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

It is widely recognized that the Zagarola–Smits velocity scale UZS serves as a suitable outer velocity scale for adverse-pressure-gradient (APG) turbulent boundary layers (TBLs). In this paper, a relationship between UZS, the edge velocity Ue of the boundary layer, and the skin friction coefficient Cf is established. An alternative outer velocity scale, denoted as Uf, is proposed for APG TBLs based on Ue and Cf. This proposition is validated based on several high-quality databases from the literature, along with the presently obtained experimental APG database. As UZS, the Uf-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 Cf, or equivalently the friction velocity, for APG TBLs.