A multifractal model for the momentum transfer process in wall-bounded flows

Xiang Yang, A. Lozano-Durán

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τ l , where l is the filtering length scale. According to the multifractal formalism, (τ' 2 ) ∼ log(Re τ )) and (exp(pτ' l )∼(L/l)ζ p in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.

    Original languageEnglish (US)
    Pages (from-to)R2
    JournalJournal of Fluid Mechanics
    Volume824
    DOIs
    StatePublished - Aug 10 2017

    Fingerprint

    wall flow
    Wall flow
    Momentum transfer
    momentum transfer
    Momentum
    formalism
    momentum
    Fluids
    Direct numerical simulation
    Channel flow
    Random processes
    cascades
    Kinetic energy
    Turbulent flow
    Shear stress
    Kinematics
    Reynolds number
    Turbulence
    real numbers
    isotropic turbulence

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics
    • Mechanics of Materials
    • Mechanical Engineering

    Cite this

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    title = "A multifractal model for the momentum transfer process in wall-bounded flows",
    abstract = "The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τ l , where l is the filtering length scale. According to the multifractal formalism, (τ' 2 ) ∼ log(Re τ )) and (exp(pτ' l )∼(L/l)ζ p in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.",
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    A multifractal model for the momentum transfer process in wall-bounded flows. / Yang, Xiang; Lozano-Durán, A.

    In: Journal of Fluid Mechanics, Vol. 824, 10.08.2017, p. R2.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A multifractal model for the momentum transfer process in wall-bounded flows

    AU - Yang, Xiang

    AU - Lozano-Durán, A.

    PY - 2017/8/10

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    N2 - The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τ l , where l is the filtering length scale. According to the multifractal formalism, (τ' 2 ) ∼ log(Re τ )) and (exp(pτ' l )∼(L/l)ζ p in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.

    AB - The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τ l , where l is the filtering length scale. According to the multifractal formalism, (τ' 2 ) ∼ log(Re τ )) and (exp(pτ' l )∼(L/l)ζ p in the log-region, where Re τ is the friction Reynolds number, p is a real number, L is an outer length scale and ζ p is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re τ = 4200.

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