Abstract
Vortex formation and the role of flow velocity shear are considered in a magnetized plasma with finite viscosity. The essential difference between a viscous-vortex and an inviscid-vortex is the existence of a radial flow, which transfers the vorticity into the core to be balanced with the diffusion due to viscosity. It is concluded that the formation of a viscous vortex (a stationary localized structure of vorticity) is generally possible in plasmas having finite viscosity.