Abstract—

The theory of acoustic gravity waves (AGW) considers free disturbances of the atmosphere within the framework of a single-frequency approach. In this case, the theory implies the existence of two separate types of waves with different natural frequencies: acoustic and gravitational. In the single-frequency approach, wave fluctuations of density, temperature, and velocity are related to each other through the spectral characteristics of the wave, and these relationships are unchanged. However, satellite observations of AGW parameters cannot always be explained within the framework of a single-frequency approach. This paper presents a two-frequency approach to studying AGWs using the model of two coupled oscillators. It is shown that the perturbed movements of the elementary volume of the medium occur simultaneously at two natural frequencies. In this case, the connections between the wave fluctuations of the parameters are determined by the initial conditions, which can be arbitrary. Solutions in real functions for an isothermal atmosphere are obtained. The conditions under which single-frequency AGWs are obtained from the general two-frequency solution are investigated. The AGW waveforms measured from the satellite for velocities and displacements in single-frequency and dual-frequency modes are numerically simulated. The results of simulating two-frequency AGWs agree with the data of satellite measurements. Two-frequency AGWs are not always implemented at two different frequencies. It is shown that, when the frequencies approach each other, the beat effect occurs and two closely related modes become indistinguishable. At the same wavelength, they have one center frequency and one phase velocity. The main feature of the two-frequency approach to the study of AGW is the expansion of the relationships between the wave parameters of the medium. This makes it possible to achieve satisfactory agreement of the model waveforms with the data of satellite measurements. Thus, the use of a two-frequency AGW treatment opens up new possibilities in the interpretation of experimental data.

中文翻译：

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两频声引力波和卫星测量模拟

摘要-

声重力波（AGW）的理论在单频方法的框架内考虑了大气的自由扰动。在这种情况下，该理论意味着存在两种不同类型的，具有不同固有频率的波：声波和引力波。在单频方法中，密度，温度和速度的波动是通过波的频谱特性相互关联的，而这些关系是不变的。但是，不能总是在单频方法的框架内解释卫星对AGW参数的观测。本文提出了一种使用两个耦合振荡器模型研究AGW的双频方法。结果表明，介质基本体积的扰动在两个固有频率下同时发生。在这种情况下，参数的波动之间的联系由初始条件确定，可以是任意的。获得了等温气氛的实函数解。研究了从一般的两频解中获得单频AGW的条件。对从卫星测得的单频和双频模式下的速度和位移的AGW波形进行了数值模拟。模拟两频AGW的结果与卫星测量数据一致。两频AGW并不总是以两个不同的频率实现。结果表明，当频率彼此接近时，会发生拍频效应，并且两个紧密相关的模式变得难以区分。在相同的波长下 它们有一个中心频率和一个相速度。研究AGW的双频方法的主要特征是扩展了介质波参数之间的关系。这样可以使模型波形与卫星测量数据达到令人满意的一致性。因此，使用双频AGW处理为解释实验数据开辟了新的可能性。