Transformations of velocity and temperature for compressible turbulent boundary layers from subsonic to hypersonic regimes

Compressible wall-bounded turbulent flows exhibit complex mean profiles because of the pronounced compressibility effects and heat transfer. We propose a hybrid transformation framework to collapse compressible mean velocity and temperature profiles onto incompressible forms through scaling each layer by its effective transformation, with the underlying mapping functions discovered via a physics-informed symbolic regression (PISR) method. The hybrid velocity transformation incorporates an intrinsic compressibility correction for the buffer layer and a PISR-derived mapping function for the logarithmic layer. For temperature, we introduce a hybrid transformation that integrates the Mach-invariant-type transformation in the viscous sublayer and a novel PISR-derived scaling in the logarithmic layer. The performance of these transformations is evaluated across compressible turbulent boundary layers with free-stream Mach numbers ranging from 0.5 to 8 and wall-to-recovery-temperature ratios ranging from 0.25 to 1. The hybrid velocity transformation outperforms Griffin–Fu–Moin transformation for the transformed mean velocity profiles, with the mean integrated percent error across the dataset decreasing from 1.67 % to 0.96 %. The hybrid temperature transformation performs better than the Mach-invariant-type and Trettel–Larsson-type transformations for mean temperature profiles. Moreover, the inverse hybrid velocity and temperature transformations can effectively predict the compressible mean velocity and temperature profiles with only wall conditions.