Data-Driven Time-Dependent Bases for Turbulent Airfoil Wake–Extreme Gust Interactions

We analyze interactions between turbulent airfoil wakes and extreme gusts using a data-driven framework with time-dependent bases. The current approach represents each snapshot with time-varying bases consisting of two-dimensional in-plane modes and one-dimensional spanwise modes, together with a reduced covariance matrix. By deriving closed-form evolution equations, we advance these components using a small rolling window, eliminating the need for full-history storage. Applied to extreme vortex gust–airfoil interactions at [Formula: see text], we reveal that the first in-plane mode dominates before impingement, while the second mode gains energy postimpingement, amplified by gust intensity. During impingement, leading modes exhibit multiscale features such as shear-layer roll-up and fine-scale turbulence. The temporal evolution of the mode-energy spectrum and its rank gaps further quantifies these interactions. A large leading-mode gap indicates energy concentrated in a few coherent structures, leading to faster recovery, whereas a smaller gap indicates energy distributed across many modes, consistent with richer multiscale activity and delayed restabilization. These trends also follow the transient lift dynamics, with higher amplitude and more oscillations indicated by a rise in the leading singular values. This work may provide a foundation for time-varying data-driven modal analysis of extreme gust encounters.