Formation of complex rotational structures in convective and isothermal magnetized zones

We study the development of a complex rotation law in the magnetized convective and isothermal zones of stars and planetary atmospheres through the decomposition of vector quantities in terms of orthogonal vector spherical harmonics. In the case of a solar-type extended convective zone, it is assumed that (a) the transformation of thermal into magnetic energy is favorable from the viewpoint of energy balance, (b) the state that is supported with minimum energy loss is realized, and (c) the condition of minimum entropy production consistent with the two previous requirements is satisfied. To find the rotation law of a zone, weak interaction between variations in the rotation and magnetic-field distributions is assumed. Two possible zones of generation of the solar magnetic field are considered. The first is located in the lower half of the solar convective zone and possesses a latitude dependence of the rotational velocity similar to that observed. The second zone is located just below the surface, and has a rotational velocity that decreases sharply with height and depends only weakly on latitude. We also study simple equilibrium structures, in particular, those describing the super-rotation of the medium in a convective or isothermal zone. Realization of such super-rotation in an isothermal zone is associated with the outflow of matter and fields toward upper layers.