Correctness of the problem of propagation of nonlinear acoustic-gravity waves in the atmosphere from pressure variations on the lower boundary

Yu. Kudryaeva ; S. Kshevetskii ; N. Gavrilov ; E. Golikova

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 4, pp. 393-412

Résumé

Currently, there are international microbarograph networks, with high resolution recording the wave pressure variations on the Earth's surface. This increases the interest in the problems of wave propagation in the atmosphere from variations in the atmospheric pressure. A complete system of nonlinear hydrodynamic equations for an atmospheric gas with lower boundary conditions in the form of wavelike variations on the Earth's surface is considered. Since the wave amplitudes near the Earth's surface are small, linearized equations are used in the analysis of the problem correctness. With the help of the wave energy functional method, it is shown that in the non-dissipative case, the solution of the boundary value problem is uniquely determined by the variable pressure field on the Earth's surface. The corresponding dissipative problem is correct if, in addition to the pressure field, suitable conditions on the velocity and temperature on the Earth's surface are given. In the case of an isothermal atmosphere, the problem admits analytical solutions that are harmonic in the variables $x$ and $t$. A good agreement between numerical solutions and analytical ones is shown. The study has shown that in the boundary value problem, the temperature and density can rapidly vary near the lower boundary. An example of the solution of a three-dimensional problem with variable pressure on the Earth's surface, taken from experimental observations, is given. The developed algorithms and computer programs can be used to simulate the atmospheric waves from pressure variations on the Earth's surface.