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EYE
Note: This section is very very complicated)

The "eye" is a roughly circular area of light winds and fair weather found at the center of a tropical cyclone. Although the winds are calm at the axis of rotation, strong winds may extend well into the eye. There is little or no precipitation and sometimes blue sky or stars can be seen! The eye is the region of lowest surface pressure and warmest temperatures aloft - the eye temperature may be 10ºC warmer or more at an altitude of 12 km than the surrounding environment, though only 0-2°C warmer at the surface in the tropical cyclone. Eyes range in size from 8 km to over 200 km across, but most are approximately 30-60 km in diameter. The eye is surrounded by the eyewall, the roughly circular area of deep convection which is the area of highest surface winds in the tropical cyclone. The eye is composed of air that is slowly sinking and the eyewall has a net upward flow as a result of many moderate - occasionally strong - updrafts and downdrafts. The eye's warm temperatures are due to compressional warming of of the subsiding air.

The general mechanisms by which the eye and eyewall are formed are not fully understood, although observations have shed some light on the problem. The calm eye of the tropical cyclone shares many qualitative characteristics with other vortical systems such as tornadoes, waterspouts, dust devils and whirlpools. The eye feature is a fundamental component to all rotating fluids. It has been believed that supergradient wind flow present near the radius of maximum winds (RMW) causes air to be centrifuged out of the eye into the eyewall, thus accounting for the subsidence in the eye. 

The cloud-free eye may be due to a combination of dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent caused by the moist convection of the eyewall.

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