Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows

An exact relationship for the local skin friction is derived for the compressible turbulent wall-bounded flow (channel, pipe, flat plate). This expression is an extension of the compressible case of that derived by Fukagata [Phys. Fluids 14, L73 (2002)] in the case of incompressible wall-bounded flows. This decomposition shows that the skin friction can be interpreted as the contribution of four physical processes, i.e., laminar, turbulent, compressible, and a fourth coming from the interaction between turbulence and compressibility. Compressible numerical simulations show that, even at Mach number M=2 , the main contribution comes from the turbulence, i.e., the Reynolds stress term.