Three-dimensional turbulent diffusion versus critical phenomena

Abstract

The critical exponent, nu , of the correlated (or coherent) length of a turbulent cluster has been related to the minimal fractal dimension, Dmin, of multifractal isotropic turbulence. The relationship has turned out to be nu Dmin=3/2. For the homogeneous case, Dmin=3 and hence, nu =1/2 (the so-called mean-field approach of the theory of critical phenomena). For Dmin approximately=2.36 (the well known turbulent value), nu approximately=0.63. This result allows one to classify this case as the critical phenomenon of the so-called 'thermal' class of universality. Transition to the 'percolation' class of universality ( nu approximately=0.9) is determined by the boundary conditions.