The evolution of a vortex in glow discharge plasma is studied analytically. Specifically, the mechanism of local energy deposition into the flow by the plasma is considered and its effect on the structure of an inviscid vortex is analyzed. The vortex is modeled by a set of Euler's equations while the energy transferred by the plasma into the gas is represented by Rayleigh mechanism. In this mechanism, the amount of heat addition is a function of local gas density. The analysis indicates that the plasma can have a considerable effect on the structure of a vortex. The inviscid calculations show that in a uniform discharge, a 1 cm vortex dies out in a fraction of a second.