Turbulent/nonturbulent interfaces in high-resolution direct numerical simulation of temporally evolving compressible turbulent boundary layers

Turbulent/nonturbulent interfaces (TNTIs) are studied in the direct numerical simulation of temporally evolving turbulent boundary layers at Mach numbers 0.8 and 1.6 with Reynolds number based on the momentum thickness of about 2200. The computational grid size determined based solely on the wall unit results in insufficient resolutions near the TNTI even though it yields the well-known profiles of global statistics such as mean velocity and rms velocity fluctuations. The insufficient resolution near the TNTI layer causes the spiky patterns of the enstrophy isosurface used for detecting the outer edge of the TNTI layer and the thicker TNTI layer thickness. With the higher-resolution direct numerical simulation, where the resolution is determined based on both the wall unit and the smallest length scale of turbulence underneath the TNTI layer, we investigate the structures of the TNTI layer and the entrainment process in the compressible turbulent boundary layers. The mean vorticity profile and enstrophy evolutions near the TNTI layer show that the structure of the TNTI layer is similar to incompressible free shear flows: The thickness of the layer is about 15 times the Kolmogorov scale eta(I) in turbulence near the TNTI layer; the turbulent sublayer (TSL) and viscous superlayer (VSL) are found based on the analysis of enstrophy transport equation, where the thicknesses of the TSL and VSL are 11 eta(I)-12 eta(I) and 4 eta(I), respectively. The entrainment process across the TNTI layer is also studied based on the propagation velocity of the enstrophy isosurface and the mass transport equation in the local coordinate moving with the TNTI. The entrainment mechanism across the TNTI layer in compressible turbulent boundary layers is very similar to incompressible free shear flows until Mach number 1.6, where the mass transport within the TNTI layer is well predicted by an entrainment model based on a single vortex originally developed for incompressible flows. Furthermore, the mass entrainment rate per unit horizontal area of the temporally evolving turbulent boundary layers is consistent with the theoretical prediction for spatially evolving compressible turbulent boundary layers for both Mach numbers.