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地-气耦合气候动力系统的解析研究

ISSN号：1000-0690
期刊名称：《地理科学》
时间：0
分类：O175.29[理学—数学;理学—基础数学]
作者机构：[1]安徽师范大学数学系,安徽芜湖241000, [2]上海高校计算科学E-研究院、上海交通大学研究所,上海200240, [3]中国科学院大气物理研究所LASG,北京100029, [4]中国气象科学研究院,北京100081
相关基金：国家自然科学基金资助项目（90111011和40676016）、国家重点基础研究发展计划项目（2003CB415101-03和2004CB418304）、中国科学院创新方向性项目（KZCX3-SW-221）、上海市教育委员会E-研究院建设计划项目（N.E03004）资助.

关键词：非线性, 耦合系统, 扰动, nonlinear, coupling system, perturbation

中文摘要：

ENSO事件是影响全球气候表象大尺度的海洋一大气耦合系统，其规律和预防的研究，为当前国际学术界关注的对象。非线性摄动理论和方法在国际学术界研究中是十分热门的。许多学者做了一类常微分方程非线性奇摄动边值问题，反应扩散问题，椭圆型边值问题，双曲型初始边值问题，非线性方程奇摄动问题的冲击层解等。文章讨论一类大气物理中海一气现象的ENSO模型，在一定条件下，利用摄动理论和方法较简捷得到相应非线性问题解组的任意次近似的渐近展开式。

英文摘要：

The ENSO（El Nino/La Nino Southern Oscillation） is an exceptional event in the tropical atmosphere and ocean. It describes phenomenon of circular climate. ESNO event is a larger scale ocean-atmosphere coupled system, which affects global climate. It is a complicated nonlinear system. Its appearance affects badly climate for the global each area and the environment and so on. The global economic development and human living are gotten grievous influence and it brings many calamities. Thus to study its rule and prevention there is recently very attractive object of study in the international academic circles. Many scholars made more studies for its local and whole behaviors using different methods, such as self-anamnestic principle, by the method of Fokker-Plank equation, and the higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adapive cortrol, multi-cogradient method, perturbed situation and so on. Nonlinear perturbed theory is a very attractive object of study in the international academic circles. Many scholars considered a class of singularly perdiffusion equations, the boundary value problems of elliptic equation, the initial boundary value problems of hyperbolic eqaution, the shock layer solution of nonlinear equation for singularly perturbed problem and so on. In this paper, the sea-air phenomena ENSO in a class of atmospheric physics is discussed. Under suitable conditions, using a perturbed theory and method, we obtain simple and rapid arbitrary order to approximate asymptotic expansion of solution for the corresponding nonlinear problem.

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