## 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 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.

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.

Original language | English |
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Pages (from-to) | 369–399 |

Number of pages | 31 |

Journal | Flow, Turbulence and Combustion |

Volume | 97 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 |