📝 SummarXiv

Abstract

This study provides a carefully controlled examination of the universality of the von Karman and additive constants associated with the classical logarithmic scaling of the mean streamwise velocity profile in high-friction Reynolds number (Re_tau) turbulent boundary layers (TBLs) subjected to weak-to-moderate adverse pressure gradients (APGs). The analysis leverages a recently developed method for imposing APGs with minimal pressure gradient (PG) history effects in Melbourne's high-Re_tau TBL facility (Deshpande et al., Phys. Rev. Fluids, vol. 8, 2023), in combination with direct measurements of local friction velocity via oil-film interferometry. The von Karman constant is found to remain invariant within experimental uncertainty, while the additive coefficient decreases with both the local APG and PG history, potentially explaining reported variability in logarithmic scalings across the APG TBL literature. The facility enables manual prescription of APGs along the full test section, allowing weak PG history perturbations to be followed by extended recovery regions, while maintaining matched local PG and Re_tau at downstream measurement locations. This experimental configuration allows for systematic decoupling of the effects of Re_tau, local PGs, and PG history, enabling assessment of their individual contributions to single-point turbulence statistics and energy spectra across different TBL regions. Present results at high Re_tau show that PG history influences both small-scale and large-scale motions in the overlap and outer regions, whereas local PGs primarily affect the large-scales. The strongest effects of the local PG occur in the outer region (around 0.4delta, where delta is the boundary layer thickness), while PG history effects extend down to approximately 0.25delta, just above the logarithmic region.