Journal of Nonlinear Mathematical Physics

Volume 18, Issue 1, March 2011, Pages 109 - 120

Geometric Realization of the Two-Point Velocity Correlation Tensor for Isotropic Turbulence

Authors
Vladimir N. Grebenev*
Institute of Computational Technologies SD RAS, Lavrentjev Ave. 6, Novosibirsk, 630090, Russia, vngrebenev@gmail.com
Martin Oberlack
Technische Universität Darmstadt, Petersenstraße 30, Darmstadt 64287, Germany, oberlack@fdy.tu-darmstadt.de
*Corresponding author.
Corresponding Author
Vladimir N. Grebenev
Received 19 April 2010, Accepted 12 June 2010, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925111001192How to use a DOI?
Keywords
Homogeneous isotropic turbulence, two-point correlation tensor, Riemannian metric, von Kármán–Howarth equation
Abstract

A new geometric view of homogeneous isotropic turbulence is contemplated employing the two-point velocity correlation tensor of the velocity fluctuations. We show that this correlation tensor generates a family of pseudo-Riemannian metrics. This enables us to specify the geometry of a singled out Eulerian fluid volume in a statistical sense. We expose the relationship of some geometric constructions with statistical quantities arising in turbulence.

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 1
Pages
109 - 120
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925111001192How 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

TY  - JOUR
AU  - Vladimir N. Grebenev
AU  - Martin Oberlack
PY  - 2021
DA  - 2021/01
TI  - Geometric Realization of the Two-Point Velocity Correlation Tensor for Isotropic Turbulence
JO  - Journal of Nonlinear Mathematical Physics
SP  - 109
EP  - 120
VL  - 18
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001192
DO  - https://doi.org/10.1142/S1402925111001192
ID  - Grebenev2021
ER  -