On the invariant mean velocity profile for compressible turbulent boundary layers

An invariant mean velocity profile is derived and validated by direct numerical simulations of compressible turbulent boundary layers (CTBL) for a range of Reynolds number, Mach number and wall temperature. Near the wall, we reveal an invariance of the mean momentum equation, which derives and clarifies the semi-local scaling of the wall-normal coordinate. A near-wall multilayered modeling of the invariant spatial coordinate yields an invariant mean velocity for the inner flow. In the outer flow, an explicit invariant velocity is derived, based on a symmetry-based analytic description of the mixing length in the CTBL bulk. Thus, a whole invariant mean velocity profile is constructed, and validated to be superior to previous transformations.