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To investigate the initial formation of large-scale vortices at tropical latitudes a regional non-hydrostatic mathematical model of the wind system of the lower atmosphere, developed earlier in the Polar Geophysical Institute, is utilized. Three-dimensional distributions of the atmospheric parameters in the height range from 0 to 15 km over a limited region of the Earth’s surface are produced by the utilized model. Simulations are performed for the case when the limited three-dimensional simulation domain is intersected by an intertropical convergence zone in the west-east direction. Simulation results indicated that the origin of two convexities in the north direction in the configuration of the intertropical convergence zone can lead to the formation of three distinct tropical cyclones during the period of about four days.

Tremendous damage and numerous fatalities may be produced by severe tropical cyclonic storms and hurricanes. Therefore, prediction of tropical cyclone origin is very important problem. The physical theory of tropical cyc- lone origin is still far from completion despite of considerable efforts. Nevertheless, some aspects of tropical cyclogenesis are commonly understood, in particular, in the late stages of formation as well as in a fully developed stage (see [

In the present study, to investigate the initial stage of the origin of large-scale vortices at tropical latitudes a mathematical model of the wind system of the lower atmosphere, developed earlier in the Polar Geophysical Institute (PGI), is utilized. This mathematical model is the regional version of the non-hydrostatic mathematical model of the global wind system in the Earth’s atmosphere, developed earlier in the PGI [

The regional non-hydrostatic mathematical model of the wind system of the lower atmosphere, utilized in the present study, was earlier applied in order to investigate numerically the mechanisms responsible for the formation of large-scale vortices in the Earth’s lower atmosphere. In particular, this model was applied to investigate the formation mechanisms of a large-scale vortex over an ocean surface [

The purpose of the present study is to continue these investigations and to study numerically, applying the regional mathematical model of the wind system of the lower atmosphere, the initial stage of the origin of large- scale vortexes in the vicinity of the intertropical convergence zone. Simulations are performed for the case when the limited three-dimensional simulation domain is intersected by an intertropical convergence zone in the west- east direction. It is supposed that, at the initial moment, the intertropical convergence zone contains two convexi- ties in the north direction. Time-dependent modeling is performed during the period of about four days.

The regional mathematical model of the wind system of the lower atmosphere, developed not long ago at the PGI, is utilized in the present study. The characteristic feature of the 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 air 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.

In the utilized model, the atmospheric gas is considered as a mixture of air and water vapor, in which two types of precipitating water (namely, water microdrops and ice microparticles) can exist. The model is based on the numerical solution of the system of transport equations containing the equations of continuity for air and for the total water content in all phase states, momentum equations for the zonal, meridional, and vertical compo- nents of the air velocity, and energy equation. In the momentum equations for all components of the air velocity, the effect of the turbulence on the mean flow is taken into account by using an empirical subgrid-scale parameterization similarly to the global circulation model of the Earth’s atmosphere developed earlier in the PGI [

Thus, the utilized 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, which play an important role in energetic balance. The finite-difference method and explicit scheme are applied for solving the system of governing equa- tions.

In the utilized model, the following variables are computed at each grid node: the temperature of the mixture of air and water vapor,

where

where

where

It can be noted that the model assumes that the water microdrops can exist only in the presence of saturated water vapor on condition that

It is assumed that the three-dimensional simulation domain of the model is a part of a spherical layer stretch- ing from land and ocean surface up to the altitude of 15 km over a limited region of the Earth’s surface. In the present study, the dimensions of this region in longitudinal and latitudinal directions are 75˚ and 25˚, respectively. The calculated parameters are determined on a uniform grid. The latitude and longitude steps are equal to 0.08˚, and height step is equal to 200 m. As pointed out previously, the finite-difference method is applied for solving the system of equations. Complete details of the utilized finite-difference method and numerical schemes have been presented in the paper of Mingalev et al. [

The present study is the continuation of the investigations of the initial stage of the origin of large-scale vortices in the vicinity of an intertropical convergence zone, fulfilled earlier [

In the earlier study of Mingalev et al. [

In the present study, simulations are performed for the case when the three-dimensional simulation domain is intersected by an intertropical convergence zone in the west-east direction. It was supposed that, at the initial moment, the intertropical convergence zone contains two convexities in the north direction, with the deviations achieving a value of a few hundreds of kilometers. The initial form of the intertropical convergence zone may be easy seen from

The results of simulation indicate that, in the course of time, the initial distribution of horizontal component of the air velocity was considerably transformed. In a moment of 20 hours after the beginning of calculations, a pair of tropical cyclonic vortices arose. Their centers are close to the southern edge of the initial intertropical convergence zone. In a moment of 50 hours after the beginning of calculations, these cyclonic vortices have moved in the western direction for about 10 degrees. Simultaneously, the third cyclonic vortex arose, with its center being close to the southern edge of the initial intertropical convergence zone. All arisen cyclonic vortices have moved in the western direction. In a moment of 90 hours after the beginning of calculations, the displacement of third cyclonic vortex is about 6 degrees. The horizontal wind velocity in the cyclones can achieve values of 15 - 20 m/s in the course of time. The maximum wind velocities within the vortices are reached approximately 20 h after their origins, and then they begin to decrease slowly. The radii of these three cyclones are about 800 km.

The simulation results indicate that a key factor in the modeled formation of the triplet of tropical cyclonic vortices is the origin of convexities in the configuration of the intertropical convergence zone. The origin of these convexities leads to beginning of instability of stream air flow. This instability leads to considerable transformation of the wind field. As a consequence, the triplet of tropical cyclonic vortices arises in the lower atmosphere in the course of time. In addition to that, the initial intertropical convergence zone is broken down.

In earlier studies by the authors of the present work, the idea has been advanced that the transformation of the shape of the intertropical convergence zone can influence the process of the formation of tropical cyclones [

The present work is the continuation of the investigation of the initial stage of the origin of large-scale vortices at tropical latitudes. For this investigation, a regional non-hydrostatic mathematical model of the wind system of the lower atmosphere, developed earlier in the Polar Geophysical Institute, is utilized. The model is based on the numerical solution of the system of transport equations containing the 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 energy equation. The model produces three-dimensional distributions of the atmospheric parameters in the height range from 0 to 15 km over a limited region of the Earth's surface. Simulations are per- formed for the case when this region is intersected by the intertropical convergence zone having the specific configuration. It was supposed that, at the initial moment, the intertropical convergence zone contains two con- vexities, having the longitudinal dimension of about 1400 km and deviations in the north direction, achieving a value of a few hundreds of kilometers.

The simulation results indicated that the twin tropical cyclones were formed during the period of about 20 hours. Their centers are close to the southern edge of the initial intertropical convergence zone. Besides, in a moment of approximately 50 hours after the beginning of calculations, third tropical cyclone arose whose center is close to the southern edge of the initial intertropical convergence zone, too. The arisen triplet of tropical cyc- lonic vortices has moved in the western direction. The horizontal wind velocity in the cyclones can achieve val- ues of 15 - 20 m/s in the course of time. The radii of these three cyclones are about 800 km.

The simulation results have shown that the cause for the formation of tropical large-scale vortices in the vicinity of the intertropical convergence zone is a rise of instability of stream air flow present in this zone. The cause for the rise of this instability is the origin of the convexities in the configuration of the intertropical convergence zone. This instability leads to considerable transformation of the air flow. As a result, the intertropical convergence zone may be broken and tropical large-scale vortices can be formed in the vicinity of the initial position of the intertropical convergence zone in the course of time.

It may be expected that the simulation results of the present study, as well of studies by Mingalev et al. [

It can be noticed that, according to observations, not each cyclonic vortex, arisen in the lower atmosphere, has the potential to grow up to the long-live large-scale atmospheric vortex. It is known that, sometimes, a vortex, initially arisen in the lower atmosphere, can be attenuated in the course of time and will not achieve a status of the long-live large-scale atmospheric vortex. This peculiarity may take place for the large-scale vortices arisen in the calculations of the present study, with further transformation of the originated vortices depending on en- vironmental conditions, in particular, on the degree of saturation of air by water vapor.

Simulations of the present study were limited by the time interval of approximately four days. Unfortunately, more prolonged time intervals are impossible for the utilized mathematical model because of limited sizes of its simulation domain and owing to tendency of the modeled vortices to move and to abandon the simulation do- main in the course of time.

This work was partly supported by Grant No. 13-01-00063 from the Russian Foundation for Basic Research.