A new perspective on skin-friction contributions in adverse-pressure-gradient turbulent boundary layers

For adverse-pressure-gradient turbulent boundary layers, the study of integral skin-friction contributions still poses significant challenges. Beyond questions related to the integration boundaries and the derivation procedure, which have been thoroughly investigated in the literature, an important issue is how different terms should be aggregated. The nature of these flows, which exhibit significant in-homogeneity in the streamwise direction, usually results in cancellation between several contributions with high absolute values. We propose a formulation of the identity derived by Fukagata et al. (2002), which we obtained from the convective form of the governing equations. A new skin-friction contribution is defined, considering wall-tangential convection and pressure gradient together. This contribution is related to the evolution of the dynamic pressure in the mean flow. The results of the decomposition are examined for a broad range of pressure-gradient conditions and different flow-control strategies. We found that the new formulation of the identity allows to readily identify the different regimes of near-equilibrium conditions and approaching separation. It also provides a more effective description of control effects. A similar aggregation between convection and pressure-gradient terms is also possible for any other decomposition where in-homogeneity contributions are considered explicitly.