THE CONVECTIVE STABILITY OF A THIN VISCOUS DISC

We prove that the presence of viscosity does not affect stability to a xisymmetric convective modes of a thin differentially rotating disc wi th no thermal conduction but in which viscosity is taken fully into ac count. In such a case the Schwarzschild criterion is necessary and suf ficient 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 E lstner et al. (1989) and described by the authors as a correction to t he Schwarzschild criterion is a manifestation of these. However, when viscosity is taken fully into account, such instabilities cannot be di scussed within the framework of a local analysis, a fully global treat ment being required.