Local stability analysis of interface region of astrophysical viscous shear flows with a gradual velocity gradient

In this paper, we extend the stability analysis of cold sharp shear flows to warm astrophysical cases with, inevitable, gradual velocity gradient in the interface region in the presence of viscosity effect. Using linear perturbation theory as well as the local approximation method, the instability growth rate of the excited electromagnetic modes has been investigated for the relativistic and non-relativistic cases of solar wind interacting with interstellar plasma medium. Results show that astrophysical shear systems with a small velocity gradient in the transition region are more stable rather than larger ones. Moreover, dependent on the viscosity coefficient value, the viscosity effects could have a positive role on the instability growth rate of the system in some range of initial bulk velocity, while it plays a destructive role in other velocity ranges.