  Using the anelastic approximation of linearized hydrodynamic equations, we
investigate the development of axially symmetric small perturbations in thin
Keplerian discs. Dispersion relation is found as a solution of general
Sturm-Liouville eigenvalue problem for different values of relevant physical
parameters (viscosity, heat conductivity, disc semithickness). The analysis
reveals the appearance of overstable mode for Prandtl parameter higher than
some critical value. These modes have a viscous-convective nature and can serve
as a seed for turbulence in astrophysical discs even in the absence of magnetic
fields.
