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A direct numerical simulation of a turbulent pipe ow at a high Reynolds number of Reτ = 3008 over a long axial domain length (30R) was performed. The stream- wise 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 uctuations, 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 pop- ulation 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.
Physics of fluids
Direct numerical simulation of a 30R long turbulent pipe flow at Re τ = 3008