Mechanisms of Wake Oscillations in Supersonic Flow Past Bluff Bodies

While vortex shedding behind bluff bodies in subsonic and incompressible flows is well studied, the dynamics of supersonic wakes remain less understood. Previous research on supersonic flow past cylinders has focused primarily on surface quantities such as drag, pressure, and separation locations. However, the mechanisms driving unsteady oscillations in the wake have received limited attention. In this work, we use the Hypersonic High-Order High-Performance Code (H$^3$PC) based on entropy stable discontinuous spectral element method to simulate supersonic flow over circular and square cylinders across a range of Mach and Reynolds numbers. We investigate wake oscillation frequencies and their underlying causes. Consistent with recent experimental findings by Schmidt and Shepherd, our results indicate that the oscillations are not caused by vortex shedding from the body but are instead driven by acoustic waves trapped within the subsonic region between the separation points and the slipline convergence zone. This study provides new insight into the acoustic feedback mechanisms responsible for wake instabilities in supersonic flows.