  This work assesses several popular transformations for the velocity profile
through their application to several types of non-canonical compressible
wall-bounded turbulent flows. Specifically, this work explores DNS databases of
high-enthalpy boundary layers with dissociation and vibrational excitation,
supercritical channel and boundary-layer flows, and adiabatic boundary layers
with pressure gradients. The transformations considered include the van Driest
[Van Driest, J. Aeronaut. Sci., 18(1951):145-216], Zhang et al. [Zhang et al.,
Phys. Rev. Lett., 109(2012):054502], Trettel-Larsson [Trettel and Larsson,
Phys. Fluids, 28(2016):026102], data-driven [Volpiani et al., Phys. Rev.
Fluids, 5(2020):052602], and total-stress-based [Griffin et al., Proc. Natl.
Acad. Sci. U.S.A., 118(2021):e2111144118] transformations. The Trettel-Larsson
transformation collapses velocity profiles of high-enthalpy temporal boundary
layers but not the spatial boundary layers considered. For supercritical
channel flows, the Trettel-Larsson transformation also performs well over the
entire inner layer. None of the transformations above works for supercritical
boundary layers. For all the considered methods, the transformed velocity
profiles of boundary layers with weak pressure gradients coincide well with the
universal incompressible law of the wall. In summary, all these popular methods
fail to deliver uniform performance for non-canonical compressible wall-bounded
flows in the logarithmic region, and a more sophisticated version, which
accounts for these different physics, is needed. The data-driven and
total-stress-based transformations perform well in the viscous sublayer for all
the considered flows.
