This thesis proposed and developed a novel data-driven infrastructure, named the Koopman Linear-Time-Invariant (Koopman-LTI) analysis, for investigating fluid-structure interaction (FSI). The Koopman-LTI globally linearizes a nonlinear fluid-structure system and disentangles its complex morphologies into sets of linear, temporally orthogonal constituents, known as the Ritz descriptors. Through a posteriori implementations on the subcritical prism wake, The Koopman-LTI established a direct constitutive relationship between fluid excitation and structural response. It also erected a phenomenological relationship atop the constitution, thus underpinning the fundamental origin of the fluid-structure correspondence. Results suggested the Koopman approximation of fluid systems is close to exa...[ Read more ]

This thesis proposed and developed a novel data-driven infrastructure, named the Koopman Linear-Time-Invariant (Koopman-LTI) analysis, for investigating fluid-structure interaction (FSI). The Koopman-LTI globally linearizes a nonlinear fluid-structure system and disentangles its complex morphologies into sets of linear, temporally orthogonal constituents, known as the Ritz descriptors. Through a posteriori implementations on the subcritical prism wake, The Koopman-LTI established a direct constitutive relationship between fluid excitation and structural response. It also erected a phenomenological relationship atop the constitution, thus underpinning the fundamental origin of the fluid-structure correspondence. Results suggested the Koopman approximation of fluid systems is close to exact, with errors in the order of numerical zeros. The subsequent analysis also revealed that the turbulent prism wake reduces down to only six spatiotemporally predominant phenomena. Two depict the shear layers dynamics and turbulence production that overwhelm the on-wind walls by instigating the reattachment-type response. Another four, manifested as harmonic modes, delineate the fluid entrainment of the Kármán vortex, which is trivial to the on-wind walls but dominates the sophisticated downstream wall and prism base. Dynamic visualization of the Koopman modes also discovered the vortex breathing phenomenon. Furthermore, parametric evidence confirms sampling convergence in four universal states: Initialization, Transition, Convergence, and Divergence. Accordingly, the notion of Linear-Time-invariance has been pragmatically defined for stationary flows. Finally, Koopman analysis with a vast inventory of observables alludes to the existence of a configuration-wise universal Koopman system. The elegance of the Koopman-LTI manifests through its implicit acquisition of fluid dynamics while bypassing the solution-deprived Navier-Stokes. The constitutive and phenomenological relationships reveal brand-new insights into FSI---one can now pinpoint the exact fluid origin of a specific pressure pattern of structural response. The Koopman-LTI’s success with inhomogeneous and anisotropic turbulence also substantiates its generality for many stochastic processes, perhaps even beyond those under fluid mechanics.