球面定常行星波的几种传播路径

近年来,Hoskins用Longuet-Hisgins首先提出的大圆理论,和球面上二维Rossby波的能量频散来解释由资料分析得到的遥相关和模式得到的遥响应,取得了重要进展。但是大圆理论是在基流角速度为常数时得到的,而在球面上讨论真实的基流难以得到解析解。本文依据Fermat原理,利用变分法,直接求得球面上普遍的射线方程,从物理上直观地导得大圆理论,对球面上常见的几种基流型式,也求得其解析解。并且应用了“平均变分原理”直接导得波作用守恒方程。

A FEW PROPAGATING APPROACHES OF THE SPHERICAL STATIONARY PLANETARY WAVES

In recent years, using the great circle routes theorem found first by Longuet-Higgins and the energy dispersion of the spherical twodimensional Rossby waves, Hoskins explained both the teleconnections gained with the data analysis and the tele-response calculated in the numerical models, and made important. advance. But the great circle routes theorem is found only when the basic flow angular velocity is constant, however the analytic solutions are difficutly found for the real basic flow on the sphere. On the basis of Fermat's principle, using the variational method, the general ray equation on the sphere is directly found.When the angular velocity of the basic flow is constant, the great circle routes theorem, visibly in the physics, is gained. For a few usual basic flow patterns, the analytical solutions can be found also. In addition, using "the average variational principle", the conservation equation of the wave action is directly found.