### 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) |
---|---|

Publisher | Computational Mechanics Inc |

Number of pages | 18 |

State | Published - 1997 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

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

**Persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows.** / Sreenivasan, Katepalli R.; Sahay, Anupam.

Research output: Book/Report › Book

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

}

TY - BOOK

T1 - Persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

AU - Sreenivasan, Katepalli R.

AU - Sahay, Anupam

PY - 1997

Y1 - 1997

N2 - We expand on our previous argument (Sreenivasan 1987) that important elements of the dynamics of wall-bounded flows reside at the wall-normal position yp 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 yp is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that the yp = O((hν/U*) 1/2 ) and show that, in a neighborhood of order R* 1/2 around yp, 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).

AB - We expand on our previous argument (Sreenivasan 1987) that important elements of the dynamics of wall-bounded flows reside at the wall-normal position yp 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 yp is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that the yp = O((hν/U*) 1/2 ) and show that, in a neighborhood of order R* 1/2 around yp, 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).

UR - http://www.scopus.com/inward/record.url?scp=0030655654&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030655654&partnerID=8YFLogxK

M3 - Book

BT - Persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows

PB - Computational Mechanics Inc

ER -