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Geophysical Fluid Dynamics, Nonautonomous Dynamical Systems, and the Climate Sciences

  • Michael GhilEmail author
  • Eric Simonnet
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Part of the Springer INdAM Series book series (SINDAMS, volume 38)

Abstract

This contribution introduces the dynamics of shallow and rotating flows that characterizes large-scale motions of the atmosphere and oceans. It then focuses on an important aspect of climate dynamics on interannual and interdecadal scales, namely the wind-driven ocean circulation. Studying the variability of this circulation and slow changes therein is treated as an application of the theory of nonautonomous dynamical systems. The contribution concludes by discussing the relevance of these mathematical concepts and methods for the highly topical issues of climate change and climate sensitivity.

Keywords

Bifurcations Climate sensitivity Double-gyre problem Low-frequency variability Pullback and random attractors Wasserstein distance Wind-driven ocean circulation 

Notes

Acknowledgements

It is a pleasure to thank M. D. Chekroun, D. Kondrashov, H. Liu, J. C. McWilliams, J. D. Neelin and I. Zaliapin for many useful discussions and their continuing interest in the questions studied here. The research reported in Sect. 3.4 was carried out jointly with M. D. Chekroun, L. De Cruz, J. Demayer, S. Pierini and S. Vannitsem [125, 168]. Figure 23 is due to M. D. Chekroun, a steadfast companion on the road to understanding NDS and RDS theory, along with their applications to climate dynamics in general. H. Liu helped with finalizing Fig. 22. It is a pleasure to thank the organizers of the INdAM Workshop on Mathematical Approaches to Climate Change Impacts—P. Cannarsa, D. Mansutti, and A. Provenzale—for the invitation to deliver a lecture and to contribute to this volume. The writing of this research-and-review paper was supported by grants N00014-12-1-0911 and N00014-16-1-2073 from the Multidisciplinary University Research Initiative (MURI) of the Office of Naval Research and by the US National Science Foundation grant OCE 1243175. This paper is TiPES contribution #4; this project has received funding from the European Union Horizon 2020 research and innovation programme under grant agreement No. 820970.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Ecole Normale Supérieure and PSL UniversityParisFrance
  2. 2.University of CaliforniaLos AngelesUSA
  3. 3.Institut de Physique de NiceCNRS & Université Côte d’AzurNiceFrance

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