On the Stability of A Self-Gravitating Fluid Layer

Abstract

This paper deals with the stability of a self-gravitating incompressible fluid layer of finite thickness. It is shown that a uniform magnetic field extending throughout the whole space and an external conducting fluid have a strong stabilizing influence but they cannot remove entirely the instability with respect to disturbances of very long wave-lengths. On the other hand, in the absence of a magnetic field, an outer medium and a differential rotation are able to remove the gravitational instability when the angular velocity of rotation is larger than a certain critical value. However, when a magnetic field is impressed on the disk, a uniform rotation cannot remove entirely the instability of the system; moreover, in this case, the coupling between the Coriolis force and the Lorentz force allows purely hydromagnetic oscillations. It is also shown that the influence of the magnetic field is reduced when allowance is made for finite electrical conductivity. Lastly, viscosity decreases the growth rate of the gravitational instability and shifts the mode of maximum instability towards long wave-lengths.