Response of smooth- and rough-wall boundary layers to non-equilibrium adverse pressure gradients

Adverse pressure gradient (APG) boundary layers were studied experimentally to determine their behaviour under non-equilibrium conditions and whether the outer layer similarity between smooth- and rough-wall cases observed under zero pressure gradient (ZPG) conditions continues to hold. Experiments were conducted in a recirculating water tunnel with smooth and rough test walls. The pressure gradient was set to produce a variety of Clauser pressure gradient parameter, β , histories. In some cases, the boundary layer was in a canonical ZPG state immediately upstream of the APG region. The APG caused a rise in the mean velocity defect and Reynolds stress profiles when normalised by the local friction velocity. In some cases, similarity between the rough- and smooth-wall cases was observed when β was matched, but exceptions were found in the strongest pressure gradient cases where β rose rapidly in terms of the dimensionless streamwise coordinate ( xu _τo ² )/( 2U _e ² θ ), where

is the friction velocity,

upper U Subscript e U e $U_e$

is the freestream velocity, and

theta θ $\theta$

is the momentum thickness, presumably because the boundary layer was farther from equilibrium. When the β history was matched, greater similarity between the rough- and smooth-wall cases was observed even in the stronger pressure gradient cases, and matching the Clauser shape factor, G , also resulted in greater similarity. Departures from similarity were more apparent for the turbulence quantities than for the mean velocity. Additional history effects were considered through comparison with cases in which the APG followed immediately downstream of a favourable pressure gradient (FPG), showing the effects of the upstream FPG were significant but short lived. Detailed measurements are presented for one APG case approaching separation. In a final comparison, cases with a ZPG following an APG were considered. The return of the mean flow to canonical ZPG behaviour appeared to follow an exponential decay, and the response of turbulence quantities was slow.