三维层结大气随高度变化基流的不稳定性及半椭圆定理

THE INSTABILITY AND SEMI ELLIPSE THEOREM OF THE BASIC FLOW CHANGED WITH HEIGHT IN THE NONHYDROSTATIC ATMOSPHERE

本文应用Ｈｏｗａｒｄ（１９６１）所用的精巧积分方法研究了三维非静力平衡层结大气随高度变化基流上重力内波的不稳定性质。给出了不稳定产生的必要条件和相速度在相速复平面上的分布规律；发展了Ｍｉｌｅｓ定理和Ｈｏｗａｒｄ半圆定理；得到了有限深度气层的半椭圆定理。并指出在随高度变化的基流中，重力内波的不稳定范围与基流的垂向结构及波传播方向有关；半椭圆的位置和长轴分别重合于Ｈｏｗａｒｄ半圆的位置和直径，而短轴则依赖于与Ｒｉｃｈａｒｄｓｏｎ数相关的参数Ｊ０。

By use of the ingenious integral manipulation introduced by Howard(1961), the instability of the basic flow changed with height in three dimensional nonhydrostatic atmosphere has been investigated in the present paper. The essential condition of instability generation and the distribution law of the phase speed on the complex phase speed coodinate plane are explicitely given. Improved Miles theorem and Howard's semicircle theorem, as well as semi ellipse theorem have been established. The semi ellipse theorem means that the complex wave velocity for any unstable mode is restricted in a semi ellipse whose major axis and centre coincide with the diameter and that of Howard's semicircle respectively, and whose minor axis depends not only on the parameters J 0,R 0 associated with the Richardson number and wave number |k| but also on the atmospheric depth parameter k 0 .