Reynolds number dependence of velocity structure functions in a turbulent pipe flow

Low-order moments of the increments δu and δu 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 number R_λ. The mean energy dissipation rate 〈ε〉 was inferred from the u spectrum 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 with R_λ. In particular, the scaling exponent ζ_v, corresponding to the v structure function, continues to increase with R_λ in contrast to the nearly unchanged value of ζ_u. The Kolmogorov constant for δu shows a smaller rate of increase with R_λ than that for δv. The level of agreement with local isotropy is examined in the context of the competing influences of R_λ 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.