Critical analysis of the methodology for deriving equations of motion O. Reynolds for turbulent flows

Abstract

Annotation The O. Reynolds equation is the only one in the scientific world that is derived from equations that are valid for a medium that has completely different surface forces than the surface forces in real turbulent flows. It is shown that by violating the formulated averaging rules and algebraic rules, additional terms were introduced into the inertial part of the Navier-Stokes equations while maintaining the surface forces that determine the nature of motion of a completely different medium, thereby turning the averaged equations into inequalities. Based on the analysis of all violations allowed during averaging, it is shown that it is impossible to obtain new equations of motion by averaging the Navier-Stokes equations, and the stresses introduced by O. Reynolds do not reflect the real stresses in a turbulent flow. When you eliminate violations of the averaging rules, all of them turn to zero. As an alternative solution to the problem, we derive equations based on equations of motion in stresses that are valid for any media, and simplify it to a form suitable for technical calculations.