An alternative outer velocity scale for adverse-pressure-gradient turbulent boundary layer

It is widely recognized that the Zagarola-Smits velocity scale U-ZS serves as a suitable outer velocity scale for adverse-pressure-gradient (APG) turbulent boundary layers (TBLs). In this paper, a relationship between U-ZS, the edge velocity U-e of the boundary layer, and the skin friction coefficient C-f is established. An alternative outer velocity scale, denoted as U-f, is proposed for APG TBLs based on U-e and C-f. This proposition is validated based on several high-quality databases from the literature, along with the presently obtained experimental APG database. As U-ZS, the U-f-normalized mean-velocity-defect distributions collapse well together at small to moderate values of the Clauser pressure-gradient parameter. As such, a new and simply empirical method is proposed to determine C-f, or equivalently the friction velocity, for APG TBLs.