Topological modes of variability of the wind-driven ocean circulation

Templexes are topological objects that encode the branching organization of a flow in phase space. We build on these objects to introduce the concept of topological modes of variability (TMVs). TMVs are defined as dynamical manifestations of algebraically defined cycles, called generatexes, in the templex; they provide a concrete link between abstract topological invariants and time-dependent behavior in a model or in observations. We apply this approach to a low-order model of the wind-driven ocean circulation, subject to both periodic and aperiodic forcing, and show how TMVs emerge or vanish over time in nonautonomous settings. The analysis reveals that TMVs allow for a qualitatively new understanding of variability in complex systems where linear modes fail to describe the nonlinear dynamics.

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Publication Details

Journal
Chaos An Interdisciplinary Journal of Nonlinear Science
Published
2025-09-01
DOI
https://doi.org/10.1063/5.0261968
Primary Topic
Nonlinear Dynamics and Pattern Formation
Type
article
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article

Topological modes of variability of the wind-driven ocean circulation

Juan Ruiz, Michael Ghil, Gisela D. Charó, Stefano Pierini et al.
1 links
Chaos An Interdisciplinary Journal of Nonlinear Science
Nonlinear Dynamics and Pattern Formation
article

Topological modes of variability of the wind-driven ocean circulation

Juan Ruiz, Michael Ghil, Gisela D. Charó, Stefano Pierini, Denisse Sciamarella
article en

Abstract

Templexes are topological objects that encode the branching organization of a flow in phase space. We build on these objects to introduce the concept of topological modes of variability (TMVs). TMVs are defined as dynamical manifestations of algebraically defined cycles, called generatexes, in the templex; they provide a concrete link between abstract topological invariants and time-dependent behavior in a model or in observations. We apply this approach to a low-order model of the wind-driven ocean circulation, subject to both periodic and aperiodic forcing, and show how TMVs emerge or vanish over time in nonautonomous settings. The analysis reveals that TMVs allow for a qualitatively new understanding of variability in complex systems where linear modes fail to describe the nonlinear dynamics.

Chaos An Interdisciplinary Journal of Nonlinear ScienceVol. 35(9)
Centre National de la Recherche Scientifique (FR), University of California, Los Angeles (US), Parthenope University of Naples (IT), Université de Versailles Saint-Quentin-en-Yvelines (FR), Universidad de Buenos Aires (AR), Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR), Université Paris Sciences et Lettres (FR), Université Paris-Saclay (FR), École Normale Supérieure - PSL (FR), Laboratoire de Météorologie Dynamique (FR), Centre National pour la Recherche Scientifique et Technique (CNRST) (MA), Laboratoire des Sciences du Climat et de l'Environnement (FR), CEA Paris-Saclay (FR), Instituto Franco-Argentino sobre Estudios de Clima y sus Impactos (AR), Imperial College London (GB), Fundación Ciencias Exactas y Naturales (AR)
Openalex Percentile: Top 73%
Nonlinear Dynamics and Pattern Formation
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