Weather in a rotating cylinder

SW VandeCarr

I agree that even for a cylinder with the dimensions given in the OP, this is still very small for modeling the weather phenomenon of the terrestrial atmosphere. There are a number of important variables that were not given such as the initial pressurization of the cylinder absent rotation, the albedo and topography of the habitat surfaces, the composition of the atmosphere , etc. We might expect a spiraling wind pattern from higher pressure (the cold pole) to lower pressure (the hot pole) along the habitat surface and I think an opposite flow of warm air along the axis from the hot pole to the cold pole. I believe this convection would oppose the tendency toward lower pressure along the axis due to rotation. However, this is really best modeled by a computer simulation with the manipulation of key variables. Often in these kinds of situations, small changes can produce surprising changes in the dynamics .

When you vastly increase the habitat size to unrealistic dimensions, things seem to get simpler. A cylinder with the radius of the earth (over 6300 km) would have outer space conditions through most of its volume with just a relatively thin layer of atmosphere over the habitat surface. Heating could possibly be delivered by radiation from points along the axis. Given 1 g at the surface, and the correct composition and volume of atmosphere, I'm thinking the Standard Atmosphere could be fairly well approximated, but the dynamics would be different because of more even heating (either constant light or artificial day/night cycles). There would be no seasons and, if we could do without a cold pole and a hot pole, the weather could be downright boring without the disasters we have on earth.

Darwin123

Some of this was solved in the Ringworld Series by Larry Niven. However, it pays to rethink these things again.
1) Altitude here means distance from the surface to the center of the axis of the cylinder. Pressure decreases with altitude.
2) If the inside surface has a complex topography, then there may be a complicated weather pattern. On the hypothesis that the inside surface of the cylinder is perfectly smooth, then maybe one would a fairly simple wind pattern dominated convection, centrifugal force and Coriolis force. The Coriolis force is a bit confusing.
Lets us follow a parcel of air starting at the cold end near the surface.
1) Parcel of air is pushed toward the warm end.
2) Coriolis force makes it spiral on an axis which is perpendicular to the axis of the cylinder.
3) When it reaches the warm end, it gets warmer and is lifted up by buoyant forces.
4) The parcel starts moving toward the cold end at a "higher altitude".
5) Coriolis forces make the parcel spiral with an axis that is perpendicular to the cylinder axis, but in the opposite direction of step 2.
6) When it gets to the cold end, it cools and sinks to the inner surface of the cylinder.

This system would probably be disturbed by sideways cyclones. In other words, storms would occur in this system. However, the rotation of these weather systems would have a "horizontal" axis rather than the "vertical" axes seen in earth type storms.
There would also be a "geostrophic" effect analogous to what we see on earth. As a parcel of air moves up, it would be shoved to the side the Coriolis force. Therefore, there would be spiral motions of air from one end of the torus to the other.
I think there would be storms. The temperature gradient would cause any equilibrium state to be unstable. You would have temperature fronts analogous to earth. However, the shape of these fronts would be determined by a Coriolis pseudoforce that was rotated relative to what we are used too.
If this was a scientific project for an astrometeorologist, then the main complication would be the Coriolis force. It would be unlike the Coriolis force seen on any planet or star. The other pseudoforces would be more "similar" to what we see on earth.
Note that there would be an "vacuum" or "partial atmosphere" on the axis of the cylinder. Also, the temperature would increase as one got closer to the axis because hot air rises. Since there is no "sun" to heat the surface, the surface would be cooler than the locations higher up. Thus, there would be no troposphere. The atmosphere would be like the stratosphere, in that temperature increases with height.
There may not be any clouds. Fogs may form on the surface. However, the temperature increases with height. So the condensation would mostly occur on the ground.
Maybe storms would come in the form of catastrophic dews! Condensation on the surface and just above the surface would mean that water there is no falling precipitation. Water just forms on the surface. You are walking along, dew starts to form, and suddenly you are underwater. Drowning!
I got the horizontal axis idea from "Ringworld" by Larry Niven. There was a storm caused by a leak in the Ringworld. The axis of the storm was sideways, so that it looked like an eye. It was called the "Eye of Kadapt."
Niven's idea was too simple. It seems to me that a real weather system would have been complicated by topography. However, he was right about the Coriolis force in such a system.
The absence of a troposphere and the rotation of the Coriolis force would be novel.

SW VandeCarr

I agree there would be no horizontal Coriolis forces (with a vertical axis) which are needed for producing the kinds of storms we have on earth. However the vertical forces (with a horizontal axis) will only be significant if the depth of atmosphere is a significant fraction of the radius of rotation. The Ringworld example makes my Earth radius cylinder look tiny by comparison. The Ringworld, if I remember correctly, had a radius of rotation of about 1 AU (about 150 million km). The speed of rotation in m/sec at the top of the vertical ringwall would be minimally less than than at the bottom, even if it were 1000 km high. Most of the atmosphere would be within 6 km of the inner surface of the ring assuming 1g at the surface. I don't think the gradient over 6/150,000,000 of the radius of rotation would be enough to produce the kinds of forces you describe.

SW VandeCarr

I'm not sure I follow this. The air is moving along the inner surface in a spiral pattern from the cold end to the warm end. The axis of this spiral pattern would be the cylinder axis itself. The return flow would be a spiral pattern at a higher altitude from the warm end to the cold end, also with its axis being the cylinder axis.

Andre

I think that the air on the hot side of the cilinder, the air expands, gets less dense and tends to move to the area of lesser gravity, which is the center, but with a strong coriolis effect. So if the cilinder rotates counter clockwise, the air moving along the hot surface is also spiraling in counterclockwise.

Meanwhile the air at the cold side contracts gets more dense and tends to move to the area with higher gravity, outwards. However doing that it has to pick up rotation, -the coriolis factor, so it will lag behind the rotation, but for the rotating observer this means that it rotates clockwise.

Anyway the combined effect causes high pressure in the areas where the air moves towards, the cold outside of the cilinder and the hot center, so the air tends to circulate away from there to the low pressure areas, both locally hot to hot and to the other side, from hot center to cold center and cold outside to warm outside. Now as these flows are counter rotating too, due to inertia, you get turbulence and mixing.

Scenario for utter chaos and any guess goes. But precipitation at the outside, spiraling down due to the coriolis effect.

Darwin123

Let us consider a parcel of air on the inner side of your cylinder. The parcel is warmer than the ambient air. It is initially still relative to the inner surface of the cylinder. However, the warm parcel starts rising do to buoyant forces. Therefore, the parcel starts moving up, where up means toward the axis of the cylinder.
The air parcel was not initially still relative to the inertial frame of the center of the ship. Initially, it was moving in a direction tangential to the inner surface of the cylinder. The initial speed of the warm parcel was the angular velocity of the cylinder times the radius of the cylinder.
The warm parcel of air meets other parcels of air that are not moving as fast in the inertial frame of the ship. A cold parcel of air close to the axis is moving at a speed equal to the same angular velocity times a smaller radius. Therefore, the warm parcel of air is going to be moving in the tangential direction faster than the cold parcels of air it meets.
This is going to take place until the warm parcel of air finds a height where it meets the parcels of air that are at the same temperature as it. However, it will still have momentum relative to the inner surface of the pendulum.
The Coriolis effect increases with the fraction of space the atmosphere takes up in the cylinder. In the Ringworld, the Coriolis effect would be extremely small. Niven made up for this fact by hypothesizing that the leak that caused the storm had started a long time ago. The storm in Niven's story was perpetual. The Coriolis force in Nivens story had thousands if not millions of years to build up an effect.
You don't have to make this "perpetual storm" assumption in your story. Your cylinder is small enough so that a storm could form in a short time, just like earth.
The atmosphere in your cylinder could take up a good fraction of the space in your cylinder. I am assuming that your cylinder is not so large that there is no atmosphere at the axis of the cylinder.
I am making these suggests based on the following hypotheses.
1) The angular velocity of your cylinder is enough to make the centripetal force of a body on the inner surface of the cylinder equal to the weight of that body on the surface of the earth.
2) The radius of your cylinder is large enough so that there is a big gradient of centrifugal force from the inner surface to the axis of the cylinder.
-Thus, there is a significant drop of air pressure from the inner surface to the axis of the cylinder.
3) The radius of your cylinder is small enough so that the Coriolis force is significant for rising air parcels.
-Thus, the air pressure is significant at the axis of the cylinder.
-The air pressure at the axis of the cylinder is a small but noticeable.

Under these conditions, the Coriolis force in the space ship will cause a noticeable "corkscrew" appearance to winds that move from the cold end of the ship to the warm end of the ship.
I believe that there will be a tendency for winds to move from the cold end to the warm end of the ship. One could call these the "trade winds" of the cylinder. The trade winds would die out near the ends of the cylinder. Air on at the ends of the cylinder would be stagnant, just as they are at the "horse altitudes" of earth.
If there was no topography in the cylinder, there would be a continuous wind moving in a corkscrew direction from cold to warm end. This wind would be very strong, similar to what you would see on Uranus or Venus. There would be no mountains or continents to slow the wind down.
If there was a complex topography inside the cylinder, then the weather would get more complicated. Mountains in the cylinder would cause turbulence, which means broken air patterns. Basins on the inner surface would collect water, producing bodies of water. Bodies of water would provide water vapor, which means storms. However, there would also be gentler winds one could use for transportation.
You may want to consider the impact of the trade winds. People living on this cylinder may prefer to trade in the direction of the trade wind. They may want to use sails to move terrestrial or marine vehicles from the cold to the warm end. However, going the other way would be hard. They may prefer balloons to go from the warm end to the cold end. They would want to catch those winds closer to the axis of the cylinder that move from warm to cold end.