can be deduced (Baldwin, and Johnson 1972). Much additional work remains 

 to determine which model for v^ is best and to pin down the appropriate 

 closure coefficient associated with it. 



All the above discussion is for onshore-offshore mixing where the 

 characteristics length scale is the surf zone width. A model for turbulent 

 mixing in the alongshore direction (longshore dispersion) has been 

 developed by Lin and Horikawa (1978) . It assumes the surf zone as an open 

 channel with triangular cross section and that the lateral variation of 

 longshore current as the primary mechanism for longshore dispersion. Rip 

 current effects are ignored. The theory when compared with observed field 

 and laboratory measurements is found to agree reasonably well. The model 

 follows concepts originally developed by Fischer (1967) for longitudinal 

 dispersion in natural water courses. Results are of interest for use in 

 two-dimensional numerical models where different cross-shore and longshore 

 dispersion processes are possible. Rip current effects must be included 

 in future efforts in this regard. 



5. Surf Zone Empiricism 



The final closure coefficient needed in all theories for comparisons 

 with measured data is the wave height to total water depth ratio, j. It 

 is often used to estimate both the breaker height and the energy decay in 

 the surf zone. An extensive discussion is presented in Chapter 3; however, 

 this section concentrates on surf zone energy dissipation and those 

 attempts to compare actual measurements with theory. 



All the longshore current theories listed in Table 3 and reviewed in 

 this chapter assume a constant y ratio across the surf zone. Is this 

 correct for all breaker types, beach slopes, wave steepnesses, etc.? 

 Collins and Weir (1969) summarized the results of four experimental inves- 

 tigations on plane beaches as shown in Figure 72. With the coordinates 

 shown, a 45° line would give constant y i^i the surf zone. In general, 

 as beach profile decreased the y ratio departed further and further from 

 being constant across the nearshore area. On flat dissipative-type beaches 

 (spilling breakers as found in the field) the y ratio changed continuously 

 as the rate of energy dissipation decreased with distance from the breaker 

 line. Distance from the breaker line is also important for determining 

 wave heights in the surf zone. This result was confirmed by laboratory 



^^BALDWIN, L.V., and JOHNSON, G.R. , "The Estimation of Turbulent Diffusivi- 

 ties from Anemometer Measurements," submitted to Journal of Fluid Mechanics. 

 Jan. 1972 (no record of JFM publication) (not in bibliography). 



^^FISCHEB, H.B., "The Mechanics of Dispersion in Natural Streams," Journal 

 of Hydraulics Division, Vol. 93, No. HY6, 1967, pp. 187-216 (not in 

 bibliography) . 



192 



