Data-driven compressibility transformation for turbulent wall layers

A scaling formula for the mean velocity and wall distance in compressible turbulent wall-bounded flows is developed. The development is both physics- and data-driven: universality in the viscous sublayer and of the Morkovin-scaled shear stress is analytically enforced, after which the remaining two free parameters are determined from direct numerical simulation data. The scaling formula is calibrated on four boundary layers up to Mach 6, and validated on seven boundary layers up to Mach 14. The proposed transformation shows an improved collapse of the mean velocity profile across different Reynolds numbers, Mach numbers, and wall thermal conditions when compared to existing ones.