The present work considers the two-dimensional barotropic evolution of thin annular rings of enhanced vorticity embedded in nearly irrotational flow. Such initial conditions imitate the observed flows in intensifying hurricanes. Using a pseudospectral numerical model, it is found that these highly unstable annuli rapidly break down into a number of mesovortices. The mesovortices undergo merger processes with their neighbors and, depending on initial conditions, they can relax to a monopole or an asymmetric quasi-steady state. In the latter case, the mesovortices form a lattice rotating approximately as a solid body. The flows associated with such vorticity configurations consist of straight line segments that form a variety of persistent polygonal shapes.Associated with each mesovortex is a local pressure perturbation, or mesolow. The magnitudes of the pressure perturbations can be large when the magnitude of the vorticity in the initial annulus is large. In cases where the mesovortices merge to form a monopole, dramatic central pressure falls are possible.