THE CONVECTIVE STABILITY OF A THIN VISCOUS DISC

We prove that the presence of viscosity does not affect stability to axisymmetric convective modes of a thin differentially rotating disc with no thermal conduction but in which viscosity is taken fully into account. In such a case the Schwarzschild criterion is necessary and sufficient for convective stability to local perturbations. In the proof we use a general formulation of local stability analysis, which allows a rigorous demonstration. Restricted particular forms of the viscous stress tensor introduced in the modelling of thin accretion discs may lead to viscous overstabilities. The additional instability found by Elstner et al. (1989) and described by the authors as a correction to the Schwarzschild criterion is a manifestation of these. However, when viscosity is taken fully into account, such instabilities cannot be discussed within the framework of a local analysis, a fully global treatment being required.