-14) 



where 



0.694 r(2i3) 



'2 



M, = / "^ (4-15) 



y 



According to Longuet-Higgins (1970a, p. 6788) , v^ is the longshore cur- 

 rent speed at the breaker position, r is a mixing coefficient which 

 ranges between 0.17 (little mixing) and 0.5 (complete mixing), but is 

 commonly about 0.2; g is the depth-to-height ratio of breaking waves 

 in shallow water taken to be 1.2 and fj? is the friction coefficient, 

 taken to be 0.01. Using these values, M,= 9.0. 



Applying equation 4-14 to the two sets of data yields predictions 

 that average about 0.43 of the measured values. In part, these predicted 

 speeds are lower because v^j, as given in Equation 4-14 is for the speed 

 at the breaker line, whereas the measured velocities are mostly from the 

 faster zone of flow shoreward of the breaker line. (Galvin and Eagleson, 

 1965.) Therefore, Equation 4-14 multiplied by 2.3 leads to the modified 

 Longuet-Higgins equation for longshore current velocity: 



V = 20.7 m(gHj,)'/^ sin 2ay , (4-16) 



used in Figure 4-16. Further developments in the Longuet-Higgins' (1970b 

 and 1971) theory permit calculation of velocity distribution, but there 

 is no experience with these predictions for longshore currents flowing 

 on erodible sand beds. 



4-48 



