Fig. 24). In their original contributions, both Collins (1972) and Battjes 

 (1974a) chose to omit the lateral mixing term since their irregular wave 

 theories provided the same effect. They recognize, however, that such a 

 term should also be included in future analysis. 



Some example results from Collins (1972) are presented in Figure 41 

 for two beach profiles. The flatter slope produces a wider surf zone and 

 broader longshore current profile. The dashlines are for regular waves with 

 the same total energy content from the original theory of Longuet-Higgins 

 (19 70). No lateral mixing stress terms are involved. The extent and magni- 

 tude of the longshore current outside the breaker line is excessive and per- 

 haps due to the lack of nonlinear interactions in Collins' approach. 



The results obtained by Battjes (1974a) are more realistic in this re- 

 gard. A weak current small-angle bed shear-stress model (eq. 51) was em- 

 ployed. For irregular waves with a narrow spectrum, Battjes took the time 



mean wave orbital velocity near the bottom. 

 This gave 



u rather than the maximum. 



- _ H , to -, 



^B - 7 [y^] 



(126) 



1 



1 



/ 



1 1 



1 



I 



6 



/ 

 / 







— 



5 



- / 







- 



4 



/ 

 - / 











/-I/25 







3 



\ / 1 





- 



2 



1 



/ / 



A^ 



^'"° 









'/ 1 



\ i 

 1 IK 



1 



^.^^^ 



200 400 



DISTANCE OFFSHORE, ft. 



600 



Figure 41. Illustration of the effect of offshore bottom slope on 

 longshore currents, deepwater wave angle = 30°, deep- 

 water wavelength = 500 feet, broken lines show longshore 

 currents for periodic waves having the same total energy 

 content (from Collins, 1972). 



141 



