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

Abstract: In this work, we introduce a novel data-driven formulation, the Koopman-Linearly-Time-Invariant (Koopman-LTI) analysis, 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 a configuration-wise universal Koopman system, which approximated the configuration's nonlinear dynamics with stellar accuracy. The Koopman-LTI also successfully decomposed the entwined morphologies of raw measurement into a linear superposition of frequency-based constituents. Most importantly, with random and anisotropic turbulence, the Koopman-LTI yielded frequency-wise identical modes for structure response and fluid excitation, thus establishing direct constitutive relations between the phenomenology of fluid and structure.