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.

arXiv comment12 pages, 6 figures, 2 multimedia files

References in corpus (5)

• On Dynamic Mode Decomposition: Theory and Applications
• Sparsity-promoting dynamic mode decomposition
• Deep Learning of Vortex Induced Vibrations
• A high-fidelity numerical study on the propulsive performance of pitching flexible plates
• Dynamics of random pressure fields over bluff bodies: a dynamic mode decomposition perspective

Cited by in corpus (3)

• A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition: Spectral Insights and Further Explorations
• The Linear-Time-Invariance Notion of the Koopman Analysis-Part 1: The Architecture, Practical Rendering on the Prism Wake, and Fluid-Structure Association
• The Linear-Time-Invariance Notion of the Koopman Analysis-Part 2: Physical Interpretations of Invariant Koopman Modes and Phenomenological Revelations