Measurements of phase shift and coherence between the streamwise velocity fluctuations at two sensors placed very close to each other have been made in fully developed turbulent flow in a smooth pipe. For the frequencies where the √coherence is near unity (i.e. the correlation between the frequency components is near unity) the phase shifts have been related to the phase velocities and angle of inclination of a "frozen" pattern of turbulence.

Several other quantities such as intensities, energy spectral densities and mean velocities have also been obtained from the data taken with each sensor and these are in good agreement with previously found values. Probability densities of the streamwise velocity fluctuations were calculated and appear to be positively skewed near the wall and negatively skewed in the central region of the flow.

The phase shift measurements indicate that the phase velocities of all but the lowest frequency components are near and somewhat below the local mean velocity in the central region of the pipe and that the disturbance fronts are perpendicular to the wall. Near the wall all the disturbances seem to be inclined - the lower frequencies making smaller angles with the wall than the higher frequencies. The angles of inclination of all disturbances increase with distance from the wall. The phase velocity appears higher than the local mean velocity in this region.

Meeting Name

Symposium on Turbulence in Liquids (1971: Oct. 4-6, Rolla, MO)


Chemical and Biochemical Engineering

Document Type

Article - Conference proceedings

Presentation Type

Contributed Paper


Measurement and Analysis of Turbulence

Document Version

Final Version

File Type





© 1972 University of Missouri--Rolla, All rights reserved.