Statistical models of large scale turbulent flow

J.J.H. Brouwers

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    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.
    Original languageEnglish
    Pages (from-to)369–399
    Number of pages31
    JournalFlow, Turbulence and Combustion
    Volume97
    Issue number2
    DOIs
    Publication statusPublished - 2016

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