Volume 15, Issue 2, August 2008, Pages 227 - 251
Lie algebra methods for the applications to the statistical theory of turbulence
V.N. GREBENEV 0, M. OBERLACK 1, A.N. GRISHKOV 2
0Institute of Computational Technologies
1Chair of Fluid Dynamics, Technische Universit ?at Darmstadt
2Institute of Mathematics and Statistics, University of Sao Paulo
Received 5 February 2008, Accepted 26 March 2008, Available Online 1 August 2008.
- https://doi.org/10.2991/jnmp.2008.15.2.9How to use a DOI?
- 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 -.
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Cite this article
TY - JOUR AU - V.N. GREBENEV AU - M. OBERLACK AU - A.N. GRISHKOV PY - 2008 DA - 2008/08 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 - https://doi.org/10.2991/jnmp.2008.15.2.9 ID - GREBENEV2008 ER -