Hannover 2010 – scientific programme

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UP: Fachverband Umweltphysik

UP 3: Greenhouse Gases and Climate

UP 3.2: Talk

Wednesday, March 10, 2010, 11:30–11:45, M 11

Primitive turbulence: kinetics, mixing length, and von Karman's constant — •Helmut Z. Baumert — IAMARIS, Hamburg

The paper presents a novel 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 r 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 -- close to the international standard value 0.4.