Feature-based manifold modeling for the quasiperiodic wake dynamics of a pair of side-by-side cylinders

We propose a feature-based manifold modeling (FeMM) framework for the quasiperiodic wake dynamics of a pair of side-by-side cylinders. The key enabler is to embed the most parsimonious mean-field manifold based on the extracted features, such as force coefficients and probing data from experiments and numerical simulations. The manifold model is then identified under the mean-field constraints of the model structure, ensuring human-interpretability. The FeMM method is demonstrated with a two-dimensional incompressible flow crossing a pair of side-by-side cylinders, exhibiting a flip-flopping wake in quasiperiodic behavior. The transient and post-transient dynamics are characterized by two coupled oscillators associated with vortex shedding and gap flow oscillations. Dynamic mode decomposition analysis reveals significant modal interactions between these two flow mechanisms, posing a serious challenge to projection-based modeling approaches, such as the Galerkin projection method. Nevertheless, the FeMM approach, based on force measurements, yields an interpretable model that accounts for the mechanisms underlying the quasiperiodic dynamics, demonstrating its applicability to higher-order dynamics with multiple scales and invariant sets. This approach is expected to have broad applicability in dynamic modeling and state estimation in various real-world scenarios.