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Fractal-Generated Turbulent Scaling Laws from a New Scaling Group of the Multi-Point Correlation Equation

Oberlack, Martin and Khujadze, George
Peinke, Joachim and Oberlack, Martin and Talamelli, Alessandro (eds.) :

Fractal-Generated Turbulent Scaling Laws from a New Scaling Group of the Multi-Point Correlation Equation.
In: Progress in Turbulence III: Proceedings of the iTi Conference in Turbulence 2008. Springer Proceedings in Physics (131). Springer, http://dx.doi.org/10.1007/978-3-642-02225-8_3 , pp. 13-19. ISBN 978-3-642-02225-8
[Book Section] , (2009)

Abstract

Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see [2]) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff’s or Loitsiansky’s integrals. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see [1, 4]) fall into this new class of solutions. Due to this specific grid a breaking of the classical scaling symmetries due to a wide range of scales acting on the flow is accomplished. This in particular leads to a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from MPC equations using the new scaling symmetry. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group. Though the latter is not obvious from the instantaneous Euler or Navier-Stokes equations it is directly implied.

Item Type: Book Section
Erschienen: 2009
Editors: Peinke, Joachim and Oberlack, Martin and Talamelli, Alessandro
Creators: Oberlack, Martin and Khujadze, George
Title: Fractal-Generated Turbulent Scaling Laws from a New Scaling Group of the Multi-Point Correlation Equation
Language: English
Abstract:

Investigating the multi-point correlation (MPC) equations for the velocity and pressure fluctuations in the limit of homogeneous turbulence a new scaling symmetry has been discovered. Interesting enought this property is not shared with the Euler or Navier-Stokes equations from which the MPC equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see [2]) though there this property only holds true for the two-point equation. Hence, in a strict sense there it is broken for higher order correlation equations. Presently using this extended set of symmetry groups a much wider class of invariant solutions or turbulent scaling laws is derived for homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff’s or Loitsiansky’s integrals. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see [1, 4]) fall into this new class of solutions. Due to this specific grid a breaking of the classical scaling symmetries due to a wide range of scales acting on the flow is accomplished. This in particular leads to a constant integral and Taylor length scale downstream of the fractal grid and the exponential decay of the turbulent kinetic energy along the same axis. These particular properties can only be conceived from MPC equations using the new scaling symmetry. The latter new scaling law may have been the first clear indication towards the existence of the extended statistical scaling group. Though the latter is not obvious from the instantaneous Euler or Navier-Stokes equations it is directly implied.

Title of Book: Progress in Turbulence III: Proceedings of the iTi Conference in Turbulence 2008
Series Name: Springer Proceedings in Physics
Number: 131
Place of Publication: http://dx.doi.org/10.1007/978-3-642-02225-8_3
Publisher: Springer
Divisions: 16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
16 Department of Mechanical Engineering
Date Deposited: 02 Sep 2011 13:15
Additional Information:

DOI: 10.1007/978-3-642-02225-8_3

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