Experiments on the structure of turbulence in fully developed pipe flow: interpretation of the measurements by a wave model

Abstract

This paper is the first of a pair that describe two-point velocity measurements made at various radial positions in water in fully developed pipe flow. Axial velocity fluctuations were measured with hot-film anemometers at two points sufficiently close together that the turbulence structure remained essentially unchanged while passing between them. Phases of the cross-spectra of these velocities were then determined and interpreted in terms of a wave model of the turbulence structure. The model assigns an axial velocity and streamwise inclination to the lines of equal phase of each frequency component of the spectra. In general, the lines of equal phase for each frequency component are inclined to the wall in the flow direction, the lower frequencies being more inclined than the higher frequencies, though all lines of equal phase at points in the central region of the pipe tend towards the perpendicular. For points near the wall the inclinations are very pronounced. In the central region, phase velocities of lower frequency components are lower than those for higher frequencies. All phase velocities could be normalized with respect to position by the local mean velocity. The group velocity of small-scale (large wavenumber) disturbances in the core region appears to be approximately constant and of the order of the local mean velocity. This leads to a modified form of Taylor's hypothesis. The variance in all the measurements increases rapidly in the region y +