Decomposition of the skin-friction coefficient of compressible boundary layers

We derive an integral formula for the skin-friction coefficient of compressible boundary layers by extending Elnahhas and Johnson [“On enhancement layer skin friction turbulence: An angular momentum approach,” J. Fluid Mech. 940, A36 (2022)] incompressible layers. The is decomposed into sum contributions laminar coefficient, change dynamic viscosity with temperature, Favre–Reynolds stresses, mean flow. This decomposition applied to numerical data turbulent layers, role each term on wall-shear stress quantified. also show that threefold integration identity Gomez et al. [“Contribution Reynolds distribution in channel flows,” Phys. Rev. E 79(3), 035301 (2009)] twofold identities Wenzel [“About influences compressibility, heat transfer pressure gradients layers,” 930, A1 Xu [“Skin-friction heat-transfer decompositions hypersonic transitional 941, A4 all simplify von Kármán equation when upper limit asymptotically large. dependence these bound studied. By using asymptotic methods, we prove multiple-integration degenerates definition number integrations