What is it about?
This article is devoted to the analysis of three existing mathematical models describing the dynamics of internal gravity waves in a stratified atmosphere and the development of two new models. The existing mathematical models are referred to as: 1) the incompressible fluid approximation, 2) the compressible fluid approximation, and 3) the anelastic gas approximation. It is shown that in the incompressible fluid approximation and in the anelastic gas approximation the temperature field is not consistent with the heat conduction equation. In the compressible fluid approximation, the temperature field is consistent with the heat conduction equation, but in this approximation, the disturbed atmosphere is described by the adiabatic equation. These factors limit the applicability of these models. Therefore, two new mathematical models are proposed in the article. The first mathematical model is an alternative to the anelastic gas approximation, but unlike the latter, the temperature field is consistent with the heat conduction equation. The second mathematical model is an alternative to the compressible fluid approximation, but unlike the latter, the disturbed atmosphere is described by the Mendeleev–Clapeyron equation.
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Why is it important?
Existing mathematical models in three approximations are employed to describe a wide range of atmospheric phenomena. Both linearized and non-linearized systems of equations can be used. Therefore, the inconsistency of these models with the temperature field obtained from the heat conduction equation, as well as the use of a less general equation of state, are fundamental shortcomings that apply not only to linearized systems of equations but also to nonlinear equations. Therefore, the use of the two new models proposed in the article to describe dynamic phenomena in the atmosphere (including nonlinear ones) eliminates this drawback.
Perspectives
The mathematical models proposed in this work have the potential to be utilized in the future to describe fundamental, essentially nonlinear phenomena in the atmosphere, such as thermal convection, vortices, etc.
Arthur Zakinyan
North-Caucasus Federal University
Read the Original
This page is a summary of: Various approximations of mathematical models of internal gravity waves in the stratified atmosphere, Physics of Fluids, July 2025, American Institute of Physics,
DOI: 10.1063/5.0274405.
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