中国地理科学(英文版) ›› 2008, Vol. 18 ›› Issue (2): 193-196.doi: 10.1007/s11769-008-0193-3

• 论文 • 上一篇    

Singularly Perturbed Solution of Coupled Model in Atmosphere-ocean for Global Climate

MO Jiaqi1,2,3, LIN Wantao4, WANG Hui5   

  1. 1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China;
    2. Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240, China;
    3. Huzhou Teachers College, Huzhou 313000, China;
    4. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
    5. Chinese Academy of Meteorological Sciences, Beijing 100081, China
  • 收稿日期:2007-08-29 修回日期:2008-02-23 出版日期:2008-06-20 发布日期:2011-12-14
  • 通讯作者: MO Jiaqi. E-mail: mojiaqi@mail.ahnu.edu.cn E-mail:mojiaqi@mail.ahnu.edu.cn
  • 基金资助:

    Under the auspices of National Natural Science Foundation of China (No. 40676016, No. 10471039);National Key Project for Basics Research (No. 2003CB415101-03, No. 2004CB418304);Key Project of Chinese Academy of Sciences (No. KZCX3-SW-221);E-Insitutes of Shanghai Municipal Education Commission (No. E03004)

Singularly Perturbed Solution of Coupled Model in Atmosphere-ocean for Global Climate

MO Jiaqi1,2,3, LIN Wantao4, WANG Hui5   

  1. 1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China;
    2. Division of Computational Science, E-Institutes of Shanghai Universities at SJTU, Shanghai 200240, China;
    3. Huzhou Teachers College, Huzhou 313000, China;
    4. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
    5. Chinese Academy of Meteorological Sciences, Beijing 100081, China
  • Received:2007-08-29 Revised:2008-02-23 Online:2008-06-20 Published:2011-12-14

摘要:

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global climate is considered. By using the multiscales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Secondly, by using the multiscales, the first order approximate equation of the model is found. Finally, second order approximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multiscales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

关键词: atmosphere-ocean, El Ni?o-Southern Oscillation, singular perturbation, approximate solution

Abstract:

A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global climate is considered. By using the multiscales method, the asymptotic solution of a simplified weakly nonlinear model is discussed. Firstly, by introducing first scale, the zeroth order approximate solution of the model is obtained. Secondly, by using the multiscales, the first order approximate equation of the model is found. Finally, second order approximate equation is formed to eliminate the secular terms, and a uniformly valid asymptotic expansion of solution is decided. The multiscales solving method is an analytic method which can be used to analyze operation sequentially. And then we can also study the diversified qualitative and quantitative behaviors for corresponding physical quantities. This paper aims at providing a valid method for solving a box model of the nonlinear equation.

Key words: atmosphere-ocean, El Ni?o-Southern Oscillation, singular perturbation, approximate solution