Coherent oscillations and acoustic waves in a supersonic cylinder wake

The supersonic wake of a circular cylinder in Mach 3 flow was studied through spectral proper orthogonal decomposition (SPOD) of high-speed focussing schlieren datasets. A wavenumber decomposition of the SPOD eigenvectors was found to be an effective tool for isolating imaging artefacts from the flow features, resulting in a clearer interpretation of the SPOD modes. The cylinder wake consists of both symmetric and antisymmetric instabilities, with the former being the dominant type. The free shear layers that form after the flow separates from the cylinder surface radiate strong Mach waves that interact with the recompression shocks to release significant disturbances into the wake. The wake shows a bimodal vortex shedding behaviour with a purely hydrodynamic instability mode around a Strouhal number of 0.2 and an aeroacoustic instability mode around Strouhal number of 0.42. The hydrodynamic mode, which is presumably the same as the incompressible case, is weaker and decays rapidly as the wake accelerates due to increasing compressibility. The aeroacoustic mode is the dominant shedding mode and persists farther into the wake because of an indirect energy input received through free-stream acoustic waves. A simple aeroacoustic feedback model based on an interaction between downstream propagating shear-layer instabilities and upstream propagating acoustic waves within the recirculation region is shown to accurately predict the shedding frequency. Based on this model, the vortex shedding in supersonic flows over a circular cylinder occurs at a universal Strouhal number (based on approach free-stream velocity and feedback path length) of approximately 0.3.