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Turbulent boundary layers under adverse pressure gradients are studied usingwell-resolved large-eddy simulations (LES) with the goal of assessing theinfluence of the streamwise pressure development. Near-equilibrium boundarylayers were identified with the Clauser parameter $\beta$. The pressuregradient is imposed by prescribing the free-stream velocity. In order tofulfill the near-equilibrium conditions, the free-stream velocity has to followa power-law distribution. The turbulence statistics pertaining to cases with aconstant Clauser pressure-gradient parameter ? were compared with cases with anon-constant pressure distribution at matched ? and friction Reynolds numberRe_tau . It was noticed that the non-constant cases appear to approach fardownstream a certain state of the boundary layer, which is uniquelycharacterised by beta? and Re_tau. The investigations on the flat plate wereextended to the flow around a wing section. Comparisons with the flat-platecases at matched Re_tau and ? revealed some interesting features: In turbulentboundary layers with strong pressure gradients in the development history theenergy-carrying structures in the outer region are strongly enhanced, which canbe detected by the pronounced wake in the mean velocity as well as the largesecond peak in the Reynolds stresses. Furthermore, a scaling law suggested byKitsios et al. (2015), proposing the edge velocity and displacement thicknessas scaling parameters, was tested on a constant pressure gradient case. Themean velocity and Reynolds stress profiles were found to be dependent on thedownstream development, indicating that their conclusion might be the result ofa too short constant pressure gradient region.

History effects and near-equilibrium in turbulent boundary layers with pressure gradient