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Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

Grebenev, Vladimir N. and Oberlack, Martin and Grishkov, A. N. :
Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence.
[Online-Edition: http://link.springer.com/article/10.1007%2Fs00033-012-0251-7]
In: Zeitschrift für Angewandte Mathematik und Physik, 64 (3) pp. 599-620. ISSN 0044-2275
[Article] , (2013)

Official URL: http://link.springer.com/article/10.1007%2Fs00033-012-0251-7

Abstract

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K 3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds 2(t) in K 3. This construction presents the template for embedding the couple (K 3, ds 2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the 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 comment the case of a negative Gaussian curvature.

Item Type: Article
Erschienen: 2013
Creators: Grebenev, Vladimir N. and Oberlack, Martin and Grishkov, A. N.
Title: Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence
Language: English
Abstract:

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K 3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds 2(t) in K 3. This construction presents the template for embedding the couple (K 3, ds 2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the 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 comment the case of a negative Gaussian curvature.

Journal or Publication Title: Zeitschrift für Angewandte Mathematik und Physik
Volume: 64
Number: 3
Publisher: Springer
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Exzellenzinitiative
Exzellenzinitiative > Clusters of Excellence
Zentrale Einrichtungen
Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI)
Date Deposited: 08 Oct 2014 08:41
Official URL: http://link.springer.com/article/10.1007%2Fs00033-012-0251-7
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