ИСТИНА

We introduce a three-dimensional model of a stratified compressible medium in a rotating co-ordinate frame, which can be considered as a model of the core of an atmospheric vortex. A complete system consists of the equations of mass and momentum balance. The lower layer is subjected to friction. In addition, we allow the inflow of mass from the underlying surface. We suppose that the velocity field inside each layer has a uniform deformation. The vertical component of the velocity vanishes on the Earth surface and on the upper lid of the atmos-phere. For simplicity, assume that the motion is isentropic. It is known that the presence of friction prevents the existence of a stable equilibrium. It is proved that in the presence of mass influx this model has an asymptotically stable state.