### 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 language | English (US) |
---|---|

Article number | 124606 |

Journal | Physical Review Fluids |

Volume | 3 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2018 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Physical Review Fluids*,

*3*(12), [124606]. https://doi.org/10.1103/PhysRevFluids.3.124606

}

*Physical Review Fluids*, vol. 3, no. 12, 124606. https://doi.org/10.1103/PhysRevFluids.3.124606

**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.

Research output: Contribution to journal › Article

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.

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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 -