  In this paper, we systematically examine the stability and dynamics of
vortices under the effect of a phenomenological dissipation used as a
simplified model for the inclusion of the effect of finite temperatures in
atomic Bose-Einstein condensates. An advantage of this simplified model is that
it enables an analytical prediction that can be compared directly (and
favorably) to numerical results. We then extend considerations to a case of
considerable recent experimental interest, namely that of a vortex dipole and
observe good agreement between theory and numerical computations in both the
stability properties (eigenvalues of the vortex dipole stationary states) and
the dynamical evolution of such configurations.
