Input-output analysis of shock boundary layer interaction

Understanding transition mechanisms in high speed boundary layers is important for predictive design and control in aeronautics. Shock boundary layer interaction, in which the inviscid pressure rise causes the incoming boundary layer to separate and reattach downstream, has a destabilizing effect on the flow. The presence of a recirculation bubble and highly concave curvature of the streamlines near reattachment can support large growth of perturbations. In this paper, we investigate the receptivity properties of an asymptotically stable shock boundary layer interaction on a slender double wedge. The optimal frequency response of the two-dimensional steady state flow subjected to external perturbations is computed. It is found that the flow is highly receptive to low-frequency streamwise vorticity perturbations of a specific spanwise wavelength in the incoming boundary layer. This results in growth of streaks post-reattachment. The most amplified spanwise wavelength scales with approximately twice the boundary layer thickness at reattachment. By excluding the role of bubble dynamics in the input-output analysis, we find that recirculation bubble plays an important role in the perturbation growth and the spanwise wavelength selection. The present work demonstrates the efficacy of input-output analysis for investigating the stability and sensitivity of compressible boundary layer flows.