Seems, I have to write again my answer to the question of air movement
inside such a cylinder. Don't like to have to work two times on it.... :-(

ABOUT AIR INSIDE A ROTATING CYLINDER

First, a few important points to be kept in mind when reading my answer:
1
Air is like all gases flexible.
2
Warm air has less weight than cold air.
3
Since even air has its weight, it also has its own inertia.

Now let me answer your question. The cylinder rotates, and its inner
sides contain objects, such as buildings, moving objects (like humans
and vehicles, maybe even animals), and also trees and other plants.
Those all will "push" the air and get thus the air into motion. Over
time, the air at around all these objects will gain almost the same
speed as the inner walls of the cylinder and the objects on it.

But since air is flexible, the air at the outer areas moves initially
faster than the air along the central middle axis of the cylinder, but
over time, that air there tends to gain speed, too, pushed by the air
from the outer areas.

However, since air has its own inertia, the air especially at the inside
will never reach a full 100% of the air movement close to the walls of
the cylinder. And that is a factor that will cause gentle winds to start
to come into existence where the air-pushing objects end (on their
roofs) and where the area with non-pushed air begins, as air will move
around the edges and corners of all objects and escape to the only
possible direction: towards the center of the cylinder.

And there is another factor that will cause the existence of gentle
winds: heat sources. Each mammal (including humans) and some other
animals (like birds) produce body heat that is usually a bit higher than
the surrounding air. Engines are also heat sources. Depending on the
light source at the one end of the cylinder, maybe even bright walls and
reflective windows or walls can become heat sources. That heated air
will move upwards towards the center axis of the cylinder due to its
lower weight, and pushes the cooler air from the center downwards
towards the cylinder walls. The opposite effect could be seen atop water
surfaces when large enough: through condensation, the air right above
those water areas will be cooler.

Another factor for wind is probably the light source self at the one end
of the cylinder. It will heat up the air, that air will rise up towards
the middle and cooler air will take that place. That cooler air will
warm up, too, and push upwards and therefore, warmer air will
concentrate along the middle axis of the cylinder, moving away from the
light source as it produces more and more warm air that follows and
pushes. More towards the other, non-illuminated end of that cylinder,
that warmer air will have cooled down and sinks downwards, and from
there back along the walls towards the light source.

This means, we have two wind directions based on heat: one from the
light source towards the other end of the cylinder, and one from the
walls (warm objects there) upwards towards the center axis. And we have
one wind direction due to the rotation of the walls with all their
objects on it, that is a little gentle wind that feels like against the
rotation of the cylinder, and exists mostly close to the larger buildings.

If that habitat cylinder would be kilometers wide, and also much longer,
the wind powers would be larger. But as it is, I believe, the wind
speeds will not exceed 3 km/hour, maybe even much less. To me, that
sounds like a pleasant location.

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