Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-10-20
Nonlinear Sciences
Chaotic Dynamics
35 pages, REVTEX, 1 figure, Phys. Rev. E, submitted
Scientific paper
10.1103/PhysRevE.59.6753
The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we firstly consider the needed general theory and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.
Arad Itai
L'vov Victor S.
Procaccia Itamar
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