Effects of spatially localised pressure gradient histories on recovery of turbulent boundary layers

arXiv:2510.16184v2 Announce Type: replace Abstract: Hot-wire anemometry is used to investigate the recovery of smooth-wall turbulent boundary layers from spatially localised (i.e. impulsive) pressure gradient history (PGH) effects. Measurements are performed at multiple stations downstream of spatial distributions of favourable-adverse pressure gradient sequences, followed by relaxation to zero-pressure-gradient (ZPG) conditions. The analysis focuses on matched friction Reynolds number, with three groups at $Re_\tau \approx 2300$, $3000$, and $5500$, where the local Clauser pressure gradient (PG) parameter $\beta$ is nominally matched at $1.7$, $0.6$, and $-0.1$, respectively. The strength of PGH is quantified using the integral history parameter $\Delta\beta$, which allows isolation of PGH as the primary source of variation. The imposed PGH amplifies the wake component of the mean velocity profile and enhances the streamwise Reynolds stress throughout the boundary layer, including the emergence of an outer peak. Spectral analysis reveals an additional outer-layer energetic feature, identified here as the PG peak, with streamwise length scales of $\lambda_x \approx 2-3\delta$, where $\delta$ is the local boundary layer thickness. This peak is different from the very-large-scale motion (VLSM), which can also be identified. Even after $\beta$ has relaxed (to zero) for sufficiently long distances, the mean flow has not recovered to ZPG state, provided $\Delta\beta$ remains non-zero. Once $\Delta\beta \lesssim 0.1$, the mean flow has recovered, as have the turbulence statistics in the inner and logarithmic regions; however, the outer-layer turbulence retains a persistent imprint of PGH. Finally, we observe that the evolution of the energetic scales during recovery involved the reorganisation of the large-scale structures - where the VLSMs appear to be shorter even after the PG peak has vanished - which indicates prolonged history effects.