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September  2008, 10(2&3, September): 401-419. doi: 10.3934/dcdsb.2008.10.401

Dynamical systems modeling of low-frequency variability in low-order atmospheric models

H. W. Broer 1, and  Renato Vitolo 2,

1. 

Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, Netherlands
2. 

College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, EX4 4QF, Exeter, United Kingdom

Received  October 2006 Revised  May 2007 Published  June 2008

The understanding of atmospheric and oceanic low-frequency variability is an old problem having both theoretical interest and practical importance, e.g., for the assessment of climate change. In this paper possible relations with dynamical systems theory are given, in particular through bifurcation theory. Firstly, a specific type of oceanic low frequency variability is described, the so-called Atlantic Multidecadal Oscillation (AMO). Then recent work is reviewed, that investigates bifurcations as these occur in a few low-order models of the atmospheric circulation. It is shown that the Shil′nikov bifurcation in the Hopf-saddle-node bifurcation scenario takes place in each of the above atmospheric models. Related strange attractors and intermittency behavior are also found, both in agreement with the theoretical expectations and with qualitative aspects of the climate variability, like the AMO. It is discussed how the latter connection may be consolidated in higher dimensional and in PDE models.
Keywords: intermittency, atmospheric dynamics, low-dimensional models., Shil$'$nikov bifurcation.
Mathematics Subject Classification: Primary: 37G35, 70K44; Secondary: 37D45, 85A2.
Citation: H. W. Broer, Renato Vitolo. Dynamical systems modeling of low-frequency variability in low-order atmospheric models. Discrete & Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 401-419. doi: 10.3934/dcdsb.2008.10.401
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