A viscous-convective instability in laminar Keplerian thin discs. II. Anelastic approximation

Using the anelastic approximation of linearised hydrodynamic equations, we investigate the development of axially symmetric small perturbations in thin Keplerian discs. The sixth-order dispersion equation is derived and numerically solved for different values of relevant physical parameters (viscosity, heat conductivity, disc semi-thickness and vertical structure). The analysis reveals the appearance of two overstable modes which split out from the classical Rayleigh inertial modes in a wide range of the parameters in both ionized and neutral gases. 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.