if Stigant's right
Well, I think we're all just speculating here. And I'm not, in any way, an expert in this stuff. I'm just arm-chairing here based on a few (possibly incorrect) ideas about how I understand the atmosphere to work.
I'm not sure how a "convection zone" would apply to an atmosphere.
I'm using "
convection zone"
to denote a sort of looping wind pattern. Think about the stable (in the sense that, while very dynamic, remain as long term features) cloud patterns that you get on Jupiter or Saturn or in a hurricane on Earth. Weather, to a large extent, is caused by air moving, and when a volume of air moves, it: 1) displaces other volumes of air, and 2) in turn, has to be replaced by other air coming in behind it. Since the atmosphere is basically a closed system, there have to be loops somewhere.
Further, air moving on Earth and other planets is a product of a couple of different forces: temperature differentials and friction with the rotating surface, pulling it in the direction of rotation. Air near the equator moves more quickly than air near the poles because rotation near the equator is quicker. However, it has to loop back at some point. On Jupiter, the rapid rotation of the planet (Jupiter is much larger than the earth, but rotates once every 11 or 12 hours) coupled with this looping back mechanism creates bands in the atmosphere. We have similar bands on Earth, but they aren't as apparent or as well defined because our weather is complicated by other, vertical forces.
The atmosphere on your planet isn't going to have friction with the surface because the rotation of the planet has (essentially) stopped. So you're not going to get these horizontal patterns. But you ARE going to get temperature differentials because the local sphere of nuclear driven fire is going to warm different parts of the surface and atmosphere at different rates. Specifically, it's going to warm the regions that are near the center of the day side more than those near the day/night terminator. This, I think, is going to create a column of rising air at the day-center which, eventually having nowhere else to go will spread out radially from the day-center, cool (as it approaches the terminator) and descend back to the surface where it will get swept back to the center to replace the air that is currently rising there. This creates a sort of do-nut of rotating air similar to a smoke ring. You might get one big do-nut that goes from day-center to terminator, or you might get several concentric don-nuts that operate at different distances from the day-center. That was my thinking, anyway (as I said, I'm not an expert or even at all well versed in meteorology)
This all assumes that the atmosphere on the day side doesn't have anywhere to go. My suspicion is that, without something preventing the air from migrating to the night side (remember, I/we think the air is going to move from the day-center towards the terminator), it will eventually go to the night side (rather than cycling back to the center) and freeze, thus becoming immobile. So (absent some mechanism to keep the air on the day side), the night side is a sink for the atmosphere. The night side can't support a gaseous atmosphere because it's too cold, and eventually the day side won't have an atmosphere either because it left for the night side. If you want an atmosphere, you have to find a way to keep it.
A similar problem was "
solved"
in Larry Niven's Ringworld books. The titular Ringworld is a ribbon orbiting a star in the habitable zone. Think about the equatorial region of a Dyson Sphere (well, the solid-shell one, not the one that Freeman Dyson actually proposed, but I digress). It's about 1000000* miles wide and about 600 millions miles long, giving it a total star-side surface area equivalent to millions of earths (I could be off by some orders of magnitude, not doing the actual calculations here, just pointing out the advantage of constructing such a system). The problem is, you couldn't possibly keep atmosphere on such a ribbon because the centripetal forces (remember, the ring is rotating) would cause the gasses to leak over the sides of the ribbon into space. The solution, in the novel, was that the ring also had walls which were hundreds of miles tall running along the sides of the ribbon, creating a sort of circular trough.
So, I also postulated a way that such a trough (this time, hemispherical rather than cylindrical) could have built up on your planet near the terminator. I'm not sure it's actually feasible. It will need to be pretty tall (100-200 miles) to contain the air. I don't think you're going to have enough volume for the mechanism that I proposed to work. But something similar will have to have been constructed (either naturally or artificially) on your planet to keep the air on the day-side.
* Edit: apparently, it was 1000000 miles wide, not 1000 miles wide... it's been a few years.
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[Last edited by stigant at 11-06-2013 02:49 PM]
I know this is a strange place to go for questions like this, but people on here seem to know everything so here goes. 
I've been working on this story idea that involves a prison colony/labor camp on the dark side of a planet where one side is always turned away from the sun. I'm aware that long-time lack of exposure to sunlight causes depression and Vitamin D deficiency, but I don't think it would cause any serious health problems that couldn't be solved with supplements. What I'm more concerned about is the cold. I know there are a lot of factors that could influence the temperature of a planet, but is there any plausible way that a planet like this could realistically be warm enough to support life on the dark side? I'm thinking of giving it an ecosystem including bioluminescent fungus that's used for light, but the story could still work if the dark side is uninhabitable and the prisoners are only able to survive here through technology.
