Establishing Direct Phenomenological Connections between Fluid and Structure by the Koopman-Linearly-Time-Invariant Decomposition

In this work, we introduce a novel data-driven formulation, the Koopman-Linearly-Time-Invariant (Koopman-LTI) decomposition, for analyzing Fluid-Structure Interactions (FSI). An implementation of the Koopman-LTI on a subcritical free-shear flow over a prism at Re=22,000 corroborated the construction of a configuration-wise universal approximation of nonlinear fluid-structure dynamics with stellar accuracy. It also successfully decomposed the entwined morphologies of raw numerical measurement into a linear superposition of distinct frequency-based constituents. Most importantly, even with random and anisotropic turbulence, the Koopman-LTI yielded identical modes for fluid motions and wall pressures, permitting direct connections of fluid and structural phenomena with phenomenological visualization.