Wall-scaled eddies and embedded shear layers in high-Reynolds-number moderate adverse-pressure-gradient boundary layers

Abstract

This study compares high-Reynolds-number turbulent boundary layers under zero and low-to-moderate adverse pressure gradients, showing similar scaling and energy contributions from the wall-scaled attached-eddy hierarchy and superstructures in both flows. The main differences occur in the outer/wake region, where APG-induced energisation is linked to an outer-scaled, embedded-shear-layer-type organisation that progressively penetrates the logarithmic region as the pressure-gradient strength increases. The analysis uses two complementary datasets for ZPG and APG boundary layers at matched friction Reynolds numbers of approximately 10,000, with minimal upstream pressure-gradient history: a new two-point hot-wire dataset and a previously published two-dimensional particle image velocimetry dataset. In the hot-wire experiment, one probe is fixed near the wall while the second traverses the full boundary layer, allowing estimation of the linear coherence spectrum. The results confirm the geometric self-similarity of the wall-scaled eddy hierarchy that remains coherent with the wall. Using the linear coherence spectrum as a spectral filter shows that most of the additional APG-induced energy is incoherent with the wall and is linearly superimposed on the wall-coherent component of the streamwise variance. This wall-incoherent contribution explains the departure of the variance profile from the inverse logarithmic law observed in canonical high-Reynolds-number boundary layers. Conditional averaging of the particle image velocimetry data identifies the structures responsible for this energy amplification. The results link enhanced outer-region Reynolds stresses, an outer inflection point in the mean velocity profile, and an ejection-sweep organisation of Reynolds shear stress, all characteristic of shear-layer dynamics.