The original model theory for uniform longshore current profile on a 

 plane beach includes many assumptions and is based upon the idealized 

 environment in Table 2. It has laid the foundation for all subsequent 

 modified theories by providing both a qualitative and an order- of -magni- 

 tude agreement with the data. Consequently, equations (61), (66), and 

 (67) plus those associated with them, must now be replaced by more general 

 and accurate formulations. Longuet-Higgins (1972b) recognized these defi- 

 ciencies and made some recommendations for improvements that were incor- 

 porated in the subsequent modified models. The major limitations of the 

 original model theory were 



(a) Bed stress model for weak currents and small angles, 



(b) wave setup effects neglected, 



(c) excessive lateral mixing stresses outside the surf zone, and 



(d) results only applicable to plane beach slopes. 



Table 3 identifies the modified theories. All include some wave 

 setup effects based upon a constant y ratio in the surf zone. For the 

 reasons just discussed, it is concluded that further refinements are 

 possible in the near future. With these limitations, two modified theories 

 have emerged recently that have shown good comparisons with experimental 

 data. 



The theory of Skovgaard, Jonsson, and Olsen (1978) is more generally 

 applicable (i.e., monotonically decreasing profiles) but requires numerical 

 solution procedures. Its key strength is a different lateral mixing form- 

 ulation outside the surf zone that matched some limited laboratory data 

 for currents and also observations of mixing intensities in nature. Its 

 major weakness is the strong current small- angle formulation for bed shear 

 stress. This assumption is inconsistent with the fundamental physical 

 fact that strong longshore currents appear when the angle of wave attack is 

 large. Small incidence angles produce nearshore circulation cells, rip 

 currents, and two-dimensional flow patterns. 



The best available analytic theory at this writing is that recently 

 developed by Kraus and Sasaki (1979), but holds only for plane beach 

 slopes. It includes wave refraction effects, wave setup, different lateral 

 mixing formulations within and beyond the breakers, and a weak current 

 large-angle bottom stress formulation. For the latter assumption, the 

 ratio of Vjj^/ugjjj is found to be relatively small in the field to justify 

 the weak current large-angle model employed. The results compared favor- 

 ably with new laboratory data (Fig. 66). The theoretical curves are fitted 

 to the data by requiring the theoretical location of the maximum velocity 

 VjQ to match the experimental results. The dimensionless longshore current 

 profile given by equation (91) and Appendix D (see also Fig. 30) with key 

 dimensionless parameter P* (eq. 92) should be employed. It should be tes- 

 ted against other laboratory and field data from which Cf and T values 

 can be determined. For bar-trough profiles, a numerical solution procedure 

 is necessary. More exact bottom shear-stress and surf zone dissipation 

 models can then be employed in the numerical procedures. 



225 



