The first part of the work presents the results of numerical experiments with the magnetohydrodynamic model of “shallow water” to assess the degree of influence of the magnetic field on the development of instabilities conditioned by a combination of inhomogeneities in the mean flow and the mean magnetic field. Normal mode calculations have confirmed the earlier obtained result on the different influence of weak and strong magnetic fields on the instability of differential rotation. Calculations have shown that a weak magnetic field stabilizes the development of instabilities, whereas a strong magnetic field, on the contrary, enhances the instability. Azimuthal inhomogeneities of differential rotation in all cases contribute to the development of instabilities. In the second part of the work, we examine the spatial structure of normal modes and make an attempt to interpret the torsional oscillations observed in the atmospheres of Earth and the Sun. Calculations have shown that regular axisymmetric disturbances can be caused by the formation of a cyclonic vortex above the pole, which is characteristic of Earth's atmosphere and, possibly, of the Sun's atmosphere. The least damped normal mode of a stable polar cyclone has a structure of torsional oscillations. Flow anomalies and the development of an anticyclonic eddy in winter at midlatitudes destroy torsional oscillations and lead to a rapid amplification of normal modes, which are more complex in structure.