Stability Analysis of Shockwave Laminar Boundary Layer Interaction Over a Cylinder

Shock wave boundary layer interactions (SWBLIs) over axisymmetric bodies exhibit complex three-dimensional unsteady dynamics distinct from their planar counterparts. In this study, we investigate the global linear instability characteristics of a laminar SWBLI induced by an oblique shock impinging on the windward surface of a cylindrical body. Large-eddy simulations (LES) are employed to obtain the base flow, which reveals a three-dimensional separation bubble and a system of counter-rotating vortex pairs wrapping around the cylinder. To extract the underlying instability mechanisms, we utilize a matrix-free Navier–Stokes-based Mean Flow Perturbation (NS-MFP) methodology. On the windward plane, the flow exhibits canonical SWBLI behavior, with spectral bands associated with bubble breathing, shear layer flapping, and Kelvin–Helmholtz instability, confirmed through Spectral Proper Orthogonal Decomposition (SPOD). Downstream of the interaction, analysis of the vortex pairs reveals coexisting absolute and elliptic instabilities. A near-zero-frequency helical global mode is identified as an absolute instability, while a higher-frequency mode is attributed to elliptic instability arising from mutual strain interactions between the vortices. These findings elucidate the instabilities governing unsteadiness in axisymmetric SWBLIs and provide critical insights into their potential impact on unsteady aerodynamic loading in high-speed flows.