Reynolds-number effects on the outer region of adverse-pressure-gradient turbulent boundary layers

We study the Reynolds-number effects on the outer region of moderate adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) and find that their small scale energy reduces with increasing friction Reynolds-number ($Re_{\tau}$). The trend is based on analyzing APG TBL data across 600 $\lesssim$ $Re_{\tau}$ $\lesssim$ 7000, and contrasts with the negligible variation in small scale energy noted for canonical wall flows. The datasets considered include those from a well-resolved numerical simulation (Pozuelo et al. 2022), which provides access to an APG TBL maintained at near-equilibrium conditions across 1000 $\lesssim$ $Re_{\tau}$ $\lesssim$ 2000, with a well-defined flow history, and a new high-$Re_{\tau}$ ($\sim$ 7000) experimental study from the large Melbourne wind tunnel, with its long test section modified to permit development of an APG TBL from a 'canonical' upstream condition. The decrease in small scale energy with $Re_{\tau}$ is revealed via decomposing the streamwise normal stresses into small and large scale contributions, based on a sharp spectral cut-off. The origin for this trend is traced back to the production of turbulent kinetic energy in an APG TBL, the small scale contribution to which is also found to decrease with $Re_{\tau}$ in the outer region. The conclusion is reaffirmed by investigating attenuation of streamwise normal stresses due to changing spatial-resolutions of the numerical grid/hotwire sensors, which reduces with increasing $Re_{\tau}$ and is found to be negligible at $Re_{\tau}$ $\sim$ 7000 in this study. The results emphasize that new scaling arguments and spatial-resolution correction schemes should be tested rigorously across a broad $Re_{\tau}$ range, particularly for the outer region of pressure gradient TBLs.