Numerical characterization of the transonic turbulent buffet via dynamical system response

Low-frequency shock oscillations in a transonic flow over airfoils occur when the angle of attack (α) exceeds a certain threshold. Informed by the global stability analysis (Crouch et al., JFM, 2024), this work investigates the transonic turbulent shock buffet over a supercritical airfoil using Reynolds-averaged Navier-Stokes simulations with various α, ranging from 4° to 7°. The freestream Mach number is 0.7, and the Reynolds number is 300,000. Both small impulsive and continuous perturbations in the angle of attack are imposed. The Hilbert transform is applied to estimate the decay rate and internal frequency as α approaches the neutral stability state from the non-buffet regime. As the decay rate decreases with increasing α, the dominant frequency exhibits minimal variation, remaining approximately constant and equal to the shock buffet frequency at large α. The response under buffet conditions is probed by slowly decreasing α, assuming pseudo-steady base-state transition. Furthermore, wide-band perturbations are created using the Fourier–Wiener series. The gain indicates that the system is sensitive to external perturbations under non-buffet conditions. When the self-sustained buffet is established, the system is no longer sensitive to external perturbations.