Lie algebra methods for the applications to the statistical theory of turbulence

DOI

10.2991/jnmp.2008.15.2.9How to use a DOI?

Abstract

Approximate Lie symmetries of the Navier-Stokes equations are used for the applica- tions to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - V.N. Grebenev
AU  - M. Oberlack
AU  - A.N. Grishkov
PY  - 2008
DA  - 2008/08/01
TI  - Lie algebra methods for the applications to the statistical theory of turbulence
JO  - Journal of Nonlinear Mathematical Physics
SP  - 227
EP  - 251
VL  - 15
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.2.9
DO  - 10.2991/jnmp.2008.15.2.9
ID  - Grebenev2008
ER  -