Spanwise velocity statistics in high-Reynolds-number turbulent boundary layers. (2nd March 2021) - Baidya, R.; Philip, J.; Hutchins, N.; Monty, J.P.; Marusic, I.
Abstract: 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 $Re$ .