The effect of pressure gradient history on inter-scale interactions in high-Reynolds number turbulent boundary layers

Abstract This study investigates inter-scale interactions in high-Reynolds number turbulent boundary layers (TBL) under the combined influence of local adverse pressure gradients (APG) and different PG histories. We develop an experimental methodology to generate both ZPG and APG TBLs with matched local flow conditions but distinct pressure gradient histories, thereby enabling a controlled decoupling of PG history effects. Well-resolved hot-wire and oil-film interferometry measurements provide normalised second- and third-order turbulence statistics. Following a triadic interaction framework, we quantify the mean nonlinear coupling across the full hierarchy of turbulent scales via the scale-decomposed skewness of streamwise velocity fluctuations. We emphasise the use of high-Reynolds number data here to clearly separate small- and large-scale motions to investigate their inter-scale coupling. The cross-term of the scale-decomposed skewness, which is traditionally related to amplitude modulation (AM) effects in canonical wall-bounded flows, is the dominant contributor to skewness in the ZPG case. However, AM alone does not fully describe inter-scale interactions in non-canonical wall-bounded flows. The introduction of local APG energises large-scale motions in the outer region and enhances both large-scale self-interactions and the AM, while the small-scale self-interactions remain largely unchanged. However, with locally matched Reynolds number and PG, cases with different PG histories also exhibit clear differences in the magnitude of these large-scale self-interactions and the AM across the TBL. Thus, PG history leaves a persistent imprint on inter-scale interactions, even where second-order statistics have converged.