The Langevin and diffusion equations for statistical velocity and displacement of marked fluid particles are formulated for turbulent flow at large Reynolds number for which Lagrangian Kolmogorov K-41 theory holds. The damping and diffusion terms in these equations are specified by the first two terms of a general expansion in powers of C −1 0 where C 0 is Lagrangian based universal Kolmogorov constant: 6 C 0 7. The equations enable the derivation of descriptions for transport by turbulent

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... uations of conserved scalars, momentum, kinetic energy, pressure and energy dissipation as a function of the derivative of their mean values. Except for pressure and kinetic energy, the diffusion coefficients of these relations are specified in closed-form with C −1 0 as constant of proportionality. The relations are verified with DNS results of channel flow at Re τ = 2000. The presented results can serve to improve or replace the diffusion models of current CFD models.