American Institute of Mathematical Sciences

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

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  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.
Keywords: tropical atmospheric circulation, dynamic transition, Walker circulation, metastable states., new mechanism of ENSO, El Niño Southern Oscillation (ENSO).
Mathematics Subject Classification: Primary: 86A10, 76U05, 35Q3.
Citation: Tian Ma, Shouhong Wang. Tropical atmospheric circulations: Dynamic stability and transitions. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1399-1417. doi: 10.3934/dcds.2010.26.1399
[1]

Rodrigo Donizete Euzébio, Jaume Llibre. Periodic solutions of El Niño model through the Vallis differential system. Discrete & Continuous Dynamical Systems, 2014, 34 (9) : 3455-3469. doi: 10.3934/dcds.2014.34.3455
[2]

Botao ZHOU, Ying XU. How the “Best” CMIP5 Models Project Relations of Asian–Pacific Oscillation to Circulation Backgrounds Favorable for Tropical Cyclone Genesis over the Western North Pacific. Inverse Problems & Imaging, 2017, 11 (2) : 107-116. doi: 10.1007/s13351-017-6088-4
[3]

Aurea Martínez, Francisco J. Fernández, Lino J. Alvarez-Vázquez. Water artificial circulation for eutrophication control. Mathematical Control & Related Fields, 2018, 8 (1) : 277-313. doi: 10.3934/mcrf.2018012
[4]

Chao Xing, Ping Zhou, Hong Luo. The steady state solutions to thermohaline circulation equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3709-3722. doi: 10.3934/dcdsb.2016117
[5]

Wu Chanti, Qiu Youzhen. A nonlinear empirical analysis on influence factor of circulation efficiency. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 929-940. doi: 10.3934/dcdss.2019062
[6]

Hongjun Gao, Jinqiao Duan. Dynamics of the thermohaline circulation under wind forcing. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 205-219. doi: 10.3934/dcdsb.2002.2.205
[7]

Jean-Pierre Eckmann, C. Eugene Wayne. Breathers as metastable states for the discrete NLS equation. Discrete & Continuous Dynamical Systems, 2018, 38 (12) : 6091-6103. doi: 10.3934/dcds.2018136
[8]

Yuri N. Fedorov, Luis C. García-Naranjo, Joris Vankerschaver. The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation. Discrete & Continuous Dynamical Systems, 2013, 33 (9) : 4017-4040. doi: 10.3934/dcds.2013.33.4017
[9]

Xiangjun Wang, Jianghui Wen, Jianping Li, Jinqiao Duan. Impact of $\alpha$-stable Lévy noise on the Stommel model for the thermohaline circulation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1575-1584. doi: 10.3934/dcdsb.2012.17.1575
[10]

Arsen R. Dzhanoev, Alexander Loskutov, Hongjun Cao, Miguel A.F. Sanjuán. A new mechanism of the chaos suppression. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 275-284. doi: 10.3934/dcdsb.2007.7.275
[11]

Nikita Kalinin, Mikhail Shkolnikov. Introduction to tropical series and wave dynamic on them. Discrete & Continuous Dynamical Systems, 2018, 38 (6) : 2827-2849. doi: 10.3934/dcds.2018120
[12]

Bo You, Chengkui Zhong, Fang Li. Pullback attractors for three dimensional non-autonomous planetary geostrophic viscous equations of large-scale ocean circulation. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1213-1226. doi: 10.3934/dcdsb.2014.19.1213
[13]

Michael Ghil. The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 189-228. doi: 10.3934/dcds.2017008
[14]

Bo You, Chunxiang Zhao. Approximation of stationary statistical properties of the three dimensional autonomous planetary geostrophic equations of large-scale ocean circulation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (8) : 3183-3198. doi: 10.3934/dcdsb.2020057
[15]

Bo You. Well-posedness for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation. Discrete & Continuous Dynamical Systems, 2021, 41 (4) : 1579-1604. doi: 10.3934/dcds.2020332
[16]

S. Huff, G. Olumolode, N. Pennington, A. Peterson. Oscillation of an Euler-Cauchy dynamic equation. Conference Publications, 2003, 2003 (Special) : 423-431. doi: 10.3934/proc.2003.2003.423
[17]

Xinliang An, Avy Soffer. Fermi's golden rule and $ H^1 $ scattering for nonlinear Klein-Gordon equations with metastable states. Discrete & Continuous Dynamical Systems, 2020, 40 (1) : 331-373. doi: 10.3934/dcds.2020013
[18]

I-Liang Chern, Chun-Hsiung Hsia. Dynamic phase transition for binary systems in cylindrical geometry. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 173-188. doi: 10.3934/dcdsb.2011.16.173
[19]

Tian Ma, Shouhong Wang. Dynamic transition and pattern formation for chemotactic systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2809-2835. doi: 10.3934/dcdsb.2014.19.2809
[20]

Taylan Sengul, Shouhong Wang. Pattern formation and dynamic transition for magnetohydrodynamic convection. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2609-2639. doi: 10.3934/cpaa.2014.13.2609

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences