### Abstract

We expand on our previous argument (Sreenivasan 1987) that important elements of the dynamics of wall-bounded flows reside at the wall-normal position y_{p} corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in the neighborhood of y_{p} is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that the y_{p} = O((hν/U_{*})^{ 1/2 }) and show that, in a neighborhood of order R_{*}^{ 1/2 } around y_{p}, only the viscous effects balance pressure-gradient terms. Here, R_{*} = hU_{*}/ν, h is the pipe radius or channel half-width, ν is the kinematic viscosity of the fluid and U_{*} is the friction velocity. This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid; in particular, it throws doubt on the validity of the classical matching principle. Even so, it is shown that the classical semi-logarithmic behavior for the mean velocity distribution can be a valid approximation. It is argued that the recently advanced power-law profiles possess a rich underlying structure, and could be good approximations to the data over an extended region (but they too are unlikely to be exact).

Original language | English (US) |
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Publisher | Computational Mechanics Inc |

Number of pages | 18 |

State | Published - 1997 |

### ASJC Scopus subject areas

- Energy Engineering and Power Technology
- Mechanical Engineering
- Condensed Matter Physics

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## Cite this

*Persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows*. Computational Mechanics Inc.