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Spanwise velocity statistics in high-Reynolds-number turbulent boundary layers

Published online by Cambridge University Press:  02 March 2021

R. Baidya Open the ORCID record for R. Baidya [Opens in a new window] ,
J. Philip ,
N. Hutchins ,
J.P. Monty  and
I. Marusic Open the ORCID record for I. Marusic [Opens in a new window]
R. Baidya*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
J. Philip
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
N. Hutchins
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
J.P. Monty
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
I. Marusic
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
*
†Email address for correspondence: baidyar@unimelb.edu.au
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Abstract

Spanwise velocity statistics from high-Reynolds-number turbulent boundary layers are reported. The dataset combines efforts spanning over a decade at the University of Melbourne to accurately capture Reynolds number ($Re$) trends for the spanwise velocity, nominally over one order of magnitude change in $Re$, using custom subminiature cross-wire probes that minimise spatial resolution effects and misalignment errors. The spanwise velocity ($v$) variance is found to exhibit an $Re$ invariant logarithmic slope in the log region, in a similar manner to the streamwise velocity ($u$), which is consistent with the existence of self-similar features within wall-bounded flows. However, unlike the $u$-variance, it appears that the logarithmic $v$-variance trend continues to extend towards the wall. The increase in the $v$-variance with $Re$ in the log region is found to be due to ‘intermediate-scale eddies’, which follow distance-from-the-wall scaling. This results in the $v$-spectrogram exhibiting a dominant energetic ridge across the intermediate-scales, a trend that is not clearly observed in the $u$-spectrogram. Other features of the $v$-spectrogram are found to be similar to the $u$-spectrogram, such as showing small-scale near-wall features that scale universally with viscous units, and the influence of large-scale $v$ signals residing in the log region that extend to the wall, resulting in a large-scale $v$ footprint in the near-wall region. The observed behaviour of the $v$-spectrogram with changing $Re$ is used to construct a model for the $v$-variance based on contributions from small-, intermediate- and large-scales, leading to a predictive tool at asymptotically high $Re$.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A35
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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