Modal Assessment of the Turbulent Near-Wake Flow Field Induced by Transonic Shock Buffet Mode

We investigate the spatio-temporal organization of the intermittently separated boundary layer and turbulent near wake of a supercritical airfoil under fully developed transonic shock buffet using high-speed focusing schlieren and Dynamic Mode Decomposition. At $M_{\infty} = 0.72$ and AoA of 5 deg, the shock oscillates quasi-sinusoidally at 113 Hz with an amplitude of $\approx 0.165c$, imprinting large-scale flapping on the separated shear layer and modulating the wake envelope. Analyses identify coexisting higher-frequency dynamics: downstream-traveling structures within the separated boundary layer (Strouhal numbers $St_c \approx 2.5-4.2$) and trailing-edge vortex shedding around 3.5–4.0 kHz ($St_c \approx 2.0-2.5$). Upstream-traveling waves interact with the shock and generate oblique fronts that wrap around the shock tip and traverse the supersonic bubble, evidencing a coupled feedback across airfoil and wake domains. Modal assessment suggests that the low-velocity wake region expands and contracts in phase with the position of the shock, while modest increases in \(M_\infty\) strengthen separation and split the wake into upper and lower streaks linked to suction-side separation and trailing-edge interaction. The findings establish a multi-frequency wake state driven by low-frequency buffet and superimposed higher-frequency shedding.