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We investigate the effects of thermal boundary conditions and Mach number onturbulence close to walls. In particular, we study the near-wall asymptoticbehavior for adiabatic and pseudo-adiabatic walls, and compare to theasymptotic behavior recently found near isothermal cold walls (Baranwal et al.(2022)). This is done by analyzing a new large database of highly-resolveddirect numerical simulations of turbulent channels with different wall thermalconditions and centerline Mach numbers. We observe that the asymptoticpower-law behavior of Reynolds stresses as well as heat fluxes does change withboth centerline Mach number and thermal-condition at the wall. Power-lawexponents transition from their analytical expansion for solenoidal fields tothose for non-solenoidal field as the Mach number is increased, though thistransition is found to be dependent on the thermal boundary conditions. Thecorrelation coefficients between velocity and temperature are also found to beaffected by these factors. Consistent with recent proposals on universalbehavior of compressible turbulence, we find that dilatation at the wall is thekey scaling parameter for this power-law exponents providing a universalfunctional law which can provide a basis for general models of near-wallbehavior.

Mach number and wall thermal boundary condition effects on near-wall compressible turbulence