### Abstract

This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log-wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log-wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driest's mixing-length model in which the damping factor varies with Reynolds number, the modified log-wake law can be extended to the entire boundary layer flow.

Original language | English (US) |
---|---|

Pages (from-to) | 421-430 |

Number of pages | 10 |

Journal | Journal of Hydraulic Research |

Volume | 43 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2005 |

### Fingerprint

### Keywords

- Logarithmic law
- Skin friction
- Turbulence
- Velocity distribution
- Velocity profile
- Wake law
- Zero-pressure-gradient boundary layers

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Water Science and Technology

### Cite this

*Journal of Hydraulic Research*,

*43*(4), 421-430. https://doi.org/10.1080/00221680509500138

**Modified log-wake law for zero-pressure-gradient turbulent boundary layers.** / Guo, Junke; Julien, Pierre Y.; Meroney, Robert N.

Research output: Contribution to journal › Article

*Journal of Hydraulic Research*, vol. 43, no. 4, pp. 421-430. https://doi.org/10.1080/00221680509500138

}

TY - JOUR

T1 - Modified log-wake law for zero-pressure-gradient turbulent boundary layers

AU - Guo, Junke

AU - Julien, Pierre Y.

AU - Meroney, Robert N.

PY - 2005/1/1

Y1 - 2005/1/1

N2 - This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log-wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log-wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driest's mixing-length model in which the damping factor varies with Reynolds number, the modified log-wake law can be extended to the entire boundary layer flow.

AB - This paper shows that the turbulent velocity profile for zero-pressure-gradient boundary layers is affected by the wall shear stress and convective inertia. The effect of the wall shear stress is dominant in the so-called overlap region and can be described by a logarithmic law in which the von Karman constant is about 0.4 while the additive constant depends on a Reynolds number. The effect of the convective inertia can be described by the Coles wake law with a constant wake strength about 0.76. A cubic correction term is introduced to satisfy the zero velocity gradient requirement at the boundary layer edge. Combining the logarithmic law, the wake law and the cubic correction produces a modified log-wake law, which is in excellent agreement with experimental profiles. The proposed velocity profile law is independent of Reynolds number in terms of its defect form, while it is Reynolds number dependent in terms of the inner variables. The modified log-wake law can also provide an accurate equation for skin friction in terms of the momentum thickness. Finally, by replacing the logarithmic law with van Driest's mixing-length model in which the damping factor varies with Reynolds number, the modified log-wake law can be extended to the entire boundary layer flow.

KW - Logarithmic law

KW - Skin friction

KW - Turbulence

KW - Velocity distribution

KW - Velocity profile

KW - Wake law

KW - Zero-pressure-gradient boundary layers

UR - http://www.scopus.com/inward/record.url?scp=24944501153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24944501153&partnerID=8YFLogxK

U2 - 10.1080/00221680509500138

DO - 10.1080/00221680509500138

M3 - Article

AN - SCOPUS:24944501153

VL - 43

SP - 421

EP - 430

JO - Journal of Hydraulic Research/De Recherches Hydrauliques

JF - Journal of Hydraulic Research/De Recherches Hydrauliques

SN - 0022-1686

IS - 4

ER -