Incorporating intrinsic compressibility effects in velocity transformations for wall-bounded turbulent flows

The law of the wall states that, after appropriate scaling, the mean velocity of incompressible turbulent flows near flat solid walls is a universal function of the wall-normal distance. An analogous law does not exist for compressible flows due to complexities arising from mean property variations and intrinsic compressibility effects, which occur when pressure directly changes the density of fluid elements. By accounting for both these effects, we propose a new velocity scaling that transforms the mean velocity of compressible flows to the incompressible law of the wall. This transformation is more accurate than the state-of-the-art, and is applicable to a wider range of flows.