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Lie Algebra of the Symmetries of the Multi-Point Equations in Statistical Turbulence Theory

Rosteck, Andreas and Oberlack, Martin (2011):
Lie Algebra of the Symmetries of the Multi-Point Equations in Statistical Turbulence Theory.
In: Journal of Nonlinear Mathematical Physics (JNMP), Atlantis Press, pp. 251-264, 18, (1), ISSN 1402-9251, [Online-Edition: http://www.worldscinet.com/jnmp/18/18supp01/S140292511100140...],
[Article]

Abstract

We briefly derive the infinite set of multi-point correlation equations based on the Navier-Stokes equations for an incompressible fluid. From this we reconsider the previously derived set of Lie symmetries, i.e. those directly induced by the ones from classical mechanics and also new symmetries. The latter are denoted statistical symmetries and have no direct counterpart in classical mechanics. Finally, we considerably extend the set of symmetries by Lie algebra methods and give the corresponding commutator tables. Due to the infinite dimensionality of the multi-point correlation equations completeness of its symmetries is not proven yet and is still an open question.

Item Type: Article
Erschienen: 2011
Creators: Rosteck, Andreas and Oberlack, Martin
Title: Lie Algebra of the Symmetries of the Multi-Point Equations in Statistical Turbulence Theory
Language: English
Abstract:

We briefly derive the infinite set of multi-point correlation equations based on the Navier-Stokes equations for an incompressible fluid. From this we reconsider the previously derived set of Lie symmetries, i.e. those directly induced by the ones from classical mechanics and also new symmetries. The latter are denoted statistical symmetries and have no direct counterpart in classical mechanics. Finally, we considerably extend the set of symmetries by Lie algebra methods and give the corresponding commutator tables. Due to the infinite dimensionality of the multi-point correlation equations completeness of its symmetries is not proven yet and is still an open question.

Journal or Publication Title: Journal of Nonlinear Mathematical Physics (JNMP)
Volume: 18
Number: 1
Publisher: Atlantis Press
Uncontrolled Keywords: Turbulence; multi-point statistics; Lie symmetry; Lie algebra
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: 17 Dec 2014 13:35
Official URL: http://www.worldscinet.com/jnmp/18/18supp01/S140292511100140...
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