Incompressible and compressible regions in near-wall supersonic turbulent channel flows

It has been recently shown that compressible turbulence exhibits a large degree of universality when the strength of dilatational motions relative to solenoidal motions in the flow is known. While this has been supported by a large number of studies of homogenous flows, the role of dilatation has not been studied as thoroughly in wall-bounded flows. It has been observed, however, that dilatation at the wall has a first-order effect on the asymptotic scaling of, for example, Reynolds stresses and turbulent heat fluxes. This is so because the analytic expansions of wall-normal velocity and temperature at the wall are constrained in different ways when the flow is incompressible (solenoidal) or compressible. Using both Direct Numerical Simulations (DNS) and analysis, we show the asymptotic power-law behavior at the wall and the transition from the incompressible to the compressible limit. Further, we study a number of statistics of wall fluctuations to show that compressible flows develop distinct regions that follow trends consistent with incompressible and compressible power-laws. We further characterize these incompressible and compressible regions and its associated Mach number effects. Additionally, we find that slow temporal changes in the main flow are seen to affect turbulent stresses normal to the wall, while shear stresses with normal-to-wall components remain unaffected.