2008/04/02 by Michael Ghil, Mickaël D. Chekroun, Eric Simonnet · 1 citation
Computer Science · Economics, Econometrics and Finance · Environmental Science · Mathematics · Physics and Astronomy · #Climate variability and models #Complex Systems and Time Series Analysis #Nonlinear Dynamics and Pattern Formation #math-ph #math.DS #math.MP #msc:34C37 #msc:34D08 #msc:34D30 #msc:34F05 #msc:35Q35 #msc:37B55 #msc:37C15 #msc:37C20 #msc:37C29 #msc:37D20 #msc:37E10 #msc:37E45 #msc:37G15 #msc:76U05 #msc:86-06 #msc:86A05 #nlin.CD
paper · pdf · doi:10.1016/j.physd.2008.03.036
published as Physica D: Nonlinear phenomena, Special Issue on The Euler Equations: 250 Years On, {\bf 237}(2008), 2111--2126 · Invited survey paper for Special Issue on The Euler Equations: 250 Years On, in Physica D: Nonlinear phenomena
openalex publication_date 2008/04/02 · arxiv created 2010/06/15 · arxiv updated 2010/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change projections. To illustrate the first point, we focus on the large-scale, wind-driven flow of the mid-latitude oceans which contribute in a crucial way to Earth's climate, and to changes therein. We study the low-frequency variability (LFV) of the wind-driven, double-gyre circulation in mid-latitude ocean basins, via the bifurcation sequence that leads from steady states through periodic solutions and on to the chaotic, irregular flows documented in the observations. This sequence involves local, pitchfork and Hopf bifurcations, as well as global, homoclinic ones. The natural climate variability induced by the LFV of the ocean circulation is but one of the causes of uncertainties in climate projections. Another major cause of such uncertainties could reside in the structural instability in the topological sense, of the equations governing climate dynamics, including but not restricted to those of atmospheric and ocean dynamics. We propose a novel approach to understand, and possibly reduce, these uncertainties, based on the concepts and methods of random dynamical systems theory. As a very first step, we study the effect of noise on the topological classes of the Arnol'd family of circle maps, a paradigmatic model of frequency locking as occurring in the nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the seasonal cycle. It is shown that the maps' fine-grained resonant landscape is smoothed by the noise, thus permitting their coarse-grained classification. This result is consistent with stabilizing effects of stochastic parametrization obtained in modeling of ENSO phenomenon via some general circulation models.