Thermal boundary condition and unsteady effects in high-speed turbulent channels.

We conduct direct numerical simulations of compressible turbulent channels in high-speed regimes, to study the near-wall behavior of turbulent statistics and the effects of Mach numbers as well as different thermal wall-boundary conditions, in particular, isothermal, adiabatic and pseudo-adiabatic. We have shown that the asymptotic behavior of Reynolds stresses change with the Mach number as well as thermal boundary conditions identifying the fluctuating dilatation at the wall as the responsible parameter. In this work, we will show that the asymptotic behavior of turbulent heat fluxes also depend on thermal boundary conditions, an effects that, in turns, depends on the level of compressibility. These effects are also studied in the budget equations which shed light on the relative importance of physical processes at different distances from the wall. We discuss how these results extend to unsteady effects which are analyzed with decaying channel simulations.