2012 , Volume 17, ¹ 5, p.23-45
Grebenev V.N., Medvedev S.B.
Homogeneous isotropic turbulence: Geometry and the admitted group transformation group
A Lagrangian system for homogeneous isotropic turbulence is considered. The system is determined on the space of correlation vectors with the metric ds2(t) of alternative signature generated by the two-point correlation tensor of the velocity fluctuations. We introduce the functional single-action (length) between these two Lagrangian points of the turbulent flow and study the group of transformations leaving distance statistics to be invariant. We show that this group of transformation with respect to spatial variables coincides with a pseudo-group Lie for the signature (++) of the metric ds2(t) and the group of conformal transformation of the space R21,1 in the case of the signature (+-).
Keywords: homogeneous isotropic turbulence, two-point velocity correlation tensor, Lagrangian system, equivalence transformation, geometry of the correlation space
Grebenev V N
Position: Senior Research Scientist
Office: Institute of computational technologies SB RAS
Address: 630090, Russia, Novosibirsk, prospect Akademika Lavrentyeva, 6
Phone Office: (383)3308570
Medvedev Sergey Borisovich
Position: Leading research officer
Office: Inctitute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentyev ave., 6
Phone Office: (383) 330-73-73
Grebenev V.N., Medvedev S.B. Homogeneous isotropic turbulence: Geometry and the admitted group transformation group // Computational technologies. 2012. V. 17. ¹ 5. P. 23-45