厄尔尼诺-南方涛动海-气振子系统的同伦映射解（英文）  

The Homotopic Mapping Solution to the Sea-air Oscillator System for the EI Nio-southern Oscillation

作　　者：史娟荣[1] 林万涛[2] 莫嘉琪[3] SHI Juan-rong;LIN Wan-tao;MO Jia-qi(Anhui Technical College of Mechanical and Electrical Engineering, Wuhu 241002;State Key Laboratory of Numerical Modeling for Atmospheric and Geophysical Fluid Dynamics,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Department of Mathematics, Anhui Normal University, Wuhu 241003)

机构地区：[1]安徽机电职业技术学院,芜湖241002 [2]中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室,北京100029 [3]安徽师范大学数学系,芜湖241003

出　　处：《工程数学学报》2017年第4期437-448,共12页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(41275062);the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A418)

摘　　要：厄尔尼诺-南方涛动是一个涉及赤道太平洋海-气交互作用的年际现象.本文的目的是创建一个求解厄尔尼诺-南方涛动模型非线性系统的渐近方法.首先利用线性齐次常微分系统的特征值理论得到了对应初值问题的解,并以此解为原系统的零次近似解,然后利用同伦映射关系式依次构造原系统的各次迭代解,最后在这基础上借助同伦映射方法研究了厄尔尼诺南方涛动系统海-气振子对应问题的渐近解,并证明了得到的渐近解的一致有效性.从得到的结果看出,同伦映射方法能够用于分析厄尔尼诺-南方涛动系统在赤道东太平洋中的海表温度异常和海-气振子的温跃层深度异常.The EI Nino-southern oscillation is an interannual phenomenon involved in the tropicalPacific ocean-atmosphere interactions.The aim of this paper is to create anasymptotic method of solve nonlinear equation for the EI Ni?no-southern oscillationsystem.Firstly,the solution to corresponding initial value problem is got by usingthe characteristic value theory for the linear homogeneous ordinary differential system.And this solution is a zero-th order approximation of solution to the originalsystem.Then,the arbitrary order iterative solutions for the original system arestructured with the help of homotopic mapping relational expressions successively.Finally,based on a class of oscillator for the EI Ni?no-southern oscillation system,employing the homotopic mapping method,the asymptotic solution to correspondingproblem is studied.And there is proved this asymptotic solution is a uniformlyvalid.The results is that the homotopic mapping method can be used for analyzingthe sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline

关 键 词：非线性 厄尔尼诺-南方涛动 海-气振子 

分 类 号：O175.14[理学—数学]