For the average flow conditions, Vg is 0.035 foot per second, T is 
6 seconds, and L is 1.0 foot. Based on the bottom roughness shape and 
the hydraulic radius, n is approximately 0.015 foot2:167. The hydrau- 
lic radius is estimated from the flow geometry as about equal to unity. 
Since Z is proportional to R_ to the 0.167 power, and therefore tends 
to unity, there is probably not much error in using this estimate. Using 
these values in equation (36) yields Z = 2.1. In Figure 28, this value 
of Z is well into the range where the sediment exchange coefficient is 
Significantly different from the momentum exchange coefficient. 
Because not enough data were obtained to define a relationship be- 
tween M and V, and because the sediment exchange coefficient could 
not be expressed as a function of the shear-stress distribution, no 
attempt was made to derive a theoretical relationship for the concentra- 
tion distribution as was done in Einstein and Chien (1954) for unidirec- 
tional flow. 
3. Sediment Suspension in an Oscillating Flow. 
This investigation was done to determine the behavior of sediment 
suspension in an oscillating flow and present a method by which the sus- 
pended load could be approximated from flow hydraulics. It is apparent 
from the field measurements of unidirectional flow (Fig. 28), and the 
results of this investigation for oscillating flow that the mechanism by 
which sediment is held in suspension is complex and not fully understood. 
For this reason, the following method for estimating the suspended load 
in oscillating flow as a function of the flow hydraulics is based on the 
general turbulent mixing length theory first proposed by O'Brien (1933). 
His derivation is as follows: 
There is a continuous up and down motion of fluid across any horizon- 
tal plane caused by the turbulent vertical velocity fluctuations. This 
exchange motion is capable of transporting suspended matter. Consider a 
horizontal reference section of unit area at a distance Y from the bed. 
The transfer of sediment in the vertical direction from the region of 
high concentration to a region of low concentration through this unit 
section will be -1/2 1, v dC/dY, where 1, is the mixing length for the 
sediment exchange, v denotes the exchange discharge through the unit 
area due to vertical velocity fluctuations, and C is the concentration 
of suspended sediment with settling velocity, V,, at elevation Y. How- 
ever, a continuous settling of particles through the unit area at a rate 
of C Vg exists. A statistical equilibrium condition is given by equa- 
tion (25). This equation is identical to the equation derived by Einstein 
(1950), but without the assumption that the origin of the sediment is the 
same as the origin of the fluid and without assuming any distribution of 
fluid exchange. 
The mixing length theory incorporates all of the factors which affect 
sediment suspension in two artificial variables, the velocity scale and 
the length scale. The velocity scale for oscillating flow was measured 
69 
