Mathematical model of influence of friction on the vortex motion

We study the influence of linear friction on the vortex motion in a non-viscous stratified compressible rotating media. Our method can be applied to describe the complex behavior of a tropical cyclone approaching land. In particular, we show that several features of the vortex in the atmosphere such as a significant track deflection, sudden decay and intensification, can be explained already by means of the simplest two dimensional barotropic model, which is a result of averaging over the height in the primitive equations of air motion in the atmosphere. Our theoretical considerations are in a good compliance with the experimental data. In contrast to other models, where first the additional physically reasonable simplifications are made, we deal with special solutions of the full system. Our method is able to explain the phenomenon of the cyclone attracting to the land and interaction of the cyclone with an island.