We investigate the effectiveness of the semi-local Reynolds number Re τ to parametrize wall-bounded flows with strong density, ρ, and viscosity, µ, gradients. Several cases are considered, namely, volumetrically heated low-Mach-number turbulent channel flows, a simultaneously heated and cooled flow with CO2 at supercritical pressure, and heated and cooled supersonic boundary layer flows. The mean density and viscosity in some of these cases vary up to a factor of nine and six, respectively. We show that, even for such high gradients in mean properties, the velocity transformation based on the semi-local Reynolds number is able to collapse the mean streamwise velocity profiles. We further-more provide evidence that the turbulent kinetic energy and streamwise vorticity budget equations are also governed by the semi-local Reynolds number. For cases with strong property variations, additional mechanisms appear that are caused by individual density (e.g., baroclinicity) or viscosity gradients. However, in the cases investigated herein, these additional mechanisms are small. The insights gained are used to improve a wall model, which is then tested in a wall-modeled large-eddy simulation (LES) of a compressible channel flow with isothermal walls.@en