Data-driven insights into fluid-structure association and energy quantification*

The linear-time-invariance notion to the Koopman Analysis (Part I - Li et al., 2022, Phys. Fluids 34(12) 125136; Part II - Li et al., 2023, J. Fluid Mech. 959, A15) and its derived augmented algorithm (Fu et al., 2023, Phys. Fluids 35(2) 025112) are recent advances in fluid mechanics, addressing the challenge of correlating nonlinear excitation and response in fluid-structure interactions (FSI). Continuing the serial research, this work presents a data-driven, Koopman-inspired approach integrated with the "Proper Orthogonal Decomposition-Dynamic Mode Decomposition-Discrete Fourier Transform Augmented Analysis (POD-DMD-DFT)" to decouple nonlinear FSI. This innovative approach first isolates energy-wise and evolution-wise significant nonlinear flow features, subsequently establishing cause-and-effect correspondences between these flow features and structure surface pressure. Dynamic visualizations of in-sync fluid-structure-coupled Koopman modes is then implemented for phenomenological analysis. Finally, FSI energy transfers is statistically quantified via spatiotemporal contribution and probability density distributions. Demonstrated based on high-fidelity direct numerical simulation and large eddy simulation of flow over typical rigid obstacles, our method offers insightful descriptions and interpretations of phenomena occurring in the flow and on the boundary (walls) of an FSI domain, and readily applies to various engineering problems given its data-driven nature.