Wellresolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius
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The statistical properties of uniform momentum zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatiotemporally resolved velocity dataset, covering a field of view of
 Award ID(s):
 2018658
 NSFPAR ID:
 10531953
 Publisher / Repository:
 Cambridge University Press
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 979
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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and axial length$R$ at friction Reynolds numbers up to$10{\rm \pi} R$ using the pseudospectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor$Re_\tau =5200$ overshoots by$\lambda$ and undershoots by$2\,\%$ the Prandtl friction law at low and high$0.6\,\%$ ranges, respectively. In addition,$Re$ in our results is slightly higher than in Pirozzoli$\lambda$ et al. (J. Fluid Mech. , vol. 926, 2021, A28), but matches well the experiments in Furuichiet al. (Phys. Fluids , vol. 27, issue 9, 2015, 095108). The loglaw indicator function, which is nearly indistinguishable between pipe and channel up to , has not yet developed a plateau farther away from the wall in the pipes even for the$y^+=250$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with$Re_\tau =5200$ – are lower in the pipe than in the channel, but the difference decreases with increasing$Re_\tau$ . While the wall value is slightly lower in the channel than in the pipe at the same$Re_\tau$ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defectpower laws if the coefficients are properly chosen. The onedimensional spectrum of the axial velocity fluctuation exhibits a$Re_\tau$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these highfidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.$k^{1}$ 
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