Berlin 2012 – scientific programme

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UP: Fachverband Umweltphysik

UP 9: Poster session

UP 9.4: Poster

Wednesday, March 28, 2012, 18:30–19:15, Poster F

Universal constants and equations of turbulent motion — •Helmut Ziegfeld Baumert¹ and Hartmut Peters² — ¹IAMARIS, Hamburg, Germany — ²Earth and Space Research, Seattle, USA

We present turbulence in analogy with the kinetic theory of gases, with dipoles made of vortex tubes as frictionless quasi-particles. Their chaotic movements are governed by Helmholtz' elementary vortex rules applied locally. Contact interactions lead either to random scatter or to the formation of likewise rotating, fundamentally unstable whirls. We predict von Karman's constant as 1/sqrt(2 pi) = 0.399 and the spatio-temporal dynamics of energy-containing time and length scales of turbulent mixing according to experiments. The above image is compatible with Kolmogorov's turbulence spectra as dissipative patches of locally space-filling bearings in the sense of Herrmann [1990]. For steady and locally homogeneous conditions our approach predicts the dimensionless pre-factor in the 3D Eulerian wavenumber spectrum as 1.8. In the Lagrangian frequency spectrum we find the integer 2. Our results improve the understanding of stratified laboratory and geophysical flows significantly. In the neutrally geophysical case our derivations are completely free of empirical relations and rest on geometry, methods from many-particle physics, and on elementary conservation laws only. In the stably stratified geophysical case the role of internal gravity waves is taken into accout using the universal mixing efficiency and, for the strength of the wave field, one site-specific empirical parameter.