Mathematical Methods of Analytical Description of Wave Disturbances in the Stratified Atmosphere

Abstract Wave disturbances are an important component of the dynamics of the Earth’s atmosphere. They propagate throughout the entire atmosphere: from the lower surface layers, where they can be generated by ground and tropospheric sources, such as earthquakes, volcanoes, tsunamis, anthropogenic sources, etc., and up to the rarefied upper layers (~500 km), where their sources are solar wind disturbances, magnetic storms, and charged particle showers. The paper considers two main methods for analytically solving the system of differential equations describing linear wave processes in a model of a stratified non-isothermal atmosphere. It is noted that the equations for linear disturbances describe the following types of waves: acoustic and internal gravity waves freely propagating at an angle to the horizon, as well as horizontal (evanescent) waves. It is shown that acoustic and gravitational waves are described within the framework of the standard method, which consists in reducing the system of linear equations to a single second-order differential equation for one of the components of the perturbed velocity. The solution of this equation allows us to determine other perturbed quantities. Analysis of this method showed that it allows us to satisfactorily describe waves in the isothermal part of the Earth’s atmosphere (thermosphere). The limitation of the specified method for considering evanescent waves is due to the fact that in this case we do not obtain a solution for all values of the horizontal wave vector. Another method, developed by us in previous works, is more acceptable for describing evanescent waves for arbitrary values of the horizontal component of the wave vector. The essence of this method is to use additional relations between the velocity components. This allows us to obtain easily integrated differential equations and find their solutions for each of the components, that is, to actually fully consider the problem of evanescent wave propagation. However, a limitation of this method is that it does not allow finding solutions in a non-isothermal atmosphere, except for the fundamental f-mode.