A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers

Xiang Yang, Mahdi Abkar

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location is modelled as a sum of additive contributions from wall-attached eddies and the number of addends is . The HRAP model admits generalized logarithmic scalings including , , , where is the streamwise velocity fluctuation, is an outer length scale, is the two-point displacement in the streamwise direction and denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.

    Original languageEnglish (US)
    Pages (from-to)354-380
    Number of pages27
    JournalJournal of Fluid Mechanics
    Volume842
    DOIs
    StatePublished - May 10 2018

    Fingerprint

    wall flow
    Wall flow
    high Reynolds number
    Reynolds number
    scalars
    Kinematics
    Turbulence
    Large eddy simulation
    kinematics
    turbulence
    vortices
    formalism
    scaling
    large eddy simulation

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

    Cite this

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    abstract = "The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy hypothesis. The HRAP model was previously used to model the kinematics of velocity fluctuations in wall turbulence: , where the instantaneous streamwise velocity fluctuation at a generic wall-normal location is modelled as a sum of additive contributions from wall-attached eddies and the number of addends is . The HRAP model admits generalized logarithmic scalings including , , , where is the streamwise velocity fluctuation, is an outer length scale, is the two-point displacement in the streamwise direction and denotes ensemble averaging. If the statistical behaviours of the streamwise velocity fluctuation and the fluctuation of a passive scalar are similar, we can expect first that the above mentioned scalings also exist for passive scalars (i.e. for being fluctuations of scalar concentration) and second that the instantaneous fluctuations of a passive scalar can be modelled using the HRAP model as well. Such expectations are confirmed using large-eddy simulations. Hence the work here presents a framework for modelling scalar turbulence in high Reynolds number wall-bounded flows.",
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    A hierarchical random additive model for passive scalars in wall-bounded flows at high Reynolds numbers. / Yang, Xiang; Abkar, Mahdi.

    In: Journal of Fluid Mechanics, Vol. 842, 10.05.2018, p. 354-380.

    Research output: Contribution to journalArticle

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