Title: Simulation and stability analysis of oblique shock wave/boundary layer interactions at Mach 5.92,
Abstract: We investigate flow instability created by an oblique shock wave impinging on
a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The
adverse pressure gradient of the oblique shock causes the boundary layer to
separate from the wall, resulting in the formation of a recirculation bubble.
For sufficiently large oblique shock angles, the recirculation bubble is
unstable to three-dimensional perturbations and the flow bifurcates from its
original laminar state. We utilize Direct Numerical Simulation (DNS) and Global
Stability Analysis (GSA) to show that this first occurs at a critical shock
angle of $\theta = 12.9^o$. At bifurcation, the least stable global mode is
non-oscillatory, and it takes place at a spanwise wavenumber $\beta=0.25$, in
good agreement with DNS results. Examination of the critical global mode
reveals that it originates from an interaction between small spanwise
corrugations at the base of the incident shock, streamwise vortices inside the
recirculation bubble, and spanwise modulation of the bubble strength. The
global mode drives the formation of long streamwise streaks downstream of the
bubble. While the streaks may be amplified by either the lift-up effect or by
Görtler instability, we show that centrifugal instability plays no role in
the upstream self-sustaining mechanism of the global mode. We employ an adjoint
solver to corroborate our physical interpretation by showing that the critical
global mode is most sensitive to base flow modifications that are entirely
contained inside the recirculation bubble.