Stress equation based scaling framework for adverse pressure gradient turbulent boundary layers

[Display omitted] •A velocity scale is proposed via a study of the mean stress balance.•This velocity scale varies with distance from the wall.•It combines the wall-shear-stress velocity with a pressure-stress-based velocity.•Zero and adverse pressure gradient turbulent boundary layers are studied. This paper provides a framework for estimating appropriate turbulent velocity scales in adverse pressure gradient turbulent boundary layers (APG TBLs) via a study of the mean stress balance. We examine the velocity scales of APG TBLs using the relationship between the Reynolds shear stress and pressure stress. It is reasoned that as distance from the wall increases the velocity scaling transitions from one dominated by the wall-shear-stress velocity scale, uτ, to a scaling dominated by the pressure stress. A velocity scale, uhyb, is proposed that varies with distance from the wall and combines the wall-shear-stress velocity with a pressure-stress-based velocity. This investigation uses new high Reynolds number (7000≲Reτ≲7800) experimental measurements, existing lower Reynolds number experimental (600≲Reτ≲2000) and computational (Reτ