Stability, Receptivity, and Sensitivity Analyses of Buffeting Transonic Flow over a Profile

A transonic flow over the OAT15A supercritical profile is considered. The interaction between the shock wave and the turbulent boundary layer is investigated through numerical simulation and global stability analysis for a wide range of angles of attack. Numerical simulations are in good agreement with previous studies and manage to reproduce the high-amplitude self-sustained shock oscillations known as shock buffet. In agreement with previous results, it is found that the buffet phenomenon is driven by an unstable global mode of the linearized Navier–Stokes equations. Analysis of the adjoint global mode reveals that the flow is most receptive to harmonic forcings on the suction side of the profile, within the boundary layer upstream of the shock foot, in the recirculation bubble downstream of the shock foot, and on the right characteristic that impinges the shock foot. An eigenvalue sensitivity analysis shows that a steady streamwise force applied either in the boundary layer or in the recirculation region, a steady cooling of the boundary layer, or a steady source of eddy viscosity (a mechanical vortex generator for example) all lead to stabilization of the buffet mode. Finally, pseudoresonance phenomena have been analyzed by performing a singular-value decomposition of the global resolvent, which revealed that, besides the low-frequency shock unsteadiness, the flow also undergoes medium-frequency unsteadiness, linked to Kelvin–Helmholtz-type instability. Such results are reminiscent of the medium-frequency perturbations observed in more traditional shock wave/boundary-layer interactions.