Results of investigations of non-isothermal turbulent flows based on stochastic equations of the continuum and equivalence of measures

The review of main results of new stochastic theory of turbulence for non-isothermal flows is presented. Based on sets of the stochastic equations for the laws of conservation and for the equivalence of measures between deterministic process and random process, the review of results of an analytical expressions is presented for main parameters of non-isothermal turbulent flow in the tube depending on the initial fluctuation in the non-turbulent medium. It is shown that the derived formulas for the critical Reynolds numbers and critical point, for the velocity and temperature profiles, for the second-order correlation and the turbulent Prandtl number, and heat transfer coefficients are in satisfactory agreement with the classical experimental data for these flow characteristics.