Correlation functions in isotropic and anisotropic turbulence: The role ofthe symmetry group

Citation
I. Arad et al., Correlation functions in isotropic and anisotropic turbulence: The role ofthe symmetry group, PHYS REV E, 59(6), 1999, pp. 6753-6765
Citations number
16
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
59
Issue
6
Year of publication
1999
Pages
6753 - 6765
Database
ISI
SICI code
1063-651X(199906)59:6<6753:CFIIAA>2.0.ZU;2-9
Abstract
The theory of fury developed turbulence is usually considered in an idealiz ed homogeneous and isotropic state. Real turbulent flows exhibit the effect s of anisotropic forcing. The analysis of correlation functions and structu re functions in isotropic and anisotropic situations is facilitated and mad e rational when performed in terms of the irreducible-representations of th e relevant symmetry group which is the group of all rotations SO(3). In thi s paper we first consider the needed general theory, and explain why we exp ect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (f or third order tensorial structure functions) and in weakly anisotropic tur bulence (for the second order structure function). The utility of the resul ting expressions for the analysis of experimental data is demonstrated in t he context of high Reynolds number measurements of turbulence in the atmosp here.