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TWO-POINT SIMILARITY SOLUTIONS OF SHEAR-FREE TURBULENT DIFFUSION, DIFFUSION-WAVES AND ITS IMPLICATIONS FOR RANS MODELS

Martin Oberlack
Chair of Fluid Dynamics, Dept. Mech. Eng., TU Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany; Center of Smart Interfaces, TU Darmstadt, Germany; GS Computational Engineering, TU Darmstadt, Germany

Silke Guenther
Hydromechanics and Hydraulics Group, Darmstadt University of Technology, Petersenstr. 13, 64287 Darmstadt, Germany

Resumo

We reconsider the problem of shear-free turbulent diffusion with no production due to a mean-velocity gradient. Turbulence is generated at the plane x1 = 0 and diffuses in the direction x1 > 0. Turbulence is homogeneous in the x2-x3 plane. This problem was first considered by Lele (1985) raising the question whether a turbulent diffusion-wave exists by analyzing the k-ε model. In the following we show, based on the infinite sequence of multi-point correlation equations, that a variety of invariant solutions (scaling laws, see e.g. Oberlack 2001) of the diffusion problem exist employing Lie-group analysis (see e.g. Bluman & Kumei 1989).