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Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra

Published online by Cambridge University Press:  12 November 2019

Woutijn J. Baars Open the ORCID record for Woutijn J. Baars [Opens in a new window]  and
Ivan Marusic Open the ORCID record for Ivan Marusic [Opens in a new window]
Woutijn J. Baars*
Affiliation:
Department of Engineering, Aarhus University, 8000 Aarhus C, Denmark
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, VIC 3010, Australia
*
†Email address for correspondence: baars@eng.au.dk
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Abstract

In wall-bounded turbulence, a multitude of coexisting turbulence structures form the streamwise velocity energy spectrum from the viscosity- to the inertia-dominated range of scales. Definite scaling-trends for streamwise spectra have remained empirically elusive, although a prominent school of thought stems from the works of Perry & Abell (J. Fluid Mech., vol. 79, 1977, pp. 785–799) and Perry et al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199), which were greatly inspired by the attached-eddy hypothesis of Townsend (The Structure of Turbulent Shear Flow, Cambridge University Press, 1976). In this paper, we re-examine the turbulence kinetic energy of the streamwise velocity component in the context of the spectral decompositions of Perry and co-workers. Two universal spectral filters are derived via spectral coherence analysis of two-point velocity signals, spanning a Reynolds-number range $Re_{\unicode[STIX]{x1D70F}}\sim O(10^{3})$ to $O(10^{6})$ and form the basis for our decomposition of the logarithmic-region turbulence into stochastically wall-detached and wall-attached portions of energy. The latter is composed of scales larger than a streamwise/wall-normal ratio of $\unicode[STIX]{x1D706}_{x}/z\approx 14$. If the decomposition is accepted, a $k_{x}^{-1}$ scaling region can only appear for $Re_{\unicode[STIX]{x1D70F}}\gtrsim 80\,000$, at a wall-normal position of $z^{+}=100$. Following Perry and co-workers, it is hypothesized that spectral contributions from turbulence structures other than attached eddies obscure a $k_{x}^{-1}$ scaling. When accepting the idea of different spectral contributions it is furthermore shown that a broad outer-spectral peak is present even at low $Re_{\unicode[STIX]{x1D70F}}$.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 882 , 10 January 2020 , A25
Copyright
© 2019 Cambridge University Press 

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