Sensitivity analysis for the control of oblique shock wave/laminar boundary layer interactions at Mach 5.92

At a transitional Reynolds number, we examine the instability of an oblique shock wave impinging on a hypersonic laminar boundary layer. Using global stability analysis we identify the critical oblique shock angle at which the 2D laminar flow first becomes unstable to 3D perturbations. The non-dimensional spanwise wavenumber selected at this bifurcation is β = 0.25. Long streamwise streaks that originate in the shear layer on top of the recirculation bubble are present in the unstable stationary global mode. We compute the adjoint eigenmodes to understand how upstream fluctuations affect the direct global modes of the system, and we see that the least stable stationary global mode is receptive to forcing inside the boundary layer and along the oblique shock wave. The wavemaker, which is defined as the sensitivity of an eigenvalue to base flow modification, is then computed. For every case, the wavemaker resides in the recirculation bubble, but it shifts towards the reattachment point as the incident shock angle increases. A calculation of the Görtler number about several 2D base flows revealed that a centrifugal instability cannot be the sole reason for bifurcation. There must be a feedback connection between Görtler vortices and the stationary behavior inside the recirculation bubble.