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 (viscous) energy reduces with increasing friction Reynolds number (Rey). The trend is based on analyzing APG TBL data across 600 less than or similar to Rey less than or similar to 7000 and contrasts with the negligible variation in small viscous-scaled energy noted for canonical wall flows. The data sets considered include those from a well-resolved numerical simulation [Pozuelo et al., J. Fluid Mech. 939, A34 (2022)], which provides access to an APG TBL maintained at near-equilibrium conditions across 1000 less than or similar to Rey less than or similar to 2000, with a well-defined flow history, and a new high-Re-y (similar to 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 Rey is revealed via decomposing the streamwise normal stresses into small-and large-scale contributions, based on a sharp spectral cutoff. 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 Rey in the outer region. The conclusion is reaffirmed by investigating attenuation of streamwise normal stresses due to changing spatial resolutions of the numerical grid or hotwire sensors, which reduces with increasing Rey and is found to be negligible at Re-y similar to 7000 in this study. The results emphasize that new scaling arguments and spatial-resolution corrections should be tested rigorously across a broad Rey range, particularly for pressure gradient TBLs.