Effects of Upstream Pressure Gradient History and Local Disequilibration on Adverse Pressure Gradient Turbulent Boundary Layers

This study introduces a unified framework to unravel the effects of pressure gradient (PG) history and local disequilibration in adverse pressure gradient (APG) turbulent boundary layers (TBLs). Using four high-fidelity datasets spanning a wide range of local PG strengths (β) and equilibrium conditions, we compare cases with matched β and Reynolds numbers (Re) estimated using different scalings. While PG history is quantified by cumulatively averaging β over Re to get β̄, local disequilibration is estimated by the streamwise gradient of β. Results show that β̄ captures trends under moderate disequilibrium but fails in strongly non-equilibrium cases, where turbulence response is delayed. Here, Zagarola–Smits-based scaling of turbulence statistics aligns with the observed behaviour, consistent with viscous scaling in the former. We also find increasing β̄ energising both the small and large scales in the outer region, while only large scales are affected near the wall.