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Transformations which leave statistics of the distance of multi particle dynamics to be invariant for isotropic turbulence

DOI: 10.1615/ICHMT.2012.ProcSevIntSympTurbHeatTransfPal.310
pages 268-271

V. N. Grebenev
Institute of Computational Technologies SD RAS, Lavrentjev ave. 6, 630090 Novosibirsk, Russia

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


We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field of the velocity fluctuations to equip the correlation space K3 by a family of metrics ds2(t). This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean (physical) space R3 with the standard metric. This allows to introduce into the consideration the function of length between fluid particles and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comments the case of a negative Gaussian curvature.

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