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

TL;DR

This paper introduces Koopman-LTI, a novel data-driven method for analyzing fluid-structure interactions, successfully establishing direct relations between fluid and structural phenomenology through frequency-based mode decomposition.

Contribution

The paper presents the Koopman-LTI analysis as a new approach for fluid-structure interaction analysis, demonstrating its ability to accurately model nonlinear dynamics and directly connect fluid and structure behaviors.

Findings

Koopman-LTI accurately models nonlinear FSI dynamics.

It decomposes complex measurements into frequency-based modes.

It establishes direct fluid-structure phenomenological relations.

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.