Structural similarity and lifetimes of turbulence structures in fully developed pipe flow

• Published in: The Physics of fluids (1958) 1987-10, Vol.30 (10), p.3006-3018
• Main Authors: Bullock, K. J., Cooper, R. E., Kronauer, R. E., Lai, J. C. S.
• Format: Article
• Language: English
• ISSN: 0031-9171; 2163-4998
• DOI: 10.1063/1.866079

Cross correlation measurements of the longitudinal velocity fluctuations in fully developed pipe flow have been performed with a reference hot‐wire probe at a distance y + 1 =100 from the wall for five different y + 2 locations (namely, 50, 100, 200, 400, and 600) of a second probe with zero longitudinal separation but nonzero transverse separations. The pipe flow Reynolds number is 69 000 based on the pipe radius and the centerline velocity. The covariant (Co) and quadrature (Quad) correlations, which have been determined for each of the seven frequencies ω+ used to constrain the longitudinal wavenumber k + x , have been Fourier transformed with the transverse wavenumber k + z , y + 1, y + 2, and ω+ as the independent variables. The data presented in this form enable similarity to be examined in terms of waves of different sizes and inclinations. By using a similarity variable k + y +, where k +=[k +2 x k +2 z ]1 / 2, the relative phases determined from the Co and Quad correlations and the wave intensity function for various wave angles have been shown to collapse. These results support the similarity hypothesis that the phase and intensity of the turbulance components is scaled by wave size k + and distance from the wall y +. The dimension over which a turbulence structure retains its coherence has been deduced from the correlation data for various wave angles. Two estimates for the lifetime of turbulence structures have been derived, one from the phase‐shifting effects of shear contained in the relative phase data, and the other from spectral sheet thickness data. Their significance and implications have been discussed.