Physics of auroral phenomena : proceedings of the 38th annual seminar, Apatity, 2-6 march, 2015 / [ed. board: A. G. Yahnin, N. V. Semenova]. - Апатиты : Издательство Кольского научного центра РАН, 2015. - 189 с. : ил., табл.

equations of continuity for air and for the total water content in all phase states, momentum equations for the zonal, meridional, and vertical components of the air velocity, and internal energy equation. The characteristic feature of the new version of the self-consistent mathematical model is that it is non-hydrostatic, that is the model does not include the pressure coordinate equations of atmospheric dynamic meteorology, in particular, the hydrostatic equation. Instead, the vertical component of the atmospheric gas velocity is obtained by means of a numerical solution of the appropriate momentum equation, with whatever simplifications of this equation being absent. Thus, three components of the air velocity are obtained by means of a numerical solution of the generalized Navier-Stokes equation, with the effect of the turbulence on the mean flow being taken into account by utilizing an empirical subgrid-scale parameterization similarly to the global circulation model of the Earth’s atmosphere developed earlier in the PGI [Mingalev et al., 2014a]. The another characteristic feature of the new version of the self-consistent mathematical model is that the internal energy equation for the atmospheric gas is written by using a relaxation approach, in which a heating / cooling rate of the atmospheric gas in various chemical-radiational processes is supposed to be straightly proportional to the difference between the real temperature of the atmospheric gas and an equilibrium temperature of the atmospheric gas. The latter equilibrium temperature may be given with the help of the global temperature field, obtained from one of the existing empirical models, for example, from the NRLMSISE-00 empirical model [Picone et al., 2002]. Incidentally, the relaxation approach may be applied for self-consistent numerical modeling of the global wind system and heat regime in the lower and middle atmosphere not only of the Earth but also of other planetary bodies, in particular, of Venus and Titan [Mingalev et al., 2012; 2015]. Thus, the new version of the self-consistent mathematical model is based on numerical solving of non­ simplified gas dynamic equations and produces three-dimensional time-dependent distributions of the wind components, temperature, air density, water vapor density, concentration of micro drops of water, and concentration of ice particles. The model takes into account heating / cooling of the air due to absorption / emission of infrared radiation, as well as due to phase transitions of water vapor to micro drops of water and ice particles. The finite-difference method is applied for solving the system of governing equations. The calculated parameters are determined on a uniform grid. The latitude and longitude steps are equal to 0.47°, and height step is equal to 200 m. The system of gas dynamic equations is numerically solved in a simulation domain which is a layer surrounding the Earth globally. The lower boundary of this layer coincides with the Earth’s surface which is approximated by an oblate spheroid, with the relief being taken into account. A planetary surface can contain mountains and depressions. This surface is approximated by using one of the existing digital maps of the surface relief of a planet. The upper boundary of the simulation domain is the sphere lying at the altitude of 75 km over the equator sea level. The complete details of the utilized finite-difference method and numerical schemes have been presented in the paper of Mingalev et al. [2010]. Simulation results To demonstrate the ability of the self-consistent mathematical model of the global wind system and heat regime of the atmosphere, which takes into account the relief of a planet, to simulate global distributions of the gas dynamic parameters of the Earth’s lower and middle atmosphere we have made calculations for one concrete situation. The initial moment of the calculations has corresponded to 10.30 UT for 16 January that is for winter in the northern hemisphere. Simulations were performed for conditions corresponding to moderate solar activity (FWJ = 101) and low geomagnetic activity (Kp = 1). At the initial moment, the neutral gas density at the lower boundary and air temperature in all simulation domain were taken from the NRLMSISE-00 empirical model [Picone et al., 2002], moreover, all components of the neutral wind velocity were equal to zero. The variations of the atmospheric parameters with time were calculated during the period for about 17 days. Simulation results indicated that, after initial moment, three-dimensional global distributions of the gas dynamic parameters of the lower and middle atmosphere, calculated with the help of the model, changed essentially. The gas dynamic parameters, in particular the zonal, meridional, and vertical components of the air velocity, are changeable , functions not only of latitude and longitude but also of altitude. Maximal absolute values of the horizontal and vertical components of the air velocity are larger at higher altitudes. To the latest moment of calculations, at levels of the mesosphere, the horizontal wind velocity has achieved values of more than 70 m/s, whereas, the vertical component of the air velocity has achieved values of more than 10 m/s. Maximal absolute values of the upward vertical wind component are more than the maximal module of the downward vertical wind component. The results of simulation indicate that, in the course of time, the global distributions of the gas dynamic parameters of the lower and middle atmosphere of the Earth acquire a tendency to fluctuate, with the period of the fluctuations being close to one day. Thus, daily variations of the gas dynamic parameters, conditioned by the rotation of the Earth around its axis, may be reproduced by the self-consistent mathematical model of the global wind system and heat regime of the atmosphere, which takes into account the relief of a planet. The distribution of the vector of the horizontal component of the neutral wind velocity as a function of a longitude and latitude at the altitude of 0,6 km is shown in Fig. 1, with arrows being absent in the regions where the The improvement o fthe numerical mode! o fthe global wind system o fthe atmosphere by taking into account the reliefo fa planet 185