We consider the oscillations of the atmosphere around a stratified back ground density and entropy distribution under the gravitation on the flat Earth. The atmosphere is supposed to be an ideal gas and the motion is supposed to be governed by the compressible Euler equations. The density distribution of the back ground equilibrium is supposed to touch the vacuum at the finite height of the stratosphere. Considering the linearized approximation for small perturbations, we show that time periodic oscillations with a sequence of time periods which accumulate to infinity, say, slow and slow oscillations, so called `g-modes', can appear when the square of the Brunt-Vaisala frequency is positive everywhere for the considered back ground equilibrium.

中文翻译：

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关于平坦地球上分层大气的绝热振荡

我们考虑在平坦地球上的引力作用下，围绕分层背景密度和熵分布的大气振荡。大气应该是一种理想气体，运动应该由可压缩的欧拉方程控制。背景平衡的密度分布应该在平流层的有限高度接触真空。考虑到小扰动的线性近似，我们表明，当 Brunt-Vaisala 的平方时，可以出现具有累积到无穷大的时间周期序列的时间周期振荡，例如，缓慢和缓慢的振荡，所谓的“g 模式”。对于所考虑的背景平衡，频率处处为正。