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A Mechanism for Atmospheric Regime Behavior

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  • 1 Royal Netherlands Meteorological Institute, De Bilt, and Department of Mathematics, Utrecht University, Utrecht, Netherlands
  • | 2 Royal Netherlands Meteorological Institute, De Bilt, and Institute for Marine and Atmospheric Research, Utrecht University, Utrecht, Netherlands
  • | 3 Department of Mathematics, Utrecht University, Utrecht, Netherlands
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Abstract

Adopting the viewpoint that atmospheric flow regimes can be associated with steady states, this work investigates the hypothesis that regime transitions in deterministic atmosphere models are related to the existence of heteroclinic connections between these steady states. A low-order barotropic model with topography is studied, in which topographic and barotropic instabilities are the mechanisms dominating the dynamics. By parameter tuning, the Hopf bifurcation corresponding to barotropic instability can be made to coincide with one of the saddle-node bifurcations that are due to the topography in the model. This coincidence is called a fold-Hopf bifurcation. Among the dynamical structures related to such a bifurcation are heteroclinic connections and homoclinic orbits, connected to the equilibria. A heteroclinic cycle back and forth between the equilibria, existing in the truncated normal form of the fold-Hopf bifuraction, will be perturbed in the full model, leaving orbits homoclinic to one of the equilibria. The impact of these mathematical structures explains several characteristics of regime behavior known from previous model studies.

Current affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York

Corresponding author address: D. T. Crommelin, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185. Email: crommelin@cims.nyu.edu

Abstract

Adopting the viewpoint that atmospheric flow regimes can be associated with steady states, this work investigates the hypothesis that regime transitions in deterministic atmosphere models are related to the existence of heteroclinic connections between these steady states. A low-order barotropic model with topography is studied, in which topographic and barotropic instabilities are the mechanisms dominating the dynamics. By parameter tuning, the Hopf bifurcation corresponding to barotropic instability can be made to coincide with one of the saddle-node bifurcations that are due to the topography in the model. This coincidence is called a fold-Hopf bifurcation. Among the dynamical structures related to such a bifurcation are heteroclinic connections and homoclinic orbits, connected to the equilibria. A heteroclinic cycle back and forth between the equilibria, existing in the truncated normal form of the fold-Hopf bifuraction, will be perturbed in the full model, leaving orbits homoclinic to one of the equilibria. The impact of these mathematical structures explains several characteristics of regime behavior known from previous model studies.

Current affiliation: Courant Institute of Mathematical Sciences, New York University, New York, New York

Corresponding author address: D. T. Crommelin, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185. Email: crommelin@cims.nyu.edu

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