On low-frequency unsteadiness in shock-wave–turbulent boundary layer interaction with varying corner curvature

The physical mechanism of low-frequency unsteadiness in shock-wave/turbulent boundary layer interaction (STBLI) is studied using direct numerical simulations at Mach 2. 9 with momentum-thickness Reynolds number Re_ 2400 over three ramp configurations with varying corner curvature. The configurations include a sharp 24^ compression ramp (R24) and two curved ramps with radii of 7 (C7) and 14 (C14) times the boundary layer thickness. By varying the ramp curvature, the extent of separation is controlled while maintaining sufficient streamline concavity to ensure that the Görtler number remains above its critical threshold. Cases R24 and C7 exhibit a mean separation with a detached shear layer accompanied by pronounced low-frequency unsteadiness, whereas C14 shows only incipient separation with markedly attenuated low-frequency unsteadiness. Sparsity-promoting dynamic mode decomposition reveals the emergence and downstream growth of counter-rotating structures in both low- and mid-frequency bands in all cases. In R24 and C7, these structures undergo growth and merging within the detached shear layer, giving rise to large-scale low-frequency motion, while in C14, their growth remains gradual and largely frequency-independent. The interactions between the counter-rotating structures and detached shear layer redistribute energy toward lower wavenumbers with a reduction at mid-wavenumbers. During this phase, the streamwise enstrophy dominates the enstrophy magnitude. Enstrophy transport analysis shows that the wall-normal-to-streamwise enstrophy tilting dominates the initial generation of streamwise enstrophy, whereas stretching is the primary source of the subsequent downstream growth and alignment. The results suggest that the interaction between the detached shear layer and counter-rotating structures develops into large-scale structures that govern the low-frequency unsteadiness in STBLI.