A hurricane with an Annular Eye is normally a well developed, steady state hurricane. I don't classify Irene as well developed.
But the smooth round circular Eye is nearly annular.
Similar to looking into a piece of pipe, or the hole in a doughnut.

From Wikipedia:
An annular hurricane, also known as a truck tire or doughnut hurricane,[1] is a tropical cyclone in the Atlantic or Eastern Pacific Oceans that features a large, symmetric eye surrounded by a thick ring of intense convection. This type of storm is not prone to the fluctuations in intensity associated with eyewall replacement cycles, unlike typical intense tropical cyclones. Annular hurricanes also tend to persist, even when encountering environmental conditions which easily dissipate most other hurricanes. Forecasters have difficulty predicting the behavior of annular hurricanes; they are a recently recognized phenomenon, and as such, little is known about their tendencies. Because of this, they can be more dangerous than typical hurricanes.

http://en.wikipedia.org/wiki/Annular_hurricane