NUMERICAL ANALYSIS OF THE CONDITIONS FOR THE OCCURRENCE OF FREE CONVECTION OF DRYAIR IN THE ATMOSPHERE

Ntroduction. The current state of issues related to the study of the processes of dynamics of atmospheric phenomena, which are quite complex multiparameter in nature, requires a comprehensive approach. This direction of research is determined by the application, along with the analytical method, of numerical methods for obtaining solutions to the problems under consideration. The use of these methods allows you to get a solution to the problem in a general form, expressed through certain coefficients, the finding of which, of course, requires the imposition of additional conditions. However, the use of numerical methods allows to a greater extent to conduct a mathematical analysis of the solutions obtained, as well as the behavior of these dependencies under various speciied parameters, which in turn allows you to form a holistic view of the dynamics of processes when changing certain parameters. Materials and methods of the research. Methods of mathematical modeling of the processes of air particle movement. The basis of these methods are equations describing the dynamics of air, as well as the processes of transfer of radiant energy, heat and moisture in the atmosphere. When constructing the boundary problem of the dynamics of the environment under consideration, it is necessary to set boundary conditions that determine the scope of determining the problem to be solved, as well as the state of the system at the boundaries of this region. In the work, the solution of the problem under study is carried out by numerical methods using a set of tools of the computer program Maple 2021, which allows solving a system of partial differential equations of the second order. Also, using the numerical methods of the program, equations of trajectories and current lines of the air particle were obtained, as well as corresponding graphs were constructed. The results of the study and their discussion. The paper conducts a study, as well as a mathematical and numerical analysis of the mathematical model of dry air dynamics in the presence of small pressure perturbations in the atmosphere, which leads to a violation of the stationary state of the environment and the emergence of convection movements. The main task of the study was to find a general solution to the system of equations describing the dynamics of dry air without taking into account the viscosity of the medium, to obtain an equation of the trajectory of the air particle, as well as to conduct a qualitative analysis of the type of expressions obtained at different values of constant integration. The analysis of the obtained results allows to obtain numerical values of critical constants, included as parameters in the obtained equations of the trajectory of the air particle, and responsible for the occurrence of convective movements of the medium under consideration. Conclusions. In this paper, using the mathematical package Maple 2021, a general solution of the problem of determining the current function describing the motion of an air particle when a pressure disturbance occurs in the atmosphere, as well as the components of the speed of movement in the vertical plane, is obtained. A numerical analysis of the obtained solutions characterizing the migration processes in the environment is carried out. The expressions for the equation of trajectories and current lines of air particles are obtained in general form. At the given values of constant integration, the types of the obtained dependencies were graphically presented. Analysis of graphs shows that under certain conditions associated with some critical values of constant integration, closed curvilinear trajectories of motion are observed. Deviations from the speciied values of these constant data in the direction of greater or smaller values lead either to the non-closure of the trajectory, or to a change in the shape and size of the closed cell.

Dry air convection, pressure disturbance, density disturbance, temperature disturbance, Euler's equation, heat equation

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