Coherent structures in DNS of turbulent boundary layers at Mach 3

We demonstrate that the data from DNS of turbulent boundary layers at Mach 3 exhibit the same local flow features found in both supersonic and incompressible experiments, such as long, low-speed structures in the log region and hairpin vortex packets. Instantaneous plots of the streamwise mass-flux show very long low-momentum structures in the log layer. We use Taylor's hypothesis to generate a velocity map in the log region with a streamwise length of about 2305, where δ is the boundary layer thickness. The map indicates that the low-speed structures attain streamwise lengths of order 1005. Length scales obtained from correlations of the streamwise mass flux severely under predict the extent of these structures, most likely due to their significant meandering in the spanwise direction. A hairpin packet-finding algorithm is employed to determine the average packet properties, and we find that the streamwise length of the Mach 3 packets is less than one-third of that observed at subsonic conditions. Adopting the technique of Brown & Thomas, ¹ we observe a connection between elevated levels of wall shear stress and hairpin packets. Visualization of the instantaneous turbulence structure shows that groups of hairpin packets are frequently located above the long, low-momentum structures, consistent with the very large-scale motion model of Kim & Adrian.².