High-Reynolds-number effects in supersonic turbulent channel flow

The effect of the Reynolds number in a compressible isothermal channel flow is investigated through a series of direct numerical simulations (DNS). The bulk Mach number based on the wall temperature is kept fixed at 1.5, and the bulk Reynolds number is increased up to Re-tau approximate to 1000. Previous work at lower Reynolds number confirmed the validity of Morkovin's hypothesis but questioned the use of van Driest velocity transformation in the presence of heated walls. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi-local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer.