ИСТИНА

We study of the behavior of a vortex in a compressible rotating threedimensional media in which there is a separation of horizontal and vertical processes, such that the averaging over the height can be applied. The resulting model is the 2D model of compressible barotropic rotating nonviscous medium. In contrast to other model, where first the additional physically reasonable simplifications are made, we deal with special classes of solutions to the full system. This allows us not to lose the symmetries of the model and to catch the complicated features of the full model. The main model, which is expected to apply the results, is a full model of the atmosphere, an example of vortex in the media is a tropical cyclone. We examine the stability of the vortex with respect to a break of the axial symmetry and the influence of dry friction on the trajectory and characteristics of the vortex. In particular, we build a mathematical model able to explain the changes of the trajectory and intensity of the vortex during landfall.