MHD theory of the stability of a viscous sphere

The problem of the stability of a sphere in the presence of a toroidal magnetic field is discussed with account taken of a small viscosity with respect to perturbations of the type n=m=2, which are decisive in the theory of the stability of spherical figures. Within the framework of the linear theory it has been established that a small kinematic viscosity in the presence of a toroidal magnetic field of order of smallness ^r, where r0.25, has no effect on the nature of the stability of the spherical figures under discussion but only changes the frequency of the vibrations. The vibration frequency is found as a function of the magnetic field induction and the kinematic viscosity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 32–35, April, 1982.