To the two-dimensional model of heat convection of dry air in the atmosphere

Introduction: Free convection is a very complex and far from studied process. It is very complex in the atmosphere, hydrosphere, mantle and core of the Earth. This is due to their huge size, which leads to an inhomogeneous distribution of temperature, density and pressure fields. In addition, the rotation of the Earth is superimposed on it, which makes it even more difficult to determine the temperature, pressure and velocity fields. It is essentially the root cause of almost all movements in the atmosphere. The energy of most movements in the ocean is 80-90% caused by the convective movements of the atmosphere and 10-20% by free convection that occurs in the ocean itself. Materials and methods: To determine the conditions for the occurrence of dry air convection within the two-dimensional model of convection, consider the equation of motion of an ideal fluid in the Euler-shaped plane in an inertial frame of reference, without taking into account the Earth's rotation [2, 4]: ди ди ди if dp) - + u - + w- = - - dt dx dz p\\dx)' dw dw dw if dp) - + u - + w- = - - \\-g dt dx dz p\\dz) . Results of the study: Cells are in the nature of shafts. This type of convection is most common in the atmosphere. Discussion and conclusion: Thus, we have found an analytical solution of the two-dimensional model of Rayleigh thermal convection of dry air in the atmosphere. Analytical solution is obtained for the stationary case. This means that for this type of motion there is a steady state like an attractor.

Rayleigh convection, analytical solution, two-dimensional model, vertical temperature gradient, equation of motion, continuity equation, heat equation, low function

1. Алексеев В. В. , Гусев А. М. Свободная конвекция в геофизических процессах // Успехи физических наук. 1983. Т. 141. Вып. 2. С. 311-342.

2. Гетлинг А. В. Конвекция Рэлея-Бенара. Структура и динамика. М. : Эдиаториал УРСС, 1999. 247 с.

3. Журавлев В. М. Нелинейные волны в многокомпонентных системах с дисперсией и диффузией. Точно решаемые модели. Ульяновск: УлГУ 2001. 200 с.

4. Ландау Л. Д. , Лифшиц Е. М. Теоретическая физика: Гидродинамика. М. : Наука, 1986. Т. 6. 736 с.

5. Матвеев Л. Т. Физика атмосферы. СПб. : Гидрометеоиздат, 2000. 779 с.

6. Emanuel, K. A. Atmospheric Convection; Oxford University Press: New York, 1994.

7. Zakinyan, R. G.; Zakinyan, A. R.; Lukinov, A. A. Two-dimensional analytical model of dry air thermal convection. Meteorol. Atmos. Phys. 2015, 127, 451-455.