Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally $2\times 1{0}^{4} \lt {\mathit{Re}}_{\tau } \lt 6\times 1{0}^{5} $ for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall.

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Fully resolved measurements of turbulent boundary layers are reported for the Reynolds number range Re τ = 6000-20 000. Despite several decades of research in wall-bounded turbulence there is still controversy over the behaviour of streamwise turbulence intensities near the wall, especially at high Reynolds numbers. Much of it stems from the uncertainty in measurement due to finite spatial resolution. Conventional hot-wire anemometry is limited for high Reynolds number measurements due to limited spatial resolution issues that cause attenuation in the streamwise turbulence intensity profile near the wall. To address this issue we use the nano-scale thermal anemometry probe (NSTAP), developed at Princeton University to conduct velocity measurements in the high Reynolds number boundary layer facility at the University of Melbourne. The NSTAP has a sensing length almost one order of magnitude smaller than conventional hot-wires. This enables us to acquire fully resolved velocity measurements of turbulent boundary layers up to Re τ = 20 000. Results show that in the near-wall region, the viscous-scaled streamwise turbulence intensity grows with Re τ in the Reynolds number range of the experiments. A second outer peak in the streamwise turbulence intensity is also shown to emerge at the highest Reynolds numbers. Moreover, the energy spectra in the near-wall region show excellent inner scaling over the small to moderate wavelength range, followed by a large-scale influence that increases with Reynolds number. Outer scaling in the outer region is found to collapse the energy spectra over high wavelengths across various Reynolds numbers.

Measurements of the streamwise component of the turbulent fluctuations in fully developed smooth and rough pipe flow are presented over an unprecedented Reynolds number range. For Reynolds numbers$R{e}_{\tau } \gt 20\hspace{0.167em} 000$, the streamwise Reynolds stress closely follows the scaling of the mean velocity profile, independent of the roughness, and over the same spatial extent. This observation extends the findings of a logarithmic law in the turbulence fluctuations as reported by Hultmark, Vallikivi & Smits (Phys. Rev. Lett., vol. 108, 2012) to include rough flows. The onset of the logarithmic region is found at a location where the wall distance is equal to ∼100 times the Kolmogorov length scale, which then marks sufficient scale separation for inertial scaling. Furthermore, in the logarithmic region the square root of the fourth-order moment also displays logarithmic behaviour, in accordance with the observation that the underlying probability density function is close to Gaussian in this region.

Well-resolved streamwise velocity spectra are reported for smooth-and rough-wall turbulent pipe flow over a large range of Reynolds numbers. The turbulence structure far from the wall is seen to be unaffected by the roughness, in accordance with Townsend's Reynolds number similarity hypothesis. Moreover, the energy spectra within the turbulent wall region follow the classical inner and outer scaling behaviour. While an overlap region between the two scalings and the associated k −1 x law are observed near R + ≈ 3000, the k −1x behaviour is obfuscated at higher Reynolds numbers due to the evolving energy content of the large scales (the very-large-scale motions, or VLSMs). We apply a semi-empirical correction (delÁlamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5-26) to the experimental data to estimate how Taylor's frozen field hypothesis distorts the pseudo-spatial spectra inferred from time-resolved measurements. While the correction tends to suppress the long wavelength peak in the logarithmic layer spectrum, the peak nonetheless appears to be a robust feature of pipe flow at high Reynolds number. The inertial subrange develops around R + > 2000 where the characteristic k −5/3x region is evident, which, for high Reynolds numbers, persists in the wake and logarithmic regions. In the logarithmic region, the streamwise wavelength of the VLSM peak scales with distance from the wall, which is in contrast to boundary layers, where the superstructures have been shown to scale with boundary layer thickness throughout the entire shear layer. Moreover, the similarity in the streamwise wavelength scaling of the large-and very-large-scale motions supports the notion that the two are physically interdependent.