A direct numerical simulation of a turbulent pipe flow at a high Reynolds number of Reτ = 3008 over a long axial domain length (30R) was performed. The streamwise mean velocity followed the power law in the overlap region (y+ = 90–300; y/R = 0.03–0.1) based on the power law indicator function. The scale separation of the Reynolds shear stresses into two components of small- and large-scale motions (LSMs) revealed that the LSMs in the outer region played an important role in constructing the constant-stress layer and the mean velocity. In the pre-multiplied energy spectra of the streamwise velocity fluctuations, the bimodal distribution was observed at both short and long wavelengths. The kx−1 region associated with the attached eddies appeared in λx/R = 2–5 and λx/y = 18–160 at y+ = 90–300, where the power law was established in the same region. The kz−1 region also appeared in λz/R = 0.3–0.6 at y+ = 3 and 150. Linear growth of small-scale energy to large-scale energy induced the kx−1 region at high Reynolds numbers, resulting in a large population of the LSMs. This result supported the origin of very-large-scale motions in the pseudo-streamwise alignment of the LSMs. In the pre-multiplied energy spectra of the Reynolds shear stress, the bimodal distribution was observed without the kx−1 region.

The relationship between the frictional drag and the velocity-vorticity correlations in wall-bounded turbulent flows is derived from the mean vorticity equation. A formula for the skin friction coefficient is proposed and evaluated with regards to three canonical wall-bounded flows: turbulent boundary layer, turbulent channel flow, and turbulent pipe flow. The frictional drag encompasses four terms: advective vorticity transport, vortex stretching, viscous, and inhomogeneous terms. Drag-reduced channel flow with the slip condition is used to test the reliability of the formula. The advective vorticity transport and vortex stretching terms are found to dominate the contributions to the frictional drag.

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Statistical measures of turbulence intensities in turbulent pipe and channel flows at a friction Reynolds number of Reτ ≈ 930 were explored by a population of large-scale motions (LSMs) and very-large-scale motions (VLSMs). Although the statistical measures characterizing these internal turbulent flows were similar in the near-wall region, the extents of the mean streamwise velocities and cross-stream components of the turbulence intensities differed in the core region. The population density of VLSMs/LSMs decreased/increased significantly in the core region of the pipe flow. The survival time of VLSMs of the pipe flow was shorter than that of the channel flow. The area fractions of the VLSMs displayed similar trends to the population density. The wall-normal and spanwise turbulence intensities in the pipe flow increased in the core regions due to the high-speed large-scale structures and associated motions above the structures. The large-scale structures increased the streamwise intensity and the Reynolds shear stress in the pipe and channel flows, whereas the effective streamwise intensities and the Reynolds shear stress were equivalent in both flows.

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