The URAPS closure for the normalized Reynolds stress

Karuna S. Koppula, Satish Muthu, André Bénard, Charles A. Petty

    Research output: Contribution to journalArticle

    • 1 Citations

    Abstract

    The Reynolds-averaged Navier-Stokes (RANS)-equation for constant property Newtonian fluids is an exact, albeit unclosed, first-order moment equation for the mean velocity field. The RANS-equation and the Reynolds-averaged continuity equation together with a model for the Reynolds stress provide a set of closed equations that govern the behavior of the mean velocity and mean pressure fields. In this turbulent mixing and beyond (TMB) paper, the key ideas related to a recently developed universal closure for the normalized Reynolds (NR)-stress are reviewed. The new approach relates the NR-stress to four characteristic time scales: a turbulent time scale, a viscous time scale, a time scale related to the mean field velocity gradient and a time scale associated with a rigid body frame-of-reference. The theory stems from an analysis of the Navier-Stokes equation and is formulated as a universal non-negative mapping of the NR-stress into itself. Consequently, all solutions of the NR-stress equation are non-negative dyadic-valued linear operators regardless of the class of benchmark flows used to determine closure parameters. The new closure model predicts that the Coriolis acceleration causes an anisotropic re-distribution of turbulent kinetic energy among the three components of the fluctuating velocity in rotating homogeneous decay.

    Original languageEnglish (US)
    Article number014052
    JournalPhysica Scripta
    Volume88
    Issue numberT155
    DOIs
    StatePublished - Jul 2013

    Profile

    Reynolds stress
    Time scales
    Closure
    closures
    Reynolds equation
    Navier-Stokes equations
    Navier-Stokes equation
    Mean field
    Non-negative
    Model
    velocity distribution
    Turbulent mixing
    Moment equations
    Continuity equation
    Newtonian fluid
    Redistribution
    Kinetic energy
    Rigid body
    Velocity field
    Linear operator

    ASJC Scopus subject areas

    • Condensed Matter Physics
    • Atomic and Molecular Physics, and Optics
    • Mathematical Physics
    • Physics and Astronomy(all)

    Cite this

    The URAPS closure for the normalized Reynolds stress. / Koppula, Karuna S.; Muthu, Satish; Bénard, André; Petty, Charles A.

    In: Physica Scripta, Vol. 88, No. T155, 014052, 07.2013.

    Research output: Contribution to journalArticle

    Koppula, Karuna S.; Muthu, Satish; Bénard, André; Petty, Charles A. / The URAPS closure for the normalized Reynolds stress.

    In: Physica Scripta, Vol. 88, No. T155, 014052, 07.2013.

    Research output: Contribution to journalArticle

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