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

doi:https://doi.org/10.1615/tsfp3.490

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

Martin Oberlack,Silke Guenther-2003-01-01-Proceeding of Third Symposium on Turbulence and Shear Flow Phenomena

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TL;DRAbstract

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).

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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).

Keywords

TurbulenceReynolds-averaged Navier–Stokes equationsTurbulent diffusionScalingPhysicsDiffusionInvariant (physics)Mathematical analysis

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