# American Institute of Mathematical Sciences

October  2010, 26(4): 1399-1417. doi: 10.3934/dcds.2010.26.1399

## Tropical atmospheric circulations: Dynamic stability and transitions

 1 Department of Mathematics, Sichuan University, Chengdu 2 Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  January 2009 Published  December 2009

In this article, we present a mathematical theory of the Walker circulation of the large-scale atmosphere over the tropics. This study leads to a new metastable state oscillation theory for the El Niño Southern Oscillation (ENSO), a typical inter-annual climate low frequency oscillation. The mathematical analysis is based on 1) the dynamic transition theory, 2) the geometric theory of incompressible flows, and 3) the scaling law for proper effect of the turbulent friction terms, developed recently by the authors.
Citation: Tian Ma, Shouhong Wang. Tropical atmospheric circulations: Dynamic stability and transitions. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1399-1417. doi: 10.3934/dcds.2010.26.1399
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