Cluster-based hierarchical network model of the fluidic pinball – cartographing transient and post-transient, multi-frequency, multi-attractor behaviour

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from sequence of bifurcations for two-dimensional incompressible flow unforced fluidic pinball. The hierarchy is guided by triple decomposition separating slowly varying base flow, dominant shedding secondary structures. All these components are kinematically resolved clusters, starting with in first layer, resolving vortex second layer distilling structures third layer. transition between clusters described directed network, called network (HiCNM) sequel. Three consecutive Reynolds number regimes different considered: (i) periodic at $Re=80$, (ii) quasi-periodic $Re=105$, (iii) chaotic $Re=130$, involving three unstable fixed points, limit cycles, two attractors attractor. HiCNM enables identifying transient post-transient multiple invariant sets manner. Both global trends local during well moderate clusters. proposed provides visual representation post-transient, multi-frequency, multi-attractor behaviour may automate identification analysis scales sets.