ИСТИНА

A 3D analytical model of axially-symmetric magnetic vortices with both a twisted fluid flow and a magnetic field is proposed. The exact solution for the 3D structure of the fluid velocity and the magnetic field is obtained within the framework of the ideal MHD equations for an incompressible fluid in a gravitational field. A quasi-stationary localised vortex arises when the radial flow that tends to concentrate vorticity in a narrow column around the axis of symmetry is balanced by the vertical vortex advection in the axial direction. The proposed analytic model may be used to parameterise observed solar tornadoes. In this new model, vortices are exponentially localized, not only in the radial direction, but also in height. Hence, unlike previous models, vortex velocity, vorticity and pressure are not only characterized by vortex radius r0 length scale, but also by a characteristic vortex height L. In this model the vortex structure in the radial direction has two distinct regions defined by the internal and external parts, i.e., r<r0 and r>r0, respectively. In the inner part of the vortex the flow and the magnetic field is directed upward, and in the outer part it is downward. The vortex structure in the z (vertical) direction can be conditionally divided into the bottom, central and top regions when z << L, z is comparable with L, and z >> L, respectively. In the bottom region the vertical and azimuthal velocity and magnetic field components are small. However, as altitude increases in the central region the vertical and azimuthal velocities increase. At altitude z = L the vertical and toroidal components, as well as vertical vorticity, attain maximum values. On the other hand, at this altitude for the radial velocity and the magnetic field components there is a turning point where they switch sign.