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

Abstract

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

References in corpus (22)

• Statistical mechanics of complex networks
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Machine Learning for Fluid Mechanics
• On Dynamic Mode Decomposition: Theory and Applications
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Cluster-based reduced-order modelling of a mixing layer
• Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
• A Spectral Clustering Approach to Lagrangian Vortex Detection
• An artificial neural network framework for reduced order modeling of transient flows
• Multi-Scale Proper Orthogonal Decomposition of Complex Fluid Flows
• Network Structure of Two-Dimensional Decaying Isotropic Turbulence
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• Low-order model for successive bifurcations of the fluidic pinball
• Coherent structure coloring: identification of coherent structures from sparse data using graph theory
• Cluster-based feedback control of turbulent post-stall separated flows
• A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator
• Network-theoretic approach to sparsified discrete vortex dynamics
• Cluster-based network model
• Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
• Network community-based model reduction for vortical flows
• Identifying vortical network connectors for turbulent flow modification
• Network broadcast analysis and control of turbulent flows

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• Learning the Latent dynamics of Fluid flows from High-Fidelity Numerical Simulations using Parsimonious Diffusion Maps