0.03 



0.02 



e.8i 



0.8(3 



-.61 



-.82 



. 















: 









s 



1 



♦ 



• 



_ 







1 



1 



♦ 



- 









e 



a. 















CL 













. < 



CO 





■ 













♦ 



_ 



_ 



X 



♦ 





1 



♦ 



- 



♦ 



J^ 



^•t' 





^ — 



t 





1 Y^ 



"T 



>- 



— Y^ 



^^^ 



+ 



- 



^ X 





♦ 





♦ 





~ 











♦ 



♦ 













♦ 





■" 



^ 











♦ 



I 













' ♦ 



- 

























' 





100 120 140 160 180 



Distance offshore (m) 



208 



220 



Figure 71. Bed shear-stress coefficients computed from equation (162) 

 and data taken at Torrey Pines Beach, California, November 

 1978 (after Thornton, 1980). 



employ for the characteristic reference velocity u and reference length 

 scale, 1. A closure coefficient (N, F, M, etc.) then is inserted in some 

 expressions (see Table 4) such as that first proposed by Longuet-Higgins 

 (1970) 



V = Nx/gh 



or later by Madsen, Ostendorf, and Reynolds (1978) 



^ = r X u^ 



L ' ' Bm 



(164) 



(165) 



Consequently, comparisons of various theories of turbulent mixing in the 

 surf zone and beyond must be in terms of vl (or pl) and not the closure 

 coefficients involved. 



189 



