A regional nonhydrostatic mathematical model of the wind system of the lower atmosphere, developed recently in the Polar Geophysical Institute, is utilized to investigate the initial stage of the origin of large-scale vortices at tropical latitudes. 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. Time-dependent modeling is performed for the cases when, at the initial moment, the simulation domain is intersected by the intertropical convergence zone (ITCZ). Calculations are made for various cases in which the initial forms of the intertropical convergence zone are different and contained convexities with distinct shapes, which are consistent with the results of satellite microwave monitoring of the Earth’s atmosphere. The results of modeling indicate that the origin of convexities in the form of the intertropical convergence zone, having distinct configurations, can lead to the formation of different large-scale vortices, in particular, a cyclonic vortex, a pair of cyclonic-anticyclonic vortices, and a pair of cyclonic vortices, during a period not longer than three days. The radii of these large-scale vortices are about 400–600 km. The horizontal wind velocity in these vortices can achieve values of 15–20 m/s in the course of time.

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A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.