The eye is so calm because the now strong surface winds that converge towards the center never reach it. The coriolis force deflects the wind slightly away from the center, causing the wind to rotate around the center of the hurricane (the eye wall), leaving the exact center (the eye) calm.
But the eye of a tornado is the most violent part.
Think hurricane.
http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/hurr/stages/cane/eye.rxml
Hurricanes are BIG motherfuckers and it's smooothe sailing 5 by 5 in the pipe !