Instability of a Rotating Sphere in Axial Flow

Abstract

In many astrophysical and geophysical situations such as in  the theories of sunspot magnetic fields, heating of solar corona and the
instability of stellar astrospheres in magnetic fields, the instability of fluid of variable density is of considerable importance. Therefore in this paper, the hydromagnetic instability of a rotating sphere in axial flow  has been studied. Assuming the fluid to be permeated by a uniform vertical magnetic field, the solution has been obtained through the use of a variational principle. The dispersion relation has been obtained for a fluid in which the density is stratified exponentially along the direction of the magnetic field. The dispersion relation has been solved  graphically and it is found that the growth rate of the unstable perturbations decreases with the effect of viscosity showing thereby stabilizing influence of viscosity. The growth rate is, however, found to increase with the effects of rotation, compressibility and magnetic resistivity. Therefore, rotation, compressibility and magnetic resistivity  are destabilizing the system.