### Scaling law of fractal-generated turbulence and its derivation from a new scaling group of the multi-point correlation equation

Oberlack, M *(Fachgebiet für Strömungsdynamik)*

Wednesday 01 October 2008, 14:30-15:00

Seminar Room 1, Newton Institute

#### Abstract

Investigating the multi-point correlation 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 multi-point correlation equations have orginally emerged. This was first observed for parallel wall-bounded shear flows (see Khujadze, Oberlack 1994, TCFD (18)) 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 turbulence. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see Vassilicos etal.) fall into this new class of solutions. This is in particular 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 multi-point equations using the new scaling symmetry since the two classical scaling groups of space and time are broken for this specific case. Hence, extended statistical scaling properties going beyond the Euler and Navier-Stokes have been clearly observed in experiments for the first time.

#### Presentation

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