Optimal spatial growth of streaks in oblique shock/boundary layer interaction

Direct numerical simulation (DNS) of oblique shock interacting with an incoming laminar boundary layer on an adiabatic at plate at Mach 5:92 is considered. Various shock angles are considered to simulate interactions at various strengths. Above a critical shock angle, the flow around the separation bubble becomes three dimensional and transition to turbulence ensues. Previous studies^{5, 11} point to the existence of three-dimensional streak like structures just before transition occurs. In order to investigate the origin and the linear amplification of steady streamwise structures after the reattachment, we use an adjoint looping algorithm suitable for investigating spatial optimal growth. We modify this approach to account for the effect of curvature of streamlines due to the presence of the separation bubble. We further comment on the role of the non-modal spatial growth in transition due to such an interaction. With this analysis we observe that the boundary layer downstream of reattachment can support significant growth. Furthermore, spanwise wavenumber of the optimal perturbation at the reattachment location matches quite well with the energetical spanwise scale observed in DNS for a range of shock angles.