In hurricane eyewalls the vertical stretching effect tends to produce an annular ring of high vorticity. If narrow enough, such vorticity rings can be very unstable. The end states of such instability can be of three types: (1) a vorticity monopole (i.e., high vorticity in the center); (2) a vortex crystal pattern (i.e., several mesovortices locked in rigid rotation); (3) a chaotic pattern of mesovortices. Which end state is observed depends on initial conditions such as ring diameter and ring width. Using a barotropic model we have performed a systematic exploration of this "initial condition phase space" in order to better understand what types of flow patterns might be expected in real hurricanes.