移极旋转坐标系中的大气动力学方程

Dynamic Equations of the Atmosphere in Rotating Coordinates of Moved Poles

本文仅研究无粘、无地形和绝热运动假定下的大气动力学问题，用分析力学的方法求得了固定在地球上的移极旋转坐标系，如直角坐标系，球坐标系和柱坐标系中的第二类Ｌａｇｒａｎｇｅ方程。从而求得普遍的大气动力学方程。所谓的视示力—Ｃｏｒｉｏｌｉｓ力和离心力—与其它各种力统一处理。当地球自转轴不为坐标系的ｚ轴时，不存在大气运动的对称和反对称性。特别值得提出的是以往很多学者利用柱坐标系来数值模拟台风（飓风）的轴对称和非轴对称性时所使用的基本方程是含糊的，本文给出了准确的基本方程。

Dynamic aspects are investigated for inviscid and adiabated atmosphere without considering topography in this paper. Lagrange's equations of the second kind are obtained by the method of analytical dynamics in rotating coordinates, such as Cartesian,spherical and cylindrical coordinates fastened to the earth with moving poles. Then general dynamic equations of the atmosphere are obtained. The so-called apparent forces (egg. Coriolis and centrifugal forces) are treated the same as other forces. There is neither symmetry nor antisymmetry of motions of the atmosphere when the axis of rotation of the earth does not coincide with the z-axis of the rotating coordinate system. It is well worth mentioning that the basic equations used by many scientists are vague when numerical simulation experiments about the axisymmetry and asymmetry of typhoon(hurricane) use cyclindrical coordinate.The exact basic equations are given in this paper.