Improving dynamic mode decomposition of tandem cylinder flow with nonlinear dictionaries

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This paper examines algorithmic nonlinear dictionary enhancements for dynamic mode decomposition (DMD) based analysis of an industrially relevant flow problem. Several nonlinear variants of DMD are used to analyze flow interacting with two tandem cylinders in a bi-stable configuration. This study investigates the coexistence of two vortex shedding regimes, distinguished by their characteristic frequencies. Using DMD, we extract coherent structures associated with each regime and consider their relation to surface pressure and far-field noise at these frequencies. Simultaneous experimental measurements of velocity fields, unsteady surface pressure, and far-field acoustic pressure are performed using high-speed particle image velocimetry, a remote microphone technique, and a far-field microphone. Two DMD algorithms are applied to investigate the flow. First, we apply kernelized extended DMD to demonstrate how a nonlinear dictionary can improve modal reliability compared with the usual linear alternative. The extracted modes are validated by analyzing their modal residuals, which are further used to explore phenomena at other frequencies and harmonics while examining the impact of dictionary depth and characteristics. Second, we study the flow physics of each shedding frequency via the Rigged DMD algorithm, which provides detailed spectral insights for dynamical systems with continuous spectra. A new kernelized Rigged DMD is introduced, showing improved accuracy in resolving generalized eigenfunctions and spectral measures compared to linear dictionaries.