to propose the following empirical equation (see Fig. 57) 



V, = 2.7 U, sin a, cos a, (156) 



J5 bm b b 



Considerable discussion of equation (156) can be found in Longuet-Higgins 

 (1970). Gourlay (1978) reanalyzed the same data using higher average ,^ 

 values of y estimated from the wave breaking criterion of Weggel (1972) 

 which includes beach-slope effects. He obtained the empirical result 



V]^ = 3.72/gHr tan e sin 2a (157) 



When using new data by Lee (1975) from western Lake Michigan, the coeffi- 

 cient in equation (157) was 2.87 and the differences attributed to the 

 coarser materials present to give a rougher bed. The empirical expression 

 by Komar (eq. 156) in revised form (using eq. 53 and taking y = 0.78) 

 could be written 



Vj^ = 0.60v^Hr sin 2a^ (158) 



Komar argued that the ratio of beach slope-to-bed friction coefficient 

 was essentially constant so that tan g did not appear in his result. 



Dette (1974a) measured longshore currents on the west coast of the 

 Island of Sylt in the North Sea for comparison with all the available formu- 

 las at that time, including those based on radiation stresses. He concluded 

 that the best agreement was obtained with the relation (in dimensionless 

 form) 



V = 0.32vgH^ sin 2a^ (159) 



If it is assumed this average longshore current is equivalent to the mid- 

 surf velocity, then these empirical results for sand beaches (like Komar 's) 

 are also independent of beach slope. 



Kraus and Sasaki (1979) analyzed why equation (156) or (158) satisfied 

 the field data over a wide range of beach slopes, breaker angles, and beach 

 materials. As demonstrated in Figure 30 based on their radiation stress 

 theory for large wave angles, it is seen that the midsurf velocity, vj, 

 remains almost constant for 0.01<F*<0.1. Here p^ _ JL r tan g is differ- 



^ ~ 2 1+3yV8 

 ent than Longuet-Higgin's P. Also, vj^ varies less than 20 percent for 

 av up to 20° and is about 0.5 over a broad range. Kraus and Sasaki show 

 why (for both laboratory and field data) P*<0.1 so that the empirically 

 determined, single factor of 2.7 in equation (156) can describe longshore 



6 S 



WEGGEL, J.R. , 'Maximum Breaker Height," Journal of Waterways y Harbors j and 



Coastal Engineering division^ Vol. 98, No. WW4, 19 72, pp. 529-548 (not in 



bibliography). 



170 



