equal to or less than various selected velocities calculated. These 
percentages were divided by two and plotted against velocity on normal 
probability paper. The percentages were divided by two in order to 
adjust for the fact that the anemometer measured the absolute effective 
velocity without regard to its direction; i.e., the velocities in each 
range were composed of an equal number of negative and positive veloci- 
ties, thereby giving twice the percentage of actual positive velocities. 
As shown in Figure 22(a, b), these plots approximate straight lines and 
the 50-percent velocity is zero, thereby indicating that the distribu- 
tion of the turbulent velocity fluctuations is approximately normal with 
a mean of zero. Similar data by Das (1968) give the same results. 
The above result suggests that the standard deviation, s, of the 
normal distribution (which equals the root-mean-square velocity) be used 
as the velocity scale describing turbulence intensity for a given eleva- 
tion. 
The data were then analyzed to determine the distribution of s with 
respect to elevation. For each sample of a voltage record, the effective 
heat transfer velocity was calculated from equation (14). From the velo- 
city record, the root-mean-square effective velocity was calculated. 
Knowing this velocity the velocity scale for the elevation at which the 
record was made was calculated from: 
s = U,/v2 , (21) 
where s is the velocity scale and is equal to the standard deviation of 
v' for the elevation of the record and flow conditions of the flume, Us 
is the root-mean-square effective heat transfer velocity of the record, 
and v2 comes from equation (20) when K' is assumed equal to unity. 
The velocity scale was plotted against elevation on semilogarithmic 
paper to give the relationships shown in Figures 23 to 26. In general, 
these relationships can be expressed by: 
Si =a Sn exp CA NY) (22) 
where s, is the value of the velocity scale (in feet per second) at the 
elevation of the crest of the artificial bed dunes, A is the slope of 
the exponential curve (in feet-!), and Y is the elevation (in feet) 
above the crest of the bed dunes. The flume flow conditions for which 
a velocity scale-elevation distribution was measured were Up = 0.353, 
0.510, 0.748, and 0.930 foot per second. 
Comparison of the four velocity-elevation distributions revealed that, 
for the range of flow conditions studied and bed roughness used, the slope 
of the exponential relationship was constant. This implies that the in- 
tensity of the turbulence decreases in a manner which is independent of 
the flow velocity generating the turbulence. The constant rate of velo- 
city decay appears to apply to elevations near the bed, within 1.5 centi- 
meters as measured with the hot-film sensor. 
56 
