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Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

Oberlack, Martin (1999):
Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows.
In: Flow, Turbulence and Combustion, Springer, pp. 111-135, 62, (2), ISSN 1386-6184,
[Online-Edition: http://www.springerlink.com/content/ph16x1350351p055/],
[Article]

Abstract

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach 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. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre 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 centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k-ε model are not consistent with most of the new turbulent scaling laws.

Item Type: Article
Erschienen: 1999
Creators: Oberlack, Martin
Title: Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows
Language: English
Abstract:

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach 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. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre 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 centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k-ε model are not consistent with most of the new turbulent scaling laws.

Journal or Publication Title: Flow, Turbulence and Combustion
Volume: 62
Number: 2
Publisher: Springer
Uncontrolled Keywords: turbulence; scaling-laws; symmetries
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 23 Aug 2011 14:50
Official URL: http://www.springerlink.com/content/ph16x1350351p055/
Additional Information:

DOI: 10.1023/A:1009929312914

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