Mechanisms of transonic buffet over supercritical airfoils revealed by direct numerical simulations
We use direct numerical simulations to study the turbulent transonic flow over a supercritical airfoil, spanning the transition from stable conditions to fully developed buffet at chord-based Reynolds numbers of $3\times10^5$ and $6\times10^5$. The Reynolds number determines the incoming boundary-layer state, thereby affecting the separation behaviour. Spectral proper orthogonal decomposition reveals a single dominant mode that emerges below onset and persists across the transition to buffet. The energy of this mode increases with the angle of attack while its spatial structure and fundamental frequency remain nearly unchanged, consistent with a global instability that saturates into a nonlinear limit cycle. Geometrical acoustics provides a first-order description of the global mode propagation and identifies two paths connecting the acoustic source, located in the near wake, to the shock. A shorter path impinges on the shock from behind, while a longer one circumvents the shock tip before reaching it from the front. Linearised shock--acoustic interaction theory predicts a stronger shock response to low-frequency, front-impinging acoustic disturbances. Space--time correlations link the establishment of a downstream path to complete boundary-layer separation, which is induced intermittently by the upstream motion of the shock. The sum of the upstream acoustic time along the front-impinging path and the downstream convective time is compatible with the measured buffet period at both Reynolds numbers. Together, these results are consistent with a unified picture of buffet, where an aeroacoustic feedback mechanism provides the physical pathways through which perturbations can sustain the global dynamics.