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


[ 1 ] Instytut Mechaniki Stosowanej, Wydział Inżynierii Mechanicznej, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.8] Mechanical engineering

Year of publication


Published in

Journal of Fluid Mechanics

Journal year: 2022 | Journal volume: vol. 934

Article type

scientific article

Publication language


  • low-dimensional models
  • wakes

EN 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 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. The transition dynamics between these clusters is described by a directed network, called the cluster-based hierarchical network model (HiCNM). 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 identification of the 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 HiCNM 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.

Date of online publication


Pages (from - to)

A24-1 - A24-44





Article: A24

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Points of MNiSW / journal


Impact Factor

3.627 [List 2020]

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