Turbulent boundary layers under adverse pressure gradients. Part 1. Decoupling the influences of local and upstream pressure gradients through high-Reynolds-number experiments

This study reports a carefully controlled examination of the universality of the von Kármán and additive coefficients associated with the classical logarithmic scaling law for the mean streamwise velocity profile in high-friction-Reynolds-number ( upper R e Subscript tau R e τ $Re_{\tau }$ ) turbulent boundary layers (TBLs) subjected to low-to-moderate adverse pressure gradients (APGs). The present approach leverages a recently developed methodology that enables systematic variation of the upstream pressure gradient (PG) history, e.g. introducing weak APG perturbations or maintaining nominally zero-pressure-gradient conditions (a ‘minimal’ PG history), while also obtaining locally matched upper R e Subscript tau R e τ $Re_{\tau }$ and beta β $\beta$ at the downstream measurement locations. As such, this unique experimental configuration allows for systematic decoupling of the influences of upper R e Subscript tau R e τ $Re_{\tau }$ , local APGs and PG history, and assessment of their individual contributions to single-point turbulence statistics and energy spectra across different regions of the TBL. The conscious choice of a high- upper R e Subscript tau R e τ $Re_{\tau }$ and low-to-moderate APG conditions yields a well-defined and sufficiently broad overlap region in the TBL streamwise velocity profile, permitting a rigorous examination of the classical logarithmic scaling law. The von Kármán coefficient was found to remain invariant across all cases, within experimental uncertainty, while the additive coefficient varied systematically with both the local APG and PG history, possibly explaining variabilities in the logarithmic scaling behaviours reported across the APG TBL literature. Local APGs were also observed to energise both large- and small-scale motions in the wake region, as expected, while PG history was found to primarily influence large-scale motions extending farther towards the overlap region. In contrast to previous lower- upper R e Subscript tau R e τ $Re_{\tau }$ studies, neither effect was observed to extend into the inner region, highlighting the importance of investigating this problem with sufficient separation of scales and TBL regions. Collectively, these measurements provide a high-fidelity dataset that reveals the underlying influence of PG history, improving fundamental understanding and providing the basis for developing composite mean velocity profile formulations for APG TBLs that account for the distinct influences of upper R e Subscri