Statistical models of large scale turbulent flow

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
C0−1
where C0 is Lagrangian based universal Kolmogorov constant: 6≲C 0 ≲7
6≲C0≲7
. The equations enable the derivation of descriptions for transport by turbulent fluctuations 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
C0−1
as constant of proportionality. The relations are verified with DNS results of channel flow at Reτ=2000. The presented results can serve to improve or replace the diffusion models of current CFD models.