MULTIFRACTAL CASCADE SYMMETRY MODEL FOR FULLY DEVELOPED TURBULENCE

Abstract

We report a symmetry model for turbulence intermittency. This is obtained by the compositions of continuous symmetry group transformations of statistical turbulent spectral equation at infinite Reynolds number limit. Flow evolution under group compositions yields velocity structure function exponents that depend on the dilation symmetry group parameter [Formula: see text] [Formula: see text] and a random parameter [Formula: see text]. The random parameter [Formula: see text] is associated with energy distribution. Since the correction to the space-filling Kolmogorov cascade is small, the value of [Formula: see text]. The asymptotic structures are filaments having dimension one, so [Formula: see text] is found to be related with [Formula: see text] by [Formula: see text]. The present model therefore depends only on [Formula: see text], and [Formula: see text] can be ascertained uniquely for [Formula: see text]. It is found that the velocity structure function exponents [Formula: see text], [Formula: see text] in present symmetry model agree well with the existing experimental, direct numerical simulation results and different phenomenological models for [Formula: see text]. For these values of [Formula: see text], the correction to Kolmogorov space-filling, universal [Formula: see text] law, belongs to the range [Formula: see text], and the fractal dimension for the support set lies in [Formula: see text].