On distributions of velocity random fields in turbulent flows

The present paper aims to derive a partial differential equation (PDE) for the single-time single-point probability density function (PDF) of velocity field turbulent flow. PDF PDE is highly non-linear parabolic-transport equation, which depends on two conditional statistical numerics important physical significance. general form classical Reynolds mean flow (O. Reynolds, Philos. Trans. R. Soc. Lond. Ser. A 186 (1895), 123–164. http://doi.org/10.1098/rsta.1895.0004) and precise formulation transport (S. B. Pope, Turbulent flows, Cambridge University Press, Cambridge, 2000. https://doi.org/10.1017/CBO9780511840531.). provides us with new method modelling turbulence. An explicit example constructed. Though seemingly artificial, it demonstrates based PDE.