  In this work, a transformation, which maps the mean velocity profiles of
compressible wall-bounded turbulent flows to the incompressible law of the wall
is proposed. Unlike existing approaches, the proposed transformation
successfully collapses, without specific tuning, numerical simulation data from
fully developed channel and pipe flows, and boundary layers with or without
heat transfer. In all these cases, the transformation is successful across the
entire inner layer of the boundary layer (including the viscous sublayer,
buffer layer, and logarithmic layer), recovers the asymptotically exact
near-wall behavior in the viscous sublayer, and is consistent with the near
balance of turbulence production and dissipation in the logarithmic region of
the boundary layer. The performance of the transformation is verified for
compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and
friction Reynolds numbers ranging from 200 to 2000. Based on physical
arguments, we show that such a general transformation exists for compressible
wall-bounded turbulence regardless of the wall thermal condition.
