The earliest effort to compare nearshore mixing theories was by Bowen 

 and Inman (1974). Table 9 presents estimates of v^ (A^) from the limited 

 available field and laboratory studies by Inman, Tait, and Nordstrom (1970) 

 and Harris, et al. (1962). Also included are vl values that Thornton 

 (1970a) used to reproduce longshore current observations with his theory. 

 Although the eddy viscosity varies over almost four orders of magnitude 

 from laboratory to field, the closure coefficient N shows a relatively 

 small range of variation from 0.009 to 0.065 with an average N i 0.03 

 across the surf zone. This value is considerably larger than that used 

 by Longuet-Higgins (1970) to verify his profile theory (N = 0.0024 to 0.0096 

 from Galvin and Eagleson, 1965, see Table 8). One explanation is that his 

 model overestimates v^ beyond the surf zone (Longuet-Higgins, 1972a) so 

 that it much smaller v-^ values are used outside the breakers, a larger mean 

 coefficient is needed to reproduce observed profiles (Bowen and Inman, 

 1974). Paradoxically, because direct measurements of eddy viscosity by 

 dye diffusion in the field are difficult, Bowen and Inman (1974) state 

 that estimates of Vt by fitting observed velocity distributions to theory 

 may be a more accurate method. 



Nielsen (1977) used the available field and laboratory data in Table 

 9 to test four different theories for v^ • These were by Longuet-Higgins 

 (1970) and Jonsson, Skovgaard, and Jacobsen (1974), and were similar to 

 Thornton (1969, 1970a), Inman, Tait, and Nordstrom (1970), and Battjes 

 (1975, 1978). The comparison is summarized in Table 10 and only for surf 

 zone mixing. Based on Nielsen's analysis of mean values of eddy viscosity 

 across the surf zone v*, the model by Longuet-Higgins is preferred. The 

 resulting empirical constant of 0.007 gives N = 0.018 which is near the 

 maximum value of 0.016 predicted by Longuet-Higgins (1970, 1972a). It is 

 not clear why these results by Nielsen for N, using essentially the same 

 data, differ from those by Bowen and Inman (1974) who obtained N s 0.03. 

 Also, the average eddy viscosity (v*) is not indicative of how the Vt 

 variation across the surf zone and beyond produces the proper longshore 

 current profile. Figures 61 and 62 give an idea of how widely vt can 

 change in this regard. 



Finally, as discussed by Nielsen (1977), Vj is riot a true eddy 

 viscosity for turbulent diffusion. It is really a combined transport- 

 dispersion coefficient since much fluid is advected shoreward in the 

 upper layers by the reference celerity for breaking waves. An excellent 

 summary of all models before 1978 can be found in Gourlay (1978). 



The trend since 1978 is to use separate models and coefficients 

 within the surf zone and beyond the breaker line (Skovgaard, Jonsson, and 

 Olsen, 1978; Kraus and Sasaki, 1979). Completely different closure coef- 

 ficients result in each region (see Table 8). It will be extremely bene- 

 ficial in the future to use the newly available field data on longshore 

 currents (NSTS) to estimate separate Vt and closure coefficients by fitting 

 the data. It will also be appropriate to consider new ways to analyze the 

 available velocity time histories across the surf zone. One possibility is 

 to use auto- and cross-correlation techniques to estimate Lagrangian 

 length scales from which Eulerian length scales and local eddy viscosities 



190 



