Scaling Relation Associated with Kolmogorov's 1941 Theory of Turbulence

One of the common features of the problems of quantum field theory, critical phenomena and turbulence is that they are characterized by having very many degrees of freedom in a region of the size of a correlation length. The parameter controlling fluctuations over many length scales within the correlation length is mass ratio, reduced temperature and Reynolds number, respectively. By comparing the scaling form of critical phenomena 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.