The base velocity, So (eq. 22), was found to be a function of the 
flume flow conditions. The relationship between s, and U, is shown 
in Figure 27. From the limited data it was only possible to determine 
an approximate mathematical relationship between s, and U,. This 
relationship is: 
See (0.0885) UR OOS57., (23) 
which, from boundary considerations, only gives approximate s, values 
in the range of experimental values of Up). 
4. Summary of Experimental Results. 
The following is a summary of the results of the turbulent velocity 
fluctuation measurements and a brief discussion of their limitations. 
a. The velocity fluctuations caused by turbulence are, for a con- 
stant elevation above the bed and a constant flow velocity, approximately 
normally distributed with a mean of zero. The standard deviation of the 
distribution, s, is used as the velocity scale to measure turbulence 
intensity at any elevation. Most turbulent velocity fluctuation measure- 
ments give approximately Gaussian results, although it is known that 
except for isotropic turbulence, the distribution cannot be Gaussian. 
b. For the range of flow conditions studied and the bed roughness 
used, the velocity scale can be expressed by equation (22). The exponen- 
tial nature of this relationship was discussed in Section II, paragraph 
4(a). The relationship also conforms to the boundary conditions of the 
flow. As expected, the turbulence intensity assumes a limiting value, 
Sp, at the ocean bottom (Y = 0). This limiting value of turbulence in- 
tensity is determined, in some manner, by the flow velocity, UL: As 
the turbulence diffuses upward its intensity decays because of viscosity. 
The body of fluid into which the turbulence diffuses is, by comparison, 
extremely large; therefore, the empirical relationship is expected to 
indicate that the turbulence intensity decays to zero at an infinite 
distance from the bed. 
c. The slope, A, of the exponential distribution of the velocity 
scale is constant with respect to elevation and constant throughout the 
range of flow conditions studied. It was found to be -10.57 feet !. 
This result is not surprising since the rate of turbulence intensity 
decay for the oscillating flow conditions measured is determined by vis- 
cosity. Therefore, for fluids of the same viscosity and density, the 
rate of decay should be constant and independent of flow velocity. 
d. The base velocity scale, s, (eq. 22), is a function of the 
flow velocity and can be approximated by equation (23). This equation 
is a best fit relationship of the empirical data and does not apply for 
flow velocities outside the measured range. This becomes obvious by 
letting Up = 0 foot per second and finding sy = 0.0557 foot per second. 
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