Huntley (1976) showed that the assumption for using equation (51) 

 based on v << u-^^ is invalid for his data so that Cf values so deduced 

 are not a true bottom friction coefficient. He defined another C* in the 

 equation of motion (neglecting lateral mixing stress) as 



1^ [pmF (n + h)] = - pC*|u|v " (161) 



where u, v Include both wave orbital velocities and turbulence. It 

 must be noted here that the right-hand side of equation (161) 

 is not the same as equation (52) where U is the total velocity vector. 

 A two-component current meter on a relatively flat beach (tan 3 = 0.01) 

 was employed to directly measure u and v, and hence U and v. From equation 

 (161) Huntley directly computed the values of C* shown in Table 8. By 

 the same procedure, C^ values were calculated using Ug in place of U in 

 equation (161). It is not clear why the term 2/it in (eq. 5) was dropped 

 from the later calculation by Huntley. The value of C^ is generally larger 

 than C* found from equation (161). The difference was found to vary across 

 the surf zone and with approach angle. It is fairly clear that the wide 

 range of Cf values deduced in the literature is partly due to the incorrect 

 weak current small- angle model employed . 



Finally, C* values based upon equation (161) must also be considered 

 somewhat questionable for the following reasons. The left-hand side of 

 equation (161) is also an approximation of the true gradient of the radia- 

 tion stress in that (a) the mass flux term is neglected, and (b) the term 

 uv is assumed independent of water depth. Only single position measurements 

 were made with a meter in the water column. In addition, lateral turbulent 

 mixing stresses are combined into C* and steady uniform flow conditions 

 must be present in the field. Huntley (1976) presented methods and arguments 

 in support of his contention that wave-induced turbulence effects were 

 relatively small compared with the wave orbital interactions. 



Recently, Thornton (1980) overcame some of these questions by directly 

 measuring the radiation stress component, S^^, offshore and by indirectly 

 computing it inshore (in the surf zone). Thus, a simple steady-state wave- 

 induced current model for a straight and parallel contour beach is employed 

 to estimate C*. 



f^ = - Th^ = - pC*|uIv (162) 



dx ^y f 



The right-hand side is identical to equation (161) but the left hand side 

 is not. 



Outside the breakers, a linear array of five pressure sensors (in 

 10-meter water depth) was used to measure S^y for a series of experiments 

 at Torrey Pines Beach, California (tan g » 0.023), in connection with the 

 NSTS (see Guza and Thornton, 1979, for details). In the surf zone, wave 

 angle measurement directional errors made this procedure inaccurate 



187 



