Koopman-inspired data-driven quantification of fluid–structure energy transfers

The linear-time-invariance notion to the Koopman analysis is a recent advance in fluid mechanics [Li et al., “The linear-time-invariance notion to the Koopman analysis: The architecture, pedagogical rendering, and fluid–structure association,” Phys. Fluids 34(12), 125136 (2022c) and Li et al., “The linear-time-invariance notion of the Koopman analysis—Part 2. Dynamic Koopman modes, physics interpretations and phenomenological analysis of the prism wake,” J. Fluid Mech. 959, A15 (2023a)], targeting the long-standing issue of correlating nonlinear excitation and response phenomena in fluid–structure interactions (FSI), or, in the simplified case, flow over rigid obstacles. Continuing the serial research, this work presents a data-driven, Koopman-inspired methodology to decouple nonlinear FSI by establishing cause-and-effect correspondences between structure surface pressure and the flow field. Exploiting unique features of the Koopman operator, the new methodology renders dynamic visualizations of in-sync, fluid–structure-coupled Koopman modes possible, fostering phenomenological analysis and statistical quantifications of FSI energy transfers. Instantaneous contribution contours and densities offer new angles to evaluate pathways of energy amplification and diminution. The methodology enables better descriptions and interpretations of phenomena occurring in the flow and on the boundary (walls) of an FSI domain and readily applies to a broad spectrum of engineering problems given its data-driven nature.