THE STABILITY OF THREE CLASSES OF STEADY BASIC STATES IN THE TWO-DIMENSIONAL COMPRESSIBLE ATMOSPHERE

In this paper,the stability of three classes of steady basic states in the two-dimensional compressible adiabatic and non-dissipation atmosphere is discussed,and the following property is exactly demonstrated that the stability of these basic states is decided by their engine matrix A in two ways:(a)the basic states are stable if A is positively definite in set,and(b)the basic states are unstable if A is negatively definite in set.

二维大气中定常广义地转流的稳定性分析

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。

可压二维大气中三类定常基态的稳定性分析

本文讨论了可压、绝热、无耗散的二维大气中三类定常基态的稳定性问题，并严格证明了这三类定常基态的稳定性性质是由基态的特征矩阵Λ的性质所决定的：ａ．若Λ在域Ｇ＋Γ内处处为正定矩阵，则基态是稳定的；ｂ．若Λ在域Ｇ＋Γ内非处处为半正定矩阵。