Scaling of turbulence near isothermal and adiabatic walls

Compressibility affects near-wall turbulence in wall-bounded flows. We have recently shown that the asymptotic behavior of turbulent fluxes at the wall differs from incompressible scaling laws with systematic trends in Mach number, M. This, however, is found to depend on the specific wall thermal conditions. To study a range of thermal conditions, we carry out very-well resolved simulations of adiabatic channels ranging from incompressible to supersonic speeds and study the asymptotic behavior of turbulent fluxes in the near-wall region. Emphasis is placed on comparisons between isothermal and adiabatic wall conditions which provide different constraints on the behavior of temperature fluctuations at the wall. At very low M, fluxes follow Taylor series as in incompressible flows but deviate significantly from incompressible or non-solenoidal Taylor-series scaling laws as M increases, especially for fluxes containing temperature or wall-normal velocity fluctuations. This is due, in part, to the increased level of dilatation at the wall as M increases which also depends on the thermal boundary condition. Adiabatic walls lead to smaller dilatational content as compared to isothermal walls for the same M. Reynolds stress budgets and implications for models are briefly discussed.