Variational mode decomposition analysis of the relationship between low-frequency shock-wave oscillations and buffet cells

This study investigates the relationship between low-frequency shock-wave oscillations and buffet cells on the main wing of the NASA common research model. The flow conditions were set at a Mach number of 0.85, Reynolds number of 2.27 $\times$ 10$^6$, and angle of attack of 4.82$^{\circ}$. Buffet cells are cellular patterns with spanwise periodicity that propagate toward the wing tip, with nondimensional frequencies (Strouhal numbers) of 0.2--0.6, higher than those of shock oscillations associated with transonic buffet. However, the physical mechanisms driving buffet cells and their interaction with low-frequency shock motion are not fully understood. This study employs variational mode decomposition-based nonstationary coherent structure (VMD-NCS) analysis applied to unsteady pressure-sensitive paint measurement data. The results reveal that the amplitude of buffet cells is not directly coupled to the low-frequency shock-wave oscillations but instead shows correlation with the boundary layer separation state. Strong buffet cell fluctuations persist in regions of sustained separation (midspan), while their amplitude varies with local separation/reattachment dynamics in regions of intermittent separation (outboard). These observations suggest that shock-waves are important to generate the adverse pressure gradient necessary for boundary layer separation, but their influence on buffet cells depends on the resulting separation behavior. This insight from experimental observations in this study is consistent with previous computational studies suggesting that buffet cell behavior depends on boundary layer separation characteristics. Moreover, this study demonstrates the effectiveness of VMD-NCS analysis for investigating nonstationary fluid phenomena with multiple spatial and temporal patterns.