An algebraic preclosure theory for the Reynolds stress

S. M. Parks, K. Weispfennig, C. A. Petty

    Research output: Contribution to journalArticle

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    Abstract

    An algebraic preclosure theory for the Reynolds stress 〈u′u′〉 is developed based on a smoothing approximation which compares the space-time relaxation of a convective-diffusive Green's function with the space-time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time τR associated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using an isotropic model for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and an eddy viscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that τRS ∼ 1, where S represents the mean shear rate. The Reynolds stress model and a set of recalibrated k-∈ transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than 20 ×〈uz〉(0)/S, a theoretical result consistent with experimental observations.

    Original languageEnglish (US)
    Pages (from-to)645-653
    Number of pages9
    JournalPhysics of Fluids
    Volume10
    Issue number3
    StatePublished - Mar 1998

    Profile

    Reynolds stress
    Addison Disease
    relaxation time
    turbulence
    Alprostadil
    Relaxation time
    Turbulence
    Anthralin
    eddy viscosity
    pressure distribution
    shear flow
    smoothing
    closures
    Green's functions
    shear
    gradients
    coefficients
    approximation
    Protoveratrines
    Cholestyramine Resin

    ASJC Scopus subject areas

    • Fluid Flow and Transfer Processes
    • Computational Mechanics
    • Mechanics of Materials
    • Physics and Astronomy(all)
    • Condensed Matter Physics

    Cite this

    Parks, S. M., Weispfennig, K., & Petty, C. A. (1998). An algebraic preclosure theory for the Reynolds stress. Physics of Fluids, 10(3), 645-653.

    An algebraic preclosure theory for the Reynolds stress. / Parks, S. M.; Weispfennig, K.; Petty, C. A.

    In: Physics of Fluids, Vol. 10, No. 3, 03.1998, p. 645-653.

    Research output: Contribution to journalArticle

    Parks, SM, Weispfennig, K & Petty, CA 1998, 'An algebraic preclosure theory for the Reynolds stress' Physics of Fluids, vol 10, no. 3, pp. 645-653.

    Parks, S. M.; Weispfennig, K.; Petty, C. A. / An algebraic preclosure theory for the Reynolds stress.

    In: Physics of Fluids, Vol. 10, No. 3, 03.1998, p. 645-653.

    Research output: Contribution to journalArticle

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