SW VandeCarr said:
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.
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 spaceship 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.