DEEP MEAN-FIELD MODELING OF TRANSIENT AND POST-TRANSIENT, MULTI-ATTRACTOR FLOW DYNAMICS - EXEMPLIFIED FOR THE FLUIDIC PINBALL

We propose three kinds of mean-field modeling strategies for the complex dynamics generally found in fluid mechanics. A key enabler is a mean-field assumption, where slowly-varying mean-field deformations are due to the fluctuating field through the Reynolds stress, resulting in a Reynolds-like decomposition. We have developed projection-based and cluster-based reduced-order models, i.e., a least-order mean-field model for the successive bifurcations (Deng et al., 2020), an aerodynamic force model associated with a Galerkin model (Deng et al., 2021), and a hierarchical network model to automate the identification of multi-attractor dynamics (Deng et al., 2022). These mean-field models are exemplified for a challenging test case of the fluidic pinball at Re = 80, characterized by six invariant sets (three steady solutions and three limit cycles) induced by the first two successive bifurcations of pitchfork and Hopf types. This work shows a paradigm for automatable reduced-order modeling of complex flows using first principles and machine learning techniques, balancing between data-driven and physics-driven approaches and improving model interpretability and generalizability.