Radiating outward from the eye wall one can see a banded structure within the clouds. These clouds are called either spiral rain bands (or spiral bands). The image below is of a hurricane (called cyclone in the Southern Hemisphere).
Image by: OSEI
There are sometimes gaps in between these bands where no rain is found. In fact, if one were to travel between the outer edge of the hurricane to its center, one would normally progress from light rain to dry back to slightly more intense rain again over and over with each period of rainfall being more intense and lasting longer until reaching the eye. Upon exiting the eye and moving towards the edge of the hurricane, one would see the same events as they did going in, but in opposite order.
A schematic of this banding feature can be seen in the diagram above. The thunderstorms are now organized into regions of rising and sinking air. Most of the air is rising, but there is a small amount found in between the thunderstorms that is sinking.