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An asymptotic $-1/2$ power-law scaling and a semi-empirical finite-$Re$ modelwere recently presented by Dixit et al. (2020) for skin friction inzero-pressure-gradient (ZPG) turbulent boundary layers (TBLs). In this work, anew derivation is presented which shows that these relations (i) fundamentallyrepresent a dynamically-consistent scaling of skin friction for nominallytwo-dimensional ZPG TBLs and fully-developed pipes and channels, and (ii) applyindividually to each of these flows. The new theoretical arguments are based ontransfer of kinetic energy from mean flow to large eddies of turbulence anddepend neither on flow geometry nor outer boundary condition, both of whichdistinguish one type of flow from the other. Using skin friction data from theliterature, it is demonstrated that the finite-$Re$ model describes, aspredicted by the theory, data from individual flows remarkably well; these datacover the complete range of laboratory/simulation Reynolds numbers to date. Itis, however, observed that performance of the model degrades while attemptingto describe data from all flows in a universal fashion. Differences in outerboundary condition and large-scale structures amongst different types of flowsappear to be responsible for this degradation. An empirical correction based onClauser's shape factor, is proposed to absorb the outer boundary conditioneffects into the scaling of skin friction. This correction leads to a newuniversal scaling and a robust, semi-empirical, universal finite-$Re$ model forskin friction in ZPG TBLs, pipes and channels. Remarkable collapse of data fromall flows in the new scaling underscores the importance of adynamically-consistent approach towards revealing universality of skin frictionin wall turbulence.

Scaling of mean skin friction in turbulent boundary layers, and fully-developed pipe and channel flows