Abstract
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 dam** and diffusion terms in these equations are specified by the first two terms of a general expansion in powers of \(C_{0}^{-1}\) where C 0 is Lagrangian based universal Kolmogorov constant: \(6\lesssim C_{0}\lesssim 7\). 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 \(C_{0}^{-1}\) as constant of proportionality. The relations are verified with DNS results of channel flow at R e τ =2000. The presented results can serve to improve or replace the diffusion models of current CFD models.
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Brouwers, J.J.H. Statistical Models of Large Scale Turbulent Flow. Flow Turbulence Combust 97, 369–399 (2016). https://doi.org/10.1007/s10494-015-9701-6
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DOI: https://doi.org/10.1007/s10494-015-9701-6