THE PRINCIPLE OF MAXIMUM RANDOMNESS IN THE THEORY OF FULLY-DEVELOPED TURBULENCE .2. ISOTROPIC DECAYING TURBULENCE

A statistical model for describing the decay of developed isotropic tu rbulence of an incompressible fluid is proposed. The model uses the di stribution function of the velocity pulsations introduced earlier by t he authors on the basis of the principle of maximum randomness of the velocity field for a given spectral energy flux. The renormalization-g roup technique and epsilon' expansion are used to calculate the correl ation functions of the velocity that occur in the equation of spectral energy balance. This leads to a closed equation for the dependence of the energy spectrum on the integral turbulence scale r(c)(t). In the inertial interval, this equation gives the Kolmogorov asymptotic spect rum, while for the time dependence of r(c)(t) and the pulsation energy e(t) it predicts the power laws r(c)(t) approximately t2/5 and r(t) a pproximately t-6/5.