大气三圈环流的动力系统模型  

Dynamical system model for three cells of the atmosphere

作　　者：刘式达[1] 付遵涛[1] 刘式适[1] 

机构地区：[1]北京大学物理学院大气与海洋科学系,气候与海-气实验室,北京100871

出　　处：《地球物理学报》2014年第6期1740-1745,共6页Chinese Journal of Geophysics

基　　金：国家自然科学基金(40975027)资助

摘　　要：定常情况下,本文利用球坐标系(λ,(?),r)的动力、热力学方程导出三维速度场(v_λ,v_(?),v_r)的动力系统.这种包括摩擦力和热传导的不可压缩大气运动的动力系统,无论从定性上还是从定量上都能描述由赤道和极地间的加热不均匀造成的三圈环流.定性上表明,在北半球经向速度v_(?)和纬向速度v_λ同符号,地表刮北风(v_(?)<0)和刮东风(v_λ<0)相对应,刮南风(v_(?)>0)和刮西风(v_λ>0)相对应.在南半球,经向速度v_(?)和纬向速度v_λ符号相反,刮北风(v_(?)<0)和刮西风(v_λ>0)相对应,刮南风(v_(?)>0)和刮东风(v_λ<0)相对应.定量分析表明球面上的压力场p可以用球调和函数p_l^m(sin(?))cosmλ来表达.当取l=6,m=0时即可导出三圈环流.在经圈剖面((?),r)上,地表的(?)_1=±56°和(?)_2=±28°左右,以及赤道是速度场的奇点,它们都是鞍点,说明在副热带是下沉运动,在中纬度是上升运动,这正是三圈环流中的Ferrel环流的特征.这样经向速度v_(?)和纬向速度v_λ相联系,经向速度v_(?)又和垂直速度相联系,那么三圈环流的三维速度场就构成了一个整体.Under the steady condition,the dynamical and thermal control equations of atmospheric motions under the spherical coordinates（λ,φ,r） are used to derived the dynamical systems of 3-dimensional velocity field（v_λ,v_φ,v_r）.Due to the existence of damping force and thermal conduction,the dynamical systems for the incompressible motions of atmosphere can be used to describe both qualitatively and quantitatively the three cells of atmosphere resulting from nonuniform heating between equator and poles.Qualitatively,the meridional velocity v_φ and zonal velocity v_λ take the same signs over the north hemisphere,the wind blows northerly（v_φ 0） and easterly（v_λ0） over the surface of the Earth,or southerly（v_φ 0） and westerly（v_λ0））.However,the meridional velocity v_φ and zonal velocity v_λ take the opposite signs over the south hemisphere,the wind blows northerly（v_φ 0） and westerly（v_λ0） over the surface of the Earth,or southerly（v_φ0） and easterly（v_λ0）.Quantitative analysis shows that the pressure field p over the sphere surface can be represented by the spherical harmonic function p_l^m（sirup） cosmλ.When l= 6,m = 0,the three cells of atmospheric circulation can be reached.On the meridional section（φ,r）,near φ_1 = ＋ 56°,φ_2 = ＋28° and equator over the surface are singular points of velocity fields.They are all saddle points,which indicates that there are air descending in the subtropics and air rising in the mid-latitudes.This is the feature of Ferrel cell.The above analysis shows that the meridional velocity v_φ connects to zonal velocity v_λ,and the meridional velocity v_φ also connects to the vertical velocity,and then the 3-dimensional velocity field of three cells constitutes a whole atmospheric circulation.

关 键 词：定性分析 定量分析 动力系统 大气三圈环流 

分 类 号：P404[天文地球—大气科学及气象学]