Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberRλ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withRλ. In particular, the scaling exponentζv, corresponding to the v structure function, continues to increase with Rλ in contrast to the nearly unchanged value of ζu. The Kolmogorov constant for δu shows a smaller rate of increase with Rλ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofRλ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow.