Conditional statistics of supersonic turbulent boundary layer in the intermittent region

The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the traditional Reynolds/Favre decomposition contaminates the Reynolds stresses and thermal statistics. Our conditional statistics provide direct evidence that turbulent flow possesses positive Reynolds shear stress everywhere, whereas non-turbulent flow carries zero Reynolds shear stress. The thermal statistics of turbulent and non-turbulent flows exhibit opposite trends in the intermittent region, and the difference can be traced back to the variation of total temperature resulting from the Prandtl number.