This paper describes a series of two-point measurements in fully developed pipe flow. Measurements of the phase shifts between the Fourier components of the axial velocity fluctuations at two points were made with three different orientations of the two points. In all cases the two points were close enough together that the turbulent structure remained essentially "frozen" while passing between the sensors. The phase velocities, C1(f), and inclinations, α(f) (defined previously by Heidrick et al. (8)), of each frequency component, f, were determined from these measurements.

In general, the Fourier components are inclined to the wall - the lower frequencies making smaller angles with the wall than the higher frequencies. The higher frequency disturbances became more nearly perpendicular to the wall in the central region of the pipe. For points very near the wall the disturbances appear to be very obliquely inclined.

In the core region, the phase velocity increases with increasing frequency and there is little discernable trend in the phase velocities with respect to position when they are normalized by the local mean velocity. The group velocity of small scale disturbances (large wavenumbers) in the core region appears to be approximately constant and of the order of the local mean velocity. This means that a "frozen" pattern hypothesis should be valid for these scales.

All measurements became more scattered at values of y+ ~<26. This may be due to the intermit- tent nature of the flow near the wall since recent studies in turbulent shear flow suggest that energy transfer from the mean flow to fluctuations near the wall may be due to local instabilities ("bursts"). Thus, the time averaged model is not entirely adequate, and it was necessary to separate out the burst intervals for further study.

By suitably processing the two-point velocity signals it was possible to determine when the flow was bursting. The behavior of the velocity and vorticity within measured bursts was determined. This behavior and short-term energy spectra within bursts indicate a weakly periodic behavior. The overall behavior of the flow was shown to be similar to the last stage of the laminar-to-turbulent flow transition.

Meeting Name

3rd Biennial Symposium on Turbulence in Liquids (1973: Sep., Rolla, MO)


Chemical and Biochemical Engineering

Document Type

Article - Conference proceedings

Presentation Type

Contributed Paper


Conditioned-Signal Analysis

Document Version

Final Version

File Type





© 1973 University of Missouri--Rolla, All rights reserved.