Relationship between vorticity near the surface and a long-lived vortex raised above it

The ability to predict the behavior of vortices is valuable for solving various scientific problems. One such problem is the evolution of tornado-like vortices near the surface and their connection with the original vortex located at a certain height above the surface. This article considers a two-dimensional axisymmetric hydrodynamic model in which the initial vorticity is maintained by an external force. Using the model, the influence of external force and temperature field on the evolution of vorticity near the surface is studied. It is shown that at relatively short times, the behavior of the resulting tornado-like vortices near the surface is universal and weakly depends on the external force and temperature field. However, over time, this influence becomes significant. It is shown that, depending on the presence of an anomaly in the temperature distribution, the vortex formed at the surface can exist for a long time.