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This is an intersting aspect of a large tropical cyclone, it forms an eye at the center where a small amount of the air sinks. A hurricane is a very strong convection of rising air. But what rises must eventually comes down. Most of it comes down far away, creating high pressures here and there. But some convections, like very strong cumulonimbus producing thunderstorms, also sees downdrafts, usually on the sides.
As a private pilot flying a very light aircraft, I know that, on a sunny day, the sun heats the ground and parcels of air rises here and there, forming cumulus clouds. Between them, the air sinks.
In the eye of a hurricane, this happens too and since the sinking air warms up by adiabatic effect, clouds evaporate, giving place to a clear sky.
