THE MAXIMAL RANDOMNESS PRINCIPLE IN D-DIMENSIONAL TURBULENCE

A set of self-consistent equations in one-loop approximation in a stat istical model of fully developed homogeneous isotropic turbulence, whi ch is based on the maximal randomness principle of the incompressible velocity field with stationary energy spectral flux, is obtained. Than ks to the applied principle the model statistics becomes essentially n on Gaussian. The set of equations does not possess the infrared and ul traviolet divergences near the obtained Kolmogorov spectral exponents. The solution of these equations leads to the Kolmogorov exponents, bu t its amplitude proportional to the Kolmogorov constant C-k is negativ e for Euclidean dimension d = 3. Systematic investigation is made of ( inertial) steady state scaling solutions for dimensions 2 < d < 2.5569 5, where constant C-k(d) becomes positive. Considered in this way, the model stability is discussed in the context of widely studied fractal aspects of turbulence.