Tropical atmospheric circulations: Dynamic stability andtransitions

Tian Ma; Shouhong Wang

doi:10.3934/dcds.2010.26.1399

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2010, Volume 26, Issue 4: 1399-1417. Doi: 10.3934/dcds.2010.26.1399

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Tropical atmospheric circulations: Dynamic stability and transitions

Tian Ma^1, and
Shouhong Wang^2,

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

Received: December 31, 2008

Published: November 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 86A10, 76U05, 35Q30.

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