Theoretical Estimates of the Critical Reynolds Number in the Flow around the Sphere on the Basis of Theory of Stochastic Equations and Equivalence of Measures

Abstract

The aim of this investigation is to show the solution for the critical Reynolds number in the flow around the sphere on the basis of theory of stochastic equations and equivalence of measures between turbulent and laminar motions. Solutions obtained by numerical methods (DNS, LES, RANS) require verification and in this case the theoretical results have special value. For today in the scientific literature, there is J. Talor’s implicit formula connecting the critical Reynolds number with the parameters of the initial fluctuations in the flow around the sphere. Here the derivation of the explicit formula is presented. The results show a satisfactory correspondence of the obtained theoretical dependence for the critical Reynolds number to the experiments in the flow around the sphere.

Keywords

• equivalence of measures
• stochastic equations
• critical Reynolds number
• critical point
• the flow around the sphere