How accurate is Morkovin's hypothesis for supersonic wall-bounded turbulent flows?

Despite extensive research and significant progress in the past decades on wall-bounded turbulence with strong heat transfer and high flow speeds, the underlying turbulence modifications are yet not fully understood. In the non-hypersonic regime, these modifications are generally understood to be a consequence of mean property variations (Morkovin's hypothesis). We perform DNS of supersonic channel flows, cancelling the effect of aerodynamic heating, to obtain negligible mean property variations. Contrary to the expectation that these cases will have negligible effects of compressibility, we observed non-negligible effects especially near the wall. Using Helmholtz decomposition, we observed that the inter-component energy transfer among the solenoidal Reynolds stresses reduces with increasing Mach number. This clearly indicates an indirect compressibility effect on the solenoidal component of velocity.