noted that additional turbulence is injected into the water column by wave 

 breaking in the surf zone . 



69. The Shields number is used as an indicator of incipient motion and 

 type of bedform development both in unidirectional flow (Shen 1971, Vanoni 

 1977) and the surf zone (Madsen and Grant 1976, Nielsen 1979, Watanabe 1988). 

 Shields numbers were calculated for the range of midflow speeds used in the 

 laboratory (Figure 22) and compared with Shields numbers for the surf zone to 

 indicate how well the laboratory transport condition replicated field condi- 

 tions. The Shields number * is defined as 



* = 7 PU \ h <10) 



(Ps - P)g d s 



where 



p = density of water, taken as 1 g/cm 3 



U* = shear speed, obtained empirically as a function of 

 midflow speed from Figure 23 (cm/sec) 



p s = density of sand, taken as 2.6 g/cm 3 for quartz 



g = acceleration due to gravity, 980 cm/sec 2 



d s = mean diameter of sand, 0.023 cm 



70. The shear speed U* was obtained empirically from a series of 

 vertical flow speed profiles measured in the laboratory. By using the 

 logarithmic law (see Part III), values of U* and the representative rough- 

 ness length z were calculated (Table 4). The profiles of flow speed over 

 the movable bottom followed the logarithmic law well, as is evidenced by the 

 high squared correlation coefficients r 2 , ranging from 0.91 to 0.99. The 

 large value of bed roughness z corresponding to a midflow speed equal to 

 45.7 cm/sec occurred with large bedforms that moved as sand was transported 

 either as saltating or bed-load material. The empirical relationship of shear 

 speed U* as a function of midflow speed is presented in Figure 23. 



71. As shown in Figure 22, the value of the Shields number at the 

 observed inception of sheet flow in the laboratory was approximately 0.58. 

 Values of Shields numbers for inception of sheet flow in an oscillatory flow 

 tank have been found to be in the range of * = 0.5 to 0.6, and other 



48 



