Why is the eye of a cyclone calm?

The center of the cyclone typically has a column of air that is slowly sinking, which is why the eyes of hurricanes are typically calm and even clear out in some cases. The converging air from outside rises upward around the periphery of the center, then diverges out the top of the system. The strongest pressure gradients exist outside the center, while in the center there is little if any pressure gradient, thus conditions tend to be calm.