Has realistic climate modelling been done for inverted Dyson spheres or similar?

Question

While there are approaches to make a habitable Dyson sphere that are technically reasonable, I am curious about what the climate would be like. For simplicity, consider a scenario where a thick shell is constructed at about 3.6 million kilometres from the sun, where surface gravity would be one g. It is supported by dynamic stabilization from the inside. Assume excess heat is radiated by some additional cooling system, like a cooling tower connected at some point of the shell or whatever. Put a star on an equatorial orbit to provide illumination, and make sure it's sufficiently far away to avoid it's gravitational pull to have more than negligible impact on the surface conditions. Assume earth-like atmosphere and surface. Can actual climate models be used here, and what would they predict? Has climate modelling been done for any megastructure of vaguely similar kind? Scientifically informed speculation, perhaps?

Edit: I chose to not assume anything about rotation of the sphere. This is of course highly significant but I can't come up with a default value, so discussion of that issue is welcome. Also, my first idea of the world is to have a lot of open water, like on earth, so there would possibly be a huge world ocean where most bodies of water are connected.

Edit2: a star in orbit provides a day-night cycle of years, so I guess a different solution is needed for what I have in mind, although extreme day-night cycles could also be interesting. I think we should assume 24 hour cycles with the same spectrum and power as on earth for the simplest scenario.

Answer 1

I'm assuming you mean "realistic" to imply that you'd expect the model to give a realistic picture of the dyson sphere's (DS's) actual weather. In that case, the answer is "probably not".

The reason is that a DS is so big that running even the simplest realistic atmospheric models on a DS would utterly overwhelm our largest supercomputers. Weather models work by dividing up the atmosphere into cells and time into slices, and using the well-understood physics of liquids and gasses to compute what's in each cell at slice N+1 based on what's in each cell as slice N. And then repeat until you've got a 24-hour, 48-hour or whatever forecast. (Wikipedia has a pretty good article on it.)

The smaller the cells and the shorter the slices, the more potential for accuracy the model has. The problem is that the number of cells for the computation goes as the fourth power of the resolution. Make the cells half as big and the slices half as big and you need 16 times the computing power. You get into a hole pretty quickly where the prediction runs slower than real time!

Likewise, go from the surface of the Earth to the surface of a Dyson sphere, and you scale up the number of cells (but not the number of slices) by the square of the ratio of the Earth's diameter to the DS's diameter: For a DS the size of Earth's orbit, that will increase the number of cells by a factor of about 500,000,000 (186 million miles/8000 miles) squared.

There are all kinds of tricks that can be used to avoid having to do a full-up simulation. One is to do a global circulation model at much lower resolution, and then embed a higher resolution weather model in a small portion of it. This has generated good results for Earth, but only after extensive tuning to get its results to match what we actually observe! When you're making so many approximations, you need "ground truth" to test against if you hope to get reliable results. We lack such ground truth for DSs.

If I had to tackle the problem, I'd probably note that Coriolis forces are tiny on the DS and that there's no variation in insolation by latitude, so chances are the DS would lack much global circulation. If so, it could be approximated by a much smaller flat plate for which we might be able to do a decent simulation.

This would miss any global effects, of course, and would be unreliable because it can't be tuned using real data, but it might provide some useful clues.

The prime rule of modelling is "All models are wrong; a good model is useful."

Answer 2

Climate Will be Whatever Its Builder's Want

Any structure as massive as a true Dyson sphere speaks of a civilization that can harness literally astronomical levels of resources and energy and put it to task. Any species that achieves this level of technology will by nature of being so advanced and possessing so much control over so much mass and energy that it would be fairly safe to assume the climate on such a construct will be whatever its builders wish it to be. It would not make sense to build something you plan to live on that you cannot control after all.

I Don't Think Anyone Has Seriously Modeled Such Constructs

That being said, where we are technologically in relation to Dyson spheres is about where Davinci was when he was drawing clockwork wing-suits in comparison to our modern day supersonic flight. Worse off actually, Davinci didn't need to prove that flight itself was possible, anyone looking at a bird knew it was. We on the other hand, can only theorize along lines of physical laws of nature and mathematics to say it is theoretically possible. We as of yet cannot look into the cosmos and see a Dyson sphere and go "well, its possible, now we just have to figure out how....." When we speak about Dyson spheres we are speaking so far in advance of where we are now that I don't think anybody has ever seriously tried to apply accurate climate models to the living surface of such a construct. If they have then its very obscure because I have never seen nor heard of such a project, and I spend a LOT of time reading about this stuff. Likely somebody has at least tried but their work was probably not taken very seriously or given much attention. They would be talking about an idea that is so theoretical and far outside of our reach at the moment that its probably just not seen as very useful. I personally refer to such work as "Trying to invent a better light-bulb before you've discovered electricity." Obviously very interesting and possibly will be looked back some day as the first tentative steps in the right direction, but not of very much serious concern in its own time.

In summary, to my knowledge nobody has applied any serious effor towards modelling the climate of a Dyson sphere. Maybe somebody in further answers here will have found such work and render my answer moot, because I find the idea very very interesting but have never seen nor can I find anything like it.