Extracting Principal Modes of Two-dimensional Shock Buffet by Using Dynamic Mode Decomposition

Self-oscillation of a shock wave, which is called a transonic shock buffet, occurs on a wing surface in a transonic flow. Lee and Crouch explained the self-sustained mechanism by different pressure wave propagations but there is no experimental evidence of which feedback loop is dominant. The principal aim of the present study is to identify the dominant feedback path of pressure waves related to the shock buffet using high-speed focusing schlieren movies. The experimental data showed that the flow fields include complicated phenomena such as a lot of pressure waves with a broad range of frequency. Therefore, we performed dynamic mode decomposition (DMD) analysis to extract dominant phenomena for the buffet. DMD modes whose frequencies corresponded to the shock oscillation frequencies were extracted and investigated. DMD modes revealed that pressure perturbations generated at the shock foot and the perturbation propagated to the height-wise direction along with the shock wave. This feedback pass is similar to that observed by Crouch using the global stability analysis for NACA 0012 airfoil.