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, and I. Marusic
Phys. Rev. Fluids 3, 124606 – Published 17 December 2018

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)] 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 et al., Phys. Rev. Fluids 2, 064602 (2017)], 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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  • Received 11 June 2018

DOI:https://doi.org/10.1103/PhysRevFluids.3.124606

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Techniques
Fluid Dynamics

Authors & Affiliations

X. I. A. Yang1, R. Baidya2, Yu Lv3, and I. Marusic2

  • 1Mechanical and Nuclear Engineering, Penn State University, Pennsylvania 16801, USA
  • 2Department of Mechanical Engineering, University of Melbourne, Melbourne, Victoria 3010, Australia
  • 3Department of Aerospace Engineering, Mississippi State University, Mississippi 39759, USA

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Vol. 3, Iss. 12 — December 2018

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