The principle of maximum randomness in the theory of fully developed turbulence. I. Homogeneous isotropic turbulence

A new approach to the description of fully developed turbulence is developed on the basis of the maximum entropy principle and the renormalization group. The Kolmogorov dimension for the velocity field is obtained, and a conjecture which explains the experimentally observed deviations from this dimension is proposed. The calculated anomalous dimension of the energy dissipation operator differs from the prediction of Kolmogorov's theory.