Rossby-wave instability in viscous discs

Rossby-wave instability (RWI), which depends on density bumps and extrema in the vortensities of differentially rotating discs, plays an important role in the evolution of protoplanetary discs. In this article, we investigate the effect of viscosity on non-axisymmetric RWI in self-graviting accretion discs. For this purpose, we add viscosity to the work of Lovelace & Hohlfeld. Consideration of viscosity complicates the problem, so we use a numerical method to investigate stable and unstable modes. We consider three ranges of viscosity: high viscosity in the range 0.1 ≤ α ≤ 0.4, moderate viscosity in the range 0.01 ≤ α < 0.1 and low viscosity in the range α < 0.01. The results show that the occurrence of RWI is related to the value of viscosity, so that the effect of high viscosity is important, while low viscosity is negligible. These results may be applied to the study of the role of RWI in planet formation and angular momentum transport for different kinds of protoplanetary discs with different viscosities.