Two-Frequency Acoustic-Gravitational Waves and Simulation of Satellite Measurements

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.