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Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and $A_{1}$

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

Scalings of the streamwise velocity energy spectra in turbulent boundary layers were considered in Part 1 (Baars & Marusic, J. Fluid Mech., vol. 882, 2020, A25). A spectral decomposition analysis provided a means to separate out attached and non-attached eddy contributions and was used to generate three spectral sub-components, one of which is a close representation of the spectral signature induced by self-similar, wall-attached turbulence. Since sub-components of the streamwise turbulence intensity $\overline{u^{2}}$ follow from an integration of the velocity energy spectra, we here focus on the scaling of the former. Wall-normal profiles and Reynolds-number trends of the three individual, additive sub-components of the streamwise turbulence intensity are examined. Based on universal trends across all Reynolds numbers considered, some evidence is given for a Townsend–Perry constant of $A_{1}=0.98$, which would describe the wall-normal logarithmic decay of the turbulence intensity per Townsend’s attached-eddy hypothesis. It is also demonstrated how this constant can be consistent with the Reynolds-number increase of the streamwise turbulence intensity in the near-wall region.

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 , A26
Copyright
© 2019 Cambridge University Press 

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