The stochastic theory of the turbulence

Abstract

The general results of new stochastic theory of turbulence for isothermal flows are presented. Stochastic equations for laws of conservation and for equivalence of measures between deterministic process and random process, the review of results of an analytical expressions are presented for the isothermal turbulent flow in the tube and for the flow on the flat plate depending on initial fluctuation in medium. An important result of a new theory is the fact that even if the fluctuation has an initial spectrum in the form of a delta-function, the modular fractal equation obtained in theory determines both the fractal equation for the diffusion process of energy transfer and the fractal generation equation of Landau type described the subsequent expansion of the spectrum. Derived formulas for critical Reynolds numbers and critical point, the velocity profile, the second-order correlation, and friction coefficients give the satisfactory agreement with the experimental data for both flows.