here is something:

"Some of the most intense tropical cyclones exhibit concentric eye walls, two or more eye wall structures centered at the circulation center of the storm. Just as the inner eye wall forms, convection surrounding the eye wall can become organized into distinct rings. Eventually, the inner eye begins to feel the effects of the subsidence resulting from the outer eye wall, and the inner eye wall weakens, to be replaced by the outer eye wall. The pressure rises due to the destruction of the inner eye wall are usually more rapid than the pressure falls due to the intensification of the outer eye wall, and the cyclone itself weakens for a short period of time."
(Willoughby et al. 1982,Willoughby 1990a )