Hierarchical random additive model for the spanwise and wall-normal velocities in wall-bounded flows at high Reynolds numbers

X. I.A. Yang, R. Baidya, Yu Lv, I. Marusic

Research output: Contribution to journalArticle

Abstract

At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)10.1103/PhysRevFluids.1.024402] reinterpreted this hypothesis and developed the "hierarchical random additive process" model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang, Phys. Rev. Fluids 2, 064602 (2017)10.1103/PhysRevFluids.2.064602], the HRAP model was used for making scaling predictions of the second-order structure function [ui′(x)-ui′(x′)][uj′(x)-uj′(x′)] in the logarithmic range, where ui's are the velocity fluctuations in the ith Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.

Original languageEnglish (US)
Article number124606
JournalPhysical Review Fluids
Volume3
Issue number12
DOIs
StatePublished - Dec 2018

Fingerprint

Additive Process
Wall flow
Additive Models
Random process
Reynolds number
Process Model
Logarithmic
Fluctuations
Cartesian
Scaling
Range of data
Fluid
Conceptual Modeling
Boundary Layer Flow
Structure-function
Shear Flow
Turbulent Flow
Model
Fidelity
Momentum

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

Cite this

@article{015cdf1b206a4cddbdaac72dfad74468,
title = "Hierarchical random additive model for the spanwise and wall-normal velocities in wall-bounded flows at high Reynolds numbers",
abstract = "At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)10.1103/PhysRevFluids.1.024402] reinterpreted this hypothesis and developed the {"}hierarchical random additive process{"} model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang, Phys. Rev. Fluids 2, 064602 (2017)10.1103/PhysRevFluids.2.064602], the HRAP model was used for making scaling predictions of the second-order structure function [ui′(x)-ui′(x′)][uj′(x)-uj′(x′)] in the logarithmic range, where ui's are the velocity fluctuations in the ith Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.",
author = "Yang, {X. I.A.} and R. Baidya and Yu Lv and I. Marusic",
year = "2018",
month = "12",
doi = "10.1103/PhysRevFluids.3.124606",
language = "English (US)",
volume = "3",
journal = "Physical Review Fluids",
issn = "2469-990X",
publisher = "American Physical Society",
number = "12",

}

Hierarchical random additive model for the spanwise and wall-normal velocities in wall-bounded flows at high Reynolds numbers. / Yang, X. I.A.; Baidya, R.; Lv, Yu; Marusic, I.

In: Physical Review Fluids, Vol. 3, No. 12, 124606, 12.2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Hierarchical random additive model for the spanwise and wall-normal velocities in wall-bounded flows at high Reynolds numbers

AU - Yang, X. I.A.

AU - Baidya, R.

AU - Lv, Yu

AU - Marusic, I.

PY - 2018/12

Y1 - 2018/12

N2 - At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)10.1103/PhysRevFluids.1.024402] reinterpreted this hypothesis and developed the "hierarchical random additive process" model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang, Phys. Rev. Fluids 2, 064602 (2017)10.1103/PhysRevFluids.2.064602], the HRAP model was used for making scaling predictions of the second-order structure function [ui′(x)-ui′(x′)][uj′(x)-uj′(x′)] in the logarithmic range, where ui's are the velocity fluctuations in the ith Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.

AB - At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)10.1103/PhysRevFluids.1.024402] reinterpreted this hypothesis and developed the "hierarchical random additive process" model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang, Phys. Rev. Fluids 2, 064602 (2017)10.1103/PhysRevFluids.2.064602], the HRAP model was used for making scaling predictions of the second-order structure function [ui′(x)-ui′(x′)][uj′(x)-uj′(x′)] in the logarithmic range, where ui's are the velocity fluctuations in the ith Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.

UR - http://www.scopus.com/inward/record.url?scp=85059392657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059392657&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.3.124606

DO - 10.1103/PhysRevFluids.3.124606

M3 - Article

AN - SCOPUS:85059392657

VL - 3

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 12

M1 - 124606

ER -