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In this study, a new well-resolved large-eddy-simulation (LES) of anincompressible near-equilibrium adverse-pressure-gradient (APG) turbulentboundary layer (TBL) over a flat plate is presented. In this simulation, wehave established a near-equilibrium APG over a wide Reynolds-number range. Inthis so-called region of interest (ROI), the Clauser--Rotta pressure-gradientparameter $\beta$ exhibits an approximately constant value of around 1.4, andthe Reynolds number based on momentum thickness reaches $Re_{\theta}=8700$. Tothe authors' knowledge, this is to date the highest $Re_{\theta}$ achieved fora near-equilibrium APG TBL under an approximately constant moderate APG. Weevaluated the self-similarity of the outer region using two scalings, namelythe Zagarola--Smits and an alternative one based on edge velocity anddisplacement thickness. Our results reveal that outer-layer similarity isachieved, and the viscous scaling collapses the near-wall region of the meanflow in agreement with classical theory. Spectral analysis reveals that the APGdisplaces some small-scale energy from the near-wall to the outer region, aneffect observed for all the components of the Reynolds-stress tensor, whichbecomes more evident at higher Reynolds numbers. Generally, the effects of theAPG are more noticeable at lower Reynolds numbers. For instance, the outer peakof turbulent-kinetic-energy (TKE) production is less prominent at higher $Re$.While the scale separation increases with $Re$ in zero-pressure-gradient (ZPG)TBLs, this effect becomes accentuated by the APG. Despite the reduction of theouter TKE production at higher Reynolds numbers, the mechanisms of energizationof large scales are still present.

An adverse-pressure-gradient turbulent boundary layer with  nearly-constant $\boldsymbol{\beta \simeq 1.4}$ up to  $\boldsymbol{Re_{\theta} \simeq 8,700}$