We study the relaxation of a 2D superfluid from a nonequilibrium initial state consisting of vortices with positive and negative circulation in experimentally realizable square and rectangular traps. We focus on how like-signed quantized vortices can form clusters and show that such clustering can be understood in terms of negative temperature states of a vortex gas. Using a mean field approximation for the vortex gas, we identify an order parameter that is related to the formation of long-range correlations between like-signed vortices. It turns out that the order parameter corresponds to the streamfunction of a 2D flow field that is governed by a Boltzmann-Poisson equation. It is, therefore, associated with the emergence of a mean rotational hydrodynamic flow with a nonzero coarse-grained vorticity field. Solutions of the Boltzmann-Poisson equation in a square domain reveal that maximum entropy states of the vortex gas correspond to a large scale monopole flow field. A striking feature of this mean flow, is the spontaneous acquisition of angular momentum by a superfluid flow with a neutral vortex charge. These mean-field predictions are verified through direct simulations of a point vortex gas and 2D simulations of the Gross-Pitaevskii equation. Due to the long-range nature of the Coulomb-like interactions in point vortex flows, the negative temperature states strongly depend on the shape of the geometry. By modifying the domain to a rectangular region, we identify a geometry induced phase transition of the most probable mean flow field.