Primitive turbulence: kinetics, Prandtl's mixing length, and von Karman's constant

Helmut Z. Baumert

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arXiv · 0907.0223

Primitive turbulence: kinetics, Prandtl's mixing length, and von Karman's constant

Helmut Z. Baumert

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Abstract

The paper presents a theory of shear-generated turbulence at asymptotically high Reynolds numbers. It is based on an ensemble of dipole vortex tubes taken as quasi-particles and realized in form of rings, hairpins or filament couples of potentially finite length. In a not necesserily planar cross sectional area through a vortex tangle, taken locally orthogonal through each individual tube, the dipoles are moving with the classical dipole velocity. The vortex radius is directly related with Prandtl's classical mixing length. The quasi-particles perform dipol chaos which reminds of molecular chaos in real gases. Collisions between quasi-particles lead either to particle annihilation (turbulent dissipation) or to particle scattering (turbulent diffusion). These ideas suffice to develop a closed theory of shear-generated turbulence without empirical parameters, with analogies to birth and death processes of macromolecules. It coincides almost perfectly with the well-known K-Omega turbulence closure applied in many branches of science and technology. In the case of free homogeneous decay the TKE is shown to follow 1/t. For an adiabatic condition at a solid wall the theory predicts a logarithmic mean-flow boundary layer with von Karman's constant as 1/SQRT(2 pi)=0.399.

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Helmut Z. Baumert. 2009-07-01. Primitive turbulence: kinetics, Prandtl's mixing length, and von Karman's constant. https://arxiv.org/abs/0907.0223

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