- 1Laboratoire de Météorologie Dynamique (CNRS-IPSL) , École Normale Supérieure, Paris, France (nicolas.bodnariuk@lmd.ipsl.fr)
- 2CNRS – IRD – CONICET – UBA. Institut Franco-Argentin d’ Études sur le Climat et ses Impacts (IRL 3351 IFAECI), CABA, Argentina
- 3Department of Geosciences, École Normale Supérieure (ENS-PSL), Laboratoire de Météorologie Dynamique (CNRS-IPSL), Paris, France (sabrina.speich@lmd.ens.fr)
- 4INPHYNI, Université Côte d'Azur et CNRS, Nice, France (Eric.SIMONNET@univ-cotedazur.fr)
- 5Department of Mathematics, Imperial College London, London, UK
We use a quasi-geostrophic model of the wind-driven double-gyre to explore qualitative changes in the system's behavior through a novel topological framework called Templex. This method characterizes and classifies the system's attractors in phase space across various regimes, from low-energy, temporally smooth dynamics to highly energetic and chaotic states. Our study focuses on stationary wind stress forcing to deepen the understanding of the underlying dynamics, starting from this simplified scenario to identify the physical processes involved, while the spatial resolution is gradually increased up to 5 km x 5 km.
The original system of partial differential equations describing the flow is converted into a set of ordinary differential equations using finite-difference methods. We take advantage of the Julia programming language to build the model, apply continuation methods, and perform stability analyses along the branches of a bifurcation tree, subject to pseudo-adiabatic variations in wind intensity. Our findings emphasize the effectiveness of topological methods in revealing the structural aspects of bifurcations, and in examining new pathways to study dynamical systems in geosciences. Moreover, we present novel insights on the existence of an attractor in the infinite-dimensional system, bridging the gap between topological results obtained numerically and the original mathematical model.
Through this presentation, we aim to foster discussion on the potential of topological approaches to advance the understanding of nonlinear systems in geophysical fluid dynamics.
How to cite: Bodnariuk, N., Sciamarella, D., Speich, S., Simonnet, E., and Ghil, M.: The Wind-Driven Double-Gyre Circulation: A topological characterization of attractors across regimes, EGU General Assembly 2025, Vienna, Austria, 27 Apr–2 May 2025, EGU25-11928, https://doi.org/10.5194/egusphere-egu25-11928, 2025.