What is the natural shape of the atmosphere on a Niven ringworld?

Assuming the atmosphere on a Niven ringworld is retained by gravity, what shape would it be?

As I understand it, Niven proposed walls on either edge that would form a sort of trough for the atmosphere to sit in to avoid it leaking into space. However keeping it in a trough assumes there is sufficient gravity to retain it. He also has oceans on the outside of the ring. These also must be retained by gravity. Why then does he need a raised edge?

Assuming the cross-section of the ring is a rectangle with sufficient gravity, and there are no retaining walls, what shape would the atmosphere adopt? Would 1, 2, or 3 in my diagram be possible configurations?

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What is the natural shape of the atmosphere on a Niven ringworld?

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