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

arXiv:2510.16184v3 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 numbers 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. PGH strength is quantified using the integral history parameter {\Delta}\b{eta}, proposed by Preskett \textit{et al.} (\textit{J. Fluid Mech.}, vol. 1010, 2025, A30), 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 with streamwise length scales of $2$-$3\delta$ ($\delta$ is the local boundary layer thickness), identified as the PG peak, distinguishable from the very-large-scale motion (VLSM). Even after $\beta$ has relaxed (to zero) for sufficiently long distances, mean flow has not recovered to ZPG state. Once $\Delta\beta \lesssim 0.1$, mean flow and inner/log-layer turbulence statistics recover; however, the outer-layer turbulence retains a persistent imprint of PGH. Finally, we observe that recovery involves reorganisation of large-scale structures - where VLSMs appear to be shorter even after the PG peak has vanished - which indicates prolonged history effects.