The inertial subrange in turbulent pipe flow: centre line

The inertial subrange scaling of the axial velocity component is examined for the centre line of turbulent pipe flow for Reynolds numbers in the range $249\le Re_\lambda \le986$. Measurements were performed in the Princeton/ONR Superpipe using NSTAP probes of length, $\ell = 30~ \mu$m or 60 $\mu$m, with temporal resolution up to 300 kHz. Estimates of the dissipation rate, $\epsilon$, are made by both integration of the one-dimensional dissipation spectra and the third-order moment of the structure function. It is noticeable that neither dissipation estimate provides values of $A=\frac{\epsilon}{u_{\tau}^3/R}$ that asymptote to a constant: rather $A$ increases almost linearly with $Re_\lambda$. We show that complete similarity of the inertial range spectra is not evident: there is little support for K41, and effects of Reynolds number are not well represented by Kolmogorov's ``extended similarity hypothesis,'' K62. The second-order moment of the structure function does not show a constant value, even when compensated by K62. Direct effects of viscosity appear at the centre line where correction of the ``${4}/{5}$ths'' constant for finite Reynolds number (Lundgren 2002) yields values of $0.80~\pm0.01$