The Rossby wave instability ( RWI ) , which depends on the density bumps and extremum in the vortensities in the differentially rotating discs , plays an important role in the evolution of the protoplanetary discs .
In this article , we investigate the effect of viscosity on the non-axisymmetric RWI in the self-graviting accretion discs .
For this purpose , we add the viscosity to the work of Lovelace and Hohlfeld ( 2013 ) .
Consideration of viscosity complicates the problem so that we use the numerical method to investigate the stable and unstable modes .
We consider three ranges of viscosities : high viscosity in the ranges 0.1 \leq \alpha \leq 0.4 , moderate viscosity in the ranges 0.01 \leq \alpha < 0.1 , and low viscosity in the ranges \alpha < 0.01 .
The results show that the occurrence of the RWI is related to the value of viscosity so that the effect of high viscosity is important , while the low viscosity is negligible .
These results may be applied for the study of the RWI role in planet formation and angular momentum transport for different kinds of the protoplanetary discs with different viscosities .