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

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-, intermediateand large-scales, leading to a predictive tool at asymptotically high Re.