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

• Published in: Journal of fluid mechanics 2021-03, Vol.913, Article A35
• Main Authors: Baidya, R., Philip, J., Hutchins, N., Monty, J.P., Marusic, I.
• Format: Article
• Language: English
• Subjects: Boundary layers; Computational fluid dynamics; Eddies; Fluid flow; Friction; High Reynolds number; JFM Papers; Measurement techniques; Misalignment; Reynolds number; Scaling; Self-similarity; Sensors; Spatial discrimination; Spatial resolution; Statistical methods; Statistics; Trends; Turbulent boundary layer; Variance; Velocity
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.1129

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 $Re$.