二维大气中定常广义地转流的稳定性分析

THE STABILITY OF THE TOW DIMENSIONAL GENERALIZED GEOSTROPHIC CURRENT

本文归纳总结了在绝热、无耗散对称二维大气中定常广义地转流稳定性分析中的扰动方程组的基本特征，并将其概括为具有这类问题共同基本特征的统一形式的扰动方程组的定解问题。在此基础上，统一地证明了：１）由统一的扰动方程组所确定的定解问题的解是存在唯一的；２）基态的性质是由Λｍｉｎ（Ｇ）的性质决定的：ａ．当Λｍｉｎ（Ｇ）＞０时，基态是稳定的；ｂ．当Λｍｉｎ（Ｇ）＜０时，基态是不稳定的。３）基态的全局稳定性质可以通过局部稳定性分析来确定；４）合理的。

In discussing the basic characteristics of the perturbation equations set which describes the generalized geostrophic current stability of the two dimensional adiabatic and non dispersive symmetry atmosphere, it is obtained that the system with these characteristics can be described by the unified form equations set. According to this , the following results are demonstrated : (1) the solutions of the unified form equations set exist ; (2) the characteristics of the groundstate are decided by : a.groundstate is stable , when Λ min (G) >0; b.groundstate is unstable , when Λ min (G) <0; (3) the global stability of groundstate can be given in terms of the local one; (4) the result are effective which are obtained from reasonable and sufficient simplified analysis of local stability.