Linearized dynamics and sensitivity analysis of Mach 3 shock-wave/turbulent boundary layer interaction

Shock-wave/turbulent boundary layer interactions (STBLIs) occur in a multitude of highspeed flows, and can exhibit strong low-frequency unsteadiness. We apply global stability analysis and resolvent analysis analysis to study the linear dynamics and sensitivity of compression ramp induced Mach 3 STBLI. We focus on analysis of the mean flow extracted from LES simulations, and also examine snapshots extracted from bubble growth and collapse phases of a low-frequency dynamic event observed in a DNS. The global stability analysis of the mean flow reveals three oblique global modes, two of which are stationary modes and one of which is a traveling mode at a frequency of St = 0.076 at its most unstable spanwise wavelength. Resolvent analysis shows a region of high-gain in the low-frequency limit due to resonance with the global mode spectrum. Analysis of the low-pass snapshots shows a shift in the global linear spectrum from the growth phase to the collapse phase. While the growth phase supports oblique global instability at the ramp corner, oblique instability is suppressed during the collapse phase. Conversely, the collapse phase supports two-dimensional instability of the shear layer which is stable during the growth. The change in global stability between the mean, collapse phase, and growth phase suggests three possible mechanisms which may play a role in the low-frequency unsteadiness.