Journal of Nonlinear Mathematical Physics

<Previous Article In Issue
Volume 18, Issue Supplement 1, September 2011, Pages 251 - 264

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

Authors
Andreas M. Rosteck*, §, Martin Oberlack*, †, ‡,
*Chair of Fluid Dynamics, Department of Mechanical Engineering, TU Darmstadt, Petersenstr. 30, 64287 Darmstadt, Germany
†Center of Smart Interfaces, TU Darmstadt, Petersenstr. 32, 64287 Darmstadt, Germany
‡GS Computational Engineering, TU Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
Received 15 October 2010, Accepted 4 November 2010, Available Online 7 January 2021.
DOI
10.1142/S1402925111001404How to use a DOI?
Keywords
Turbulence; multi-point statistics; Lie symmetry; Lie algebra
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.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

<Previous Article In Issue
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - Supplement 1
Pages
251 - 264
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001404How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Andreas M. Rosteck
AU  - Martin Oberlack
PY  - 2021
DA  - 2021/01/07
TI  - Lie Algebra of the Symmetries of the Multi-Point Equations in Statistical Turbulence Theory
JO  - Journal of Nonlinear Mathematical Physics
SP  - 251
EP  - 264
VL  - 18
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001404
DO  - 10.1142/S1402925111001404
ID  - Rosteck2021
ER  -