Abstract
An analytical model of mathematical physics, which is implemented for an unbounded column of compressible atmosphere, is discussed. For the column, there are two equilibrium conditions, which are written in the form of a system of aerodynamic equations. The first condition is the classical condition of hydrostatic, which is derived from the equations of motion. The second one is derived from the continuity equation and arises due to temporal variations of air density. Two boundary conditions are selected near the solid surface: one is the magnitude of temperature and second condition is the magnitude of its vertical gradient. This allows us to consider the column without any restrictive conditions at some upper boundary. The analytical solution for adiabatic temperature can contain a sharp minimum at some height, above which the temperature rises with altitude. Herewith the temperature profile depends on the altitude linearly near the surface. The physical interpretation of the solutions based on the data of experimental measurements in the Earth's atmosphere is discussed. The analytical solution can be used to describe adiabatic atmospheric column, which is important for some applications. The research results improve understanding of processes in atmosphere and can be used for scientific and educational purposes.
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