三波作用下准地转模式的周期轨道存在性  

Existence of Periodic Orbits about Quasi-Geostrophic Model on Three Waves

作　　者：刘春 刘思波[3,4] 李秀梅 张春辉[2] 冷礼冬[2] 

机构地区：[1]高原与盆地暴雨旱涝灾害四川省重点实验室,成都610072 [2]四川省内江市气象局,内江641000 [3]成都信息工程大学,成都610225 [4]中国科学院大气物理研究所,北京100029 [5]四川省眉山市气象局,眉山620020

出　　处：《高原气象》2015年第6期1805-1811,共7页Plateau Meteorology

基　　金：国家重点基础研究发展973计划项目(2012CB417202);四川省气象局课题(川气课题2013-开发-09)

摘　　要：鉴于准地转模式和n≥3动力系统周期轨道存在性对湍流结构的重要性,对模式的4个鞍型平衡点所对应的同(异)宿轨道进行了分析。结果表明:在Poisson辛叶上,模式除了存在4条同(异)宿轨道外,对于每一个中心型平衡点,均存在一列周期轨道环绕对应的中心。通过对扰动系统中心型平衡点附近周期轨道的讨论,获得了原始三波作用下准地转模式周期解存在的条件。When dimension n≥3,the existence,nonexistence,uniqueness and stability of periodic orbits of dynamical systems,in the theory and application,are worthy of study. in the two- dimensional dynamical systems,the basic tools of study the existence of periodic orbits is Poincar- Bendixson and its corollary( ring zone principle). However,The counter example of D. Heedene display that Poincar- Bendixson has not been simply popularized in the high dimensional case. Thus,over the years,studying the existence of periodic orbits in the dynamical systems,mainly rely on the ring zone principle. To the quasi- geostrophic model in the action of the three waves,the simple pattern of exogenous,turbulent friction has been more mature,but there is less study about it is cyclical behavior. Furthermore,homoclinic orbit and heteroclinic orbit are associated with solitary wave and the vortex,and homoclinic orbit and heteroclinic orbit at rail cross- sectional intersect is the condition of chaos,also the key to study the certainty and randomness. The combination of certainty and randomness is the main methods that quasi- geostrophic model explaining the turbulent structure. So,homoclinic orbit and heteroclinic orbit are very important to the periodic and stability of quasi- geostrophic model. Through analyzing,we discover that the nonlinear has a form of three- dimensional- Hamilton,induced by the main structure- Jacobi of the quasi- geostrophic model in the action of three- wave,so the article study the topological nature of the model based on Poincar- Bendixson. Meanwhile,in viewof the importance of the quasi- geostrophic model for the structure of turbulence,homoclinic orbit and heteroclinic orbit that the balance point of the four saddle pattern corresponding to were analyzed. The analysis revealed that the presence of four different homoclinic( heteroclinic) orbit as well as the center for each type of balance exist in a column corresponding periodic orbits around the center on the Poisson symplectic leaf surface. Having a discuss

关 键 词：三波作用 准地转模式 广义Hamilton Poisson辛叶 同(异)宿轨道 周期轨道 

分 类 号：P43[天文地球—大气科学及气象学]