One-point statistics for turbulent pipe flow up to Re𝜏≈6000

Sergio Pirozzoli*, Joshua Romero, Massimiliano Fatica, Roberto Verzicco, Paolo Orlandi

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number using direct numerical simulation (DNS) of the Navier-Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately, which would extrapolate to approximately at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant, which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at, as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Original languageEnglish
Article numberA28
Pages (from-to)355-377
Number of pages23
JournalJournal of fluid mechanics
Publication statusPublished - 10 Nov 2021


  • Pipe flow
  • Turbulence simulation
  • Turbulence theory
  • UT-Hybrid-D

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