where 
C = concentration 
V, = settling velocity of the sediment particle 
E = sediment exchange coefficient (which here is assumed equal to 
the momentum exchange coefficient in unidirectional flow) 
Y = elevation above the bed 
Inserting the expressions for C and (dC/dY) obtained from equation 
(9) into equation (12) and solving for E yield: 
E = Wait 0 (13) 
In unidirectional flow and for relatively low sediment concentrations, 
it is assumed that the sediment exchange coefficient is equal to the 
momentum exchange coefficient, is a function of the fluid motion only, 
and is independent of the particle-settling velocity. For this assump- 
tion to be valid in oscillating flow, the slope of the concentration dis- 
tribution curve must be directly proportional to the settling velocity. 
Although Figure 15 indicates M is proportional to V,, it does not 
indicate direct proportionality. This discrepancy is discussed in 
Section IV. 
5. Summary of Experimental Results. 
The following is a summary of the results of the concentration meas- 
urements and a brief discussion of their limitations. 
a. The vertical distribution of sediment concentration can be ex- 
pressed by equation (9). Sediment is held in suspension by the random 
motion of turbulence which is generated in the boundary layer and is 
transported by diffusion upward while decaying continuously because of 
viscosity. As shown later in Section III, the turbulence intensity 
decays rapidly with elevation above the bed. The upper elevation to 
which the turbulence can diffuse (the water surface in the prototype 
and the wave suppressent board in the flume) is larger than the eleva- 
tion at which the turbulence intensity decays to extremely small values; 
therefore, this upper boundary can be approximated as being at infinity. 
Under these conditions it is reasonable that the empirical results given 
by equation (9) indicate an exponential decay (as is commonly found in a 
diffusion process), and only become zero at Y = infinity. As expected, 
the concentration distribution in oscillating flow is different than in 
unidirectional flow. In unidirectional flow the turbulence is distrib- 
uted between the bed and the water surface, the turbulence intensity is 
Significant at the water surface. Because the water surface is not effec- 
tively at infinity, the distribution of both the turbulence and the sedi- 
ment concentration would be different than in oscillating flow. 
42 
