Universal Model of Finite-Reynolds Number Turbulent Flow in Channels and Pipes

Abstract

In this Letter we suggest a simple and physically transparent analytical model of the pressure driven turbulent wall-bounded flows at high but finite Reynolds numbers Re. The model gives accurate qualitative description of the profiles of the mean-velocity and Reynolds-stresses (second order correlations of velocity fluctuations) throughout the entire channel or pipe in the wide range of Re, using only three Re-independent parameters. The model sheds light on the long-standing controversy between supporters of the century-old log-law theory of von-Kàrmàn and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

arXiv comment4 pages, 6 figs, re-submitted PRL according to referees comments

References in corpus (1)

• Phenomenology of Wall Bounded Newtonian Turbulence

Cited by in corpus (12)

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• Quantifying wall turbulence via a symmetry approach. Part I. A Lie group theory
• Velocity and Energy Profiles In Two- vs. Three-Dimensional Channels: Effects of Inverse vs. Direct Energy Cascade
• Karman constant and accurate mean flow prediction in a turbulent pipe
• An extension of the momentum transfer model to time-dependent pipe turbulence