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Expanded analogy between Boltzmann kinetic theory of fluids and turbulence

Expanded analogy between Boltzmann kinetic theory of fluids and turbulence,10.1017/S0022112004001211,Journal of Fluid Mechanics,Hudong Chen,Steven A.

Expanded analogy between Boltzmann kinetic theory of fluids and turbulence   (Citations: 17)
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We demonstrate that the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to higher order in the Knudsen number. This suggests that there may be a good basis for understanding turbulence in terms of Boltzmann kinetic theory. If so, turbulence may be better described in terms of `mixing times' rather than the more classical `mixing lengths'. Comparisons are made to Reynolds-stress turbulence models.
Journal: Journal of Fluid Mechanics - J FLUID MECH , vol. 519, pp. 301-314, 2004
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    • ...Discrete kinetic theory, and in particular the LBM, has recently been employed to a priori derive turbulence models based on a mean-field approximation [36,37,38] and lattice kinetic turbulence models have found much success [39]...

    Kannan N. Premnathet al. Dynamic subgrid scale modeling of turbulent flows using lattice-Boltzm...

    • ...Indeed, based on a Chapman-Enskog-like analysis, one can show that 6 N ≥ is necessary to realize the correct Navier-Stokes level thermohydrodynamics or Burnett level (in the framework of kinetic-theory-based hydrodynamics) isothermal fluid physics [6, 10, 21, 22]...
    • ...Both Navier-Stokes thermal energy fluxes or higher-order non-equilibrium moment fluxes require isotropy to at least 6th order [10]...

    Hudong Chenet al. Discrete Rotational Symmetry, Moment Isotropy, and Higher Order Lattic...

    • ...In Sects. 3 and 4 the analogy between molecular and turbulent motion [32, 33] will then be used for the construction of equations for turbulent motion...
    • ...It is of interest to note that the same nonlinear stress model can be derived from the stress transport equation by adopting the Chapman–Enskog expansion technique, which accounts for small deviations of F from the equilibrium PDF Feq [33]...

    Stefan Heinz. Unified turbulence models for LES and RANS, FDF and PDF simulations

    • ...First we use the hydrodynamic approximation, derived from kinetic equation by Chen et. al..[6] in the limit ωτ ≪ 1. Then, derivation of equations valid in an infinite range 0 < ωτ < ∞ is presented and it is shown that in the high-frequency limit ωτ → ∞, the dissipation rate W → const...
    • ...remarkable paper, Chen et. al. [6], based on thequation (1)-(2), formulated the Chapman-Enskog expansion in powers on dimensionless relaxation time ǫ = τ∂xiuj...

    Victor Yakhotet al. Stokes' second flow problem in a high-frequency limit: application to ...

    • ...This procedure was used in [19] for constructing a quadratic model for the Reynolds stresses in single-phase turbulence by solving a simple kinetic equation with a relaxation “collision term”...

    V. M. Alipchenkovet al. Differential and algebraic models for the second moments of particle v...

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