  In the present work, we motivate and explore the dynamics of a dissipative
variant of the nonlinear Schr{\"o}dinger equation under the impact of external
rotation. As in the well established Hamiltonian case, the rotation gives rise
to the formation of vortices. We show, however, that the most unstable mode
leading to this instability scales with an appropriate power of the chemical
potential $\mu$ of the system, increasing proportionally to $\mu^{2/3}$. The
precise form of the relevant formula, obtained through our asymptotic analysis,
provides the most unstable mode as a function of the atomic density and the
trap strength. We show how these unstable modes typically nucleate a large
number of vortices in the periphery of the atomic cloud. However, through a
pattern selection mechanism, prompted by symmetry-breaking, only few isolated
vortices are pulled in sequentially from the periphery towards the bulk of the
cloud resulting in highly symmetric stable vortex configurations with far fewer
vortices than the original unstable mode. These results may be of relevance to
the experimentally tractable realm of finite temperature atomic condensates.
