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**Oberlack, Martin** **Hanjalic, K. and Peeters, T. W. J. (eds.)** (1997):

*Self-Similar Mean Velocity Profiles in Plane Parallel Turbulent Shear Flows.*

In: Turbulence, Heat and Mass Transfer 2 - Proceedings of the Second International Symposium on Turbulence, Heat and Mass Transfer, Delft, The Netherlands, June 9-12, 1997, Delft University Press, pp. 111-120, [Book Section]

## Abstract

A new turbulence theory based on Lie-group analysis is presented. This theory unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The theory is derived from the Reynolds averaged Navier-Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the center of a Couette flow and in the center of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the center and the near wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation.

Item Type: | Book Section |
---|---|

Erschienen: | 1997 |

Editors: | Hanjalic, K. and Peeters, T. W. J. |

Creators: | Oberlack, Martin |

Title: | Self-Similar Mean Velocity Profiles in Plane Parallel Turbulent Shear Flows |

Language: | English |

Abstract: | A new turbulence theory based on Lie-group analysis is presented. This theory unifies a large set of self-similar solutions for the mean velocity of stationary parallel turbulent shear flows. The theory is derived from the Reynolds averaged Navier-Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the center of a Couette flow and in the center of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the center and the near wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation. |

Title of Book: | Turbulence, Heat and Mass Transfer 2 - Proceedings of the Second International Symposium on Turbulence, Heat and Mass Transfer, Delft, The Netherlands, June 9-12, 1997 |

Publisher: | Delft University Press |

Divisions: | 16 Department of Mechanical Engineering > Fluid Dynamics (fdy) 16 Department of Mechanical Engineering |

Date Deposited: | 30 Aug 2011 14:28 |

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