可压二维大气中三类定常基态的稳定性分析

THE STABILITY OF THREE CLASSES OF STEADY GROUND STATE IN THE TWO DIMENSIONAL ATMOSPHER

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。

In this paper, discussing the stability of three classes of steady groundstate in the two dimensional compressible adiabatic and non dispersive atmosphere , it is exactly demonstrated that the stability of these groundstates is decided by their engine matrix Λ: a. the groundstates are stable if Λ is positive definite in set G+Γ. b. the groundstates are unstable if Λ is negative definite in set G+Γ.