Hierarchical random additive model for wall-bounded flows at high Reynolds numbers

Xiang Yang, Charles Meneveau

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.

    Original languageEnglish (US)
    Article number011405
    JournalFluid Dynamics Research
    Volume51
    Issue number1
    DOIs
    StatePublished - Jan 17 2019

    Fingerprint

    wall flow
    Wall flow
    high Reynolds number
    Reynolds number
    Turbulence
    vortices
    Shear stress
    Momentum
    turbulence
    scaling
    shear stress
    Fluids
    Boundary layer flow
    Shear flow
    moments
    momentum
    boundary layer flow
    fluids
    Statistics
    shear flow

    All Science Journal Classification (ASJC) codes

    • Mechanical Engineering
    • Physics and Astronomy(all)
    • Fluid Flow and Transfer Processes

    Cite this

    @article{28d48f9f759b493aa81d350bfd80df55,
    title = "Hierarchical random additive model for wall-bounded flows at high Reynolds numbers",
    abstract = "High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.",
    author = "Xiang Yang and Charles Meneveau",
    year = "2019",
    month = "1",
    day = "17",
    doi = "10.1088/1873-7005/aab57b",
    language = "English (US)",
    volume = "51",
    journal = "Fluid Dynamics Research",
    issn = "0169-5983",
    publisher = "IOP Publishing Ltd.",
    number = "1",

    }

    Hierarchical random additive model for wall-bounded flows at high Reynolds numbers. / Yang, Xiang; Meneveau, Charles.

    In: Fluid Dynamics Research, Vol. 51, No. 1, 011405, 17.01.2019.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Hierarchical random additive model for wall-bounded flows at high Reynolds numbers

    AU - Yang, Xiang

    AU - Meneveau, Charles

    PY - 2019/1/17

    Y1 - 2019/1/17

    N2 - High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.

    AB - High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as related to the so-called hierarchical random additive process (HRAP), which models the near-wall momentum-carrying parts of turbulence by exploiting the self-similarity and the tree-like hierarchical organization of attached eddies. The HRAP model follows Townsend (1980 The Structure of Turbulent Shear Flow) and models boundary layer flows as collections of space-filling, self-similar, wall-attached eddies. However, instead of invoking specifically-shaped typical eddy, HRAP isolates the basic scaling properties of the phenomena by parameterizing contributions of near-wall eddies to generic flow quantities using random addends, a superposition of which leads to the real observable (fluid velocity, wall-shear stress, etc). This compact and relatively simple representation proves to be quite useful, leading to scaling predictions of many turbulence statistics. So far, the HRAP model has been used to provide estimates for scalings of single- and two-point velocity central moments, single- and two-point moment generating functions of velocity fluctuations, and variance of wall-shear stress fluctuations as a function of Reynolds number.

    UR - http://www.scopus.com/inward/record.url?scp=85062510507&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85062510507&partnerID=8YFLogxK

    U2 - 10.1088/1873-7005/aab57b

    DO - 10.1088/1873-7005/aab57b

    M3 - Article

    AN - SCOPUS:85062510507

    VL - 51

    JO - Fluid Dynamics Research

    JF - Fluid Dynamics Research

    SN - 0169-5983

    IS - 1

    M1 - 011405

    ER -