Exact solution of the Navier - Stokes equations for rotational tornado-like flow of a viscous gas

Exact self-similar solution of the Navier - Stokes equations for rotational flow of viscous gas in an infinite area is constructed. Within thin viscous core and external non-viscous regions analytical solutions are found making use of asymptotic method. It is observed that at some distance from vortex axis the formation of shock wave is possible. Using numerical analysis for systems of ordinary differential equations describing self-similar solutions, the picture of streamlines within viscous core are shown.