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Sixth International Symposium on Turbulence and Shear Flow Phenomena
June, 22-24, 2009 , Seoul National University, Seoul, Korea

DOI: 10.1615/TSFP6

FRACTAL-GENERATED TURBULENT SCALING LAWS FROM A NEW SCALING GROUP OF THE MULTI-POINT CORRELATION EQUATION

pages 108-111
DOI: 10.1615/TSFP6.170
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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 in Khujadze and Oberlack (2004) 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 the decay of homogeneous and homogeneous-isotropic turbulence which is in stark contrast to the classical power law decay arising from Birkhoff's or Loitsiansky's integrals. Beside two classical solutions two new scaling laws have been derived. In particular, we show that the experimentally observed specific scaling properties of fractal-generated turbulence (see Hurst and Vassilicos, 2007 and Seoud and Vassilicos, 2007) 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.

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