Some analytical results of the theory of equivalence measures and stochastic theory of turbulence for non-isothermal flows

Fundamentals of the new theory for the processes of transition from deterministic state to the chaos state (turbulence) for non-isothermal flows are presented.According to this theory, systems of stochastic equations of energy, momentum and mass are applied for non-isothermal flows.Then the analytical dependence for estimation of the value of the critical Reynolds number and the value of the critical point of regime change for non-isothermal and compressible flows are written.As an example, consider the classic flow of a Newtonian medium in the circular smooth tube.The values of the critical point of the beginning of the transition from laminar (deterministic) to turbulent motion for non-isothermal flows in the pipe are predicated.It is shown, that predicated values of the critical Reynolds numbers are in satisfactory agreement with the classical data.