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.

N1 - Funding Information:
X.Y. thanks C. Meneveau and P. Johnson for fruitful discussion. I.M. and R.B. acknowledge the financial support of the Australian Research Council.
Publisher Copyright:
© 2018 American Physical Society.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

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 -