An Estimation of Turbulent Vector Fields, Spectral and Correlation Functions Depending on Initial Turbulence Based on Stochastic Equations. The Landau Fractal Equation

Analytical expressions for estimation of turbulent vector fields, spectral and correlation functions depending on the initial turbulence based on stochastic equations are presented. Calculated values of exponent of the velocity profile and the second-order correlation are in satisfactory agreement with the data for classical turbulent flows. Also, with the use of stochastic equations, the two new fractal equations for generation and diffusion of turbulence are obtained. In special case, the second fractal equation takes the form of the Landau equation. As the result, the second-order correlations and turbulent Prandtl number are presented as the functions of the initial turbulence.