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Would say a heated air rise twice as fast in 2G than in the environment with standard Earth gravity?

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Initially, on an air parcel, buoyancy force would be twice as much when gravity doubles, which will impart higher initial acceleration, helping air parcel reach a higher speed before being counterbalanced by viscous forces. Of course there is much complication here, because an air parcel loses its momentum also by mixing, if the flow is turbulent. If somehow the parcel is able to maintain its identity by not mixing (very unlikely), then its final speed will be twice as much only if viscous force acting on it is a linear function of speed, but this is not the case. It may be simpler to think of a balloon rising in air. If Reynolds number is high for flow around balloon to be turbulent, then viscous force will increase quite rapidly with balloon speed, something like $\sim v^2$, so balloon's speed will be increased about $\sqrt{2}$ times when gravity is doubled.

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Yes.

The hot air rises due to the force of buoyancy as the hot air expands and becomes less dense. So, yes it rises due to gravity. The force of buoyancy is = (weight of air at regular density) - (weight of air at heated density). The weight involves g. So, yes your statement is true if we exclude complications like resistance/friction etc. As it rises, the force keeps decreasing because the air at higher level is lighter already. So, that slowness is not because gravity has decreased at a height, but mostly due to the fact that force of buoyancy has decreased. 1) air is lighter at height, 2) the hot air may have cooled as it rises. The gravity decreases with height but that impact is negligible.

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