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

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

2007-05-31

arxiv.org/abs/0705.4592v3

Physical Review Letters 100, 054504 (2008)

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevLett.100.054504

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-K\`arm\`an and Prandtl and proposers of a newer theory promoting power laws to describe the intermediate region of the mean velocity profile.

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