Abstract

As is known from multiyear theoretical and experimental studies, acoustic−gravity waves (AGW) determine the dynamics and energy balance of the atmospheres of planets and the Sun to a considerable extent. Linear wave perturbations in the atmosphere can be described with a system of second-order equations for the vertical and horizontal components of the perturbed velocity. It follows from this system that small perturbations in the atmosphere may be considered as oscillations of coupled oscillators with two degrees of freedom. This suggests that it is worth studying more thoroughly the linear acoustic−gravitational wave modes in the atmosphere with well-developed methods of the theory of oscillations. To study small perturbations in the Earth’s atmosphere, the methods of the theory of coupled oscillatory systems were used. It has been shown that acoustic−gravity waves in an isothermal atmosphere can be considered as a superposition of oscillations that occur simultaneously at two natural frequencies—acoustic and gravitational. The equations for the natural frequencies of oscillations, as well as for the components of the perturbed velocity under specified initial conditions, were derived. From the analysis of temporal changes in the components of the perturbed velocity, new features in their behavior were found. All solutions are presented with the use of real quantities only. This representation is more convenient for comparison with observational data than the complex one commonly used in the theory of acoustic−gravity waves. The conditions under which the usual single-frequency oscillation mode can be realized in the atmosphere are analyzed. The results of the study can be used to explain some features in space-borne observations of wave perturbations in the Earth’s atmosphere that do not fit the framework of the known theoretical concepts.

中文翻译：

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地球大气中的重力波的两频传播模式

摘要

从多年的理论和实验研究中可以知道，声重力波（AGW）在很大程度上决定了行星和太阳大气的动力学和能量平衡。大气中的线性波扰动可用扰动速度的垂直和水平分量的二阶方程组来描述。从该系统得出，大气中的小扰动可被认为是具有两个自由度的耦合振荡器的振荡。这表明，使用发达的振荡理论方法，更深入地研究大气中的线性声重力波模式是值得的。为了研究地球大气中的微小扰动，使用了耦合振荡系统理论的方法。已经表明，等温大气中的声重力波可以看作是在两个自然频率（声学和重力）下同时发生的振荡的叠加。推导了振荡固有频率的方程，以及在特定初始条件下的扰动速度分量。通过分析扰动速度分量的时间变化，发现了它们行为的新特征。所有解决方案仅以实际数量为准。与声重力波理论中常用的复杂表示法相比，该表示法更便于与观测数据进行比较。分析了在大气中可以实现通常的单频振荡模式的条件。