Scaling Relation Associated with Kolmogorov's 1941 Theory of Turbulence

Abstract

One of the common features of the problems of quantum field theory, critical phenomena and turbulence is that they are characterized by havingvery many degrees of freedom in a region of the size of a correlationlength. The parameter controlling fluctuations over many length scaleswithin the correlation length is mass ratio, reduced temperature andReynolds number, respectively. By comparing the scaling form of criticalphenomena and that of turbulence, it is found that the scaling relation γ=(2-η)ν known in critical phenomena is also satisfied in Kolmogorov's 1941 theory of turbulence, but the values of the scaling exponents associated with K41 theory of turbulence are very different from those of Landau's mean field theory of critical phenomena.