Spaceship Engineering & Infrastructure Challenges: Air Currents

I have a spherical spaceship that is about 2 kilometers in diameter with an outer clear, yet strong shell. This spaceship is largely made up of empty space occupied by air. Aside from this the spaceship has concentric rings that spin to produce artificial gravity on the surface of the rings. Ignoring other problems, what sort of air currents would be found inside the ship?

Edit: Also assume that most of the heat found in the ship would come from nuclear powered engines at the core of the sphere. Also the ship is largely used for scientific expeditions, with the ring surfaces being home to a living biosphere

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Spaceship Engineering & Infrastructure Challenges: Air Currents

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