Decomposition of the mean friction drag in adverse-pressure-gradient turbulent boundary layers

In this study, we exploit the Renard-Deck identity [J. Fluid Mech. 790, 339 (2016)10.1017/jfm.2016.12] to decompose the mean friction drag in adverse-pressure-gradient turbulent boundary layers (APG-TBLs) into three components, associated with viscous dissipation, turbulence kinetic energy production, and spatial growth of the flow, respectively. We consider adverse-pressure-gradient turbulent boundary layers developing on flat plates and airfoils, with friction Reynolds numbers in the range 200<2000, and with Rotta-Clauser pressure-gradient parameters (β) ranging from 0 to 50. The effects of Reynolds number, adverse pressure gradient, and the pressure-gradient history on the contributing components are individually investigated, and special attention is paid to the comparisons with zero-pressure-gradient turbulent boundary layers (ZPG-TBLs). Our results indicate that the inner peaks of the dissipation and production terms are located at y+≈6 and y+≈16.5, respectively, and their outer peaks scale with the 99% boundary-layer thickness (δ99), i.e., y/δ99≈0.7 and 0.53, respectively. These results are independent of the friction Reynolds number, the magnitude of β, and its development history. Moreover, the spatial-growth component is negative in the investigated APG-TBLs, and its magnitude increases with β.