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