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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

The dynamics of a low-order model for the Atlantic multidecadal oscillation

Pages: 73 - 107, Volume 16, Issue 1, July 2011      doi:10.3934/dcdsb.2011.16.73

 
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Henk Broer - Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, PO Box 407, 9700 AK Groningen, Netherlands (email)
Henk Dijkstra - Institute for Marine and Atmospheric Research, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands (email)
Carles Simó - Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain (email)
Alef Sterk - Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, PO Box 407, 9700 AK Groningen, Netherlands (email)
Renato Vitolo - College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park Road, EX4 4QF, Exeter, United Kingdom (email)

Abstract: Observational and model based studies provide ample evidence for the presence of multidecadal variability in the North Atlantic sea-surface temperature known as the Atlantic Multidecadal Oscillation (AMO). This variability is characterised by a multidecadal time scale, a westward propagation of temperature anomalies, and a phase difference between the anomalous meridional and zonal overturning circulations.
    We study the AMO in a low-order model obtained by projecting a model for thermally driven ocean flows onto a 27-dimensional function space. We study bifurcations of attractors by varying the equator-to-pole temperature gradient ($\Delta T$) and a damping parameter ($\gamma$).
    For $\Delta T = 20^\circ$C and $\gamma = 0$ the low-order model has a stable equilibrium corresponding to a steady ocean flow. By increasing $\gamma$ to 1 a supercritical Hopf bifurcation gives birth to a periodic attractor with the spatio-temporal signature of the AMO. Through a period doubling cascade this periodic orbit gives birth to Hénon-like strange attractors. Finally, we study the effects of annual modulation by introducing a time-periodic forcing. Then the AMO appears through a Hopf-Neĭmark-Sacker bifurcation. For $\Delta T = 24^\circ$C we detected at least 11 quasi-periodic doublings of the invariant torus. After these doublings we find quasi-periodic Hénon-like strange attractors.

Keywords:  Atlantic Multidecadal Oscillation, dynamical systems, periodic and quasi-periodic dynamics, bifurcations.
Mathematics Subject Classification:  Primary: 37N10, 37G35; Secondary: 37C55, 37D45.

Received: February 2010;      Revised: March 2010;      Available Online: April 2011.

 References