Аннотация:A new model of axially symmetric concentrated vortex generation was developed herein.In this work, the solution of a nonlinear equation for internal gravity waves in an unstable stratifiedatmosphere was obtained and analysed in the framework of ideal hydrodynamics. The relatedexpressions for the velocities in the inner and outer regions of the vortex were described by Besselfunctions and modified zeroth-order Bessel functions. The proposed new nonlinear analytical modelallows the study of the structure and dynamics of vortices in the radial region. The formation of jets(i.e., structures elongated in the vertical direction with finite components of the poloidal (radial and vertical) velocities that grow exponentially in time in an unstable stratified atmosphere) was alsoanalysed. The characteristic growth time was determined by the inverse growth rate of instability. Itis shown that a seed vertical vorticity component may be responsible for the formation of vorticeswith a finite azimuthal velocity