Examining results b, c, and d of Section III, the range of the root-mean- 
Square valluenofmuy CS) y's Os O00V25< 1S <1 0)10/5) footy pers second amine 
settling velocities of the sediments used in the experiments were 
Vg = 0.035, 0.0498, and 0.0626 foot per second. V, is then, the same 
order of magnitude as the velocity scale. As discussed earlier, the 
sediment used in the experiments had a specific gravity of 1.25. There- 
fore, the settling velocity of natural sediment would be even larger 
compared to turbulence intensity in the approximate prototype flow con- 
ditions of the experiments. 
For illustration, a typical oscillatory flow condition of this in- 
vestigation will be approximated as a quasi-steady unidirectional flow 
and compared to the field data of Figure 28. This is possible because 
the time scale for oscillation is much greater than the time scale of 
the turbulence. For example, the average flow had a period of 6 seconds 
and an amplitude of about 1 foot, Up = 0.667 foot per second. A time 
scale of turbulence can be defined as S/S where 6 is the thick- 
ness of the boundary layer and s, is the base vertical velocity fluc- 
tuation. If 6 is defined as the distance above the bed at which the 
boundary layer oscillation velocity is equal to 99 percent of the free- 
stream velocity (velocity given by linear wave theory for y = -d), 
6 can be calculated from equation (5). This calculation indicates that 
6 is equal to or less than 0.05 foot and from Figure 27, So is 0.11 foot 
per second. Therefore, the time scale for the turbulence is 0.45 second 
as compared to a 6-second time scale for the oscillation. To calculate 
the theoretical Z value for the quasi-steady unidirectional flow it is 
necessary to determine a mean flow shear velocity. The flow shear veloc- 
ity 1s given by: 
ie 
De GES) (33) 
where R is the hydraulic radius (in feet), g is the acceleration due 
to gravity (in feet per second squared), and S is the energy slope of 
the quasi-steady flow. The energy slope is obtained from Manning's 
equation by using the root-mean-square flow velocity (= 0.707 2 Il L/T), 
and estimating values of the roughness coefficient, n, and the hydrau- 
lic radius, R. The expression for the energy slope is: 
a 
See= 1 (n/ RO Pei (Sal Alin. (34) 
Substituting equation (34) into equation (33) yields: 
Big eS (GY i Ge RO OME) 5 (35) 
Using the above expression for u, in equation (29), the Z value for 
the quasi-steady flow becomes: 
A (Me) TF ROOMS GLB. an ih) < (36) 
68 
