Hurricane-force winds or gentle breezes in an O'Neill Cylinder?

Let's consider an O'Neill cylinder with a radius of 3.2km and length of 20km. In the classic O'Neill design, we have three large axis-aligned windows in the shell, alternating between purlins of habitable surface. The windows provide light, and presumably affect thermal transfer considerably.

Before we start things spinning, we pump the inner volume full of breathable air. I believe O'Neill proposed 1/2 atmosphere, 20% partial-pressure O and 30% N, but I don't have my copy of High Frontier handy at the moment.

We'll assume that the designers of the habitat have set up the mirrors and cooling system needed to maintain as comfortable a shirt-sleeve environment as possible.

We spin the cylinder at ~0.5rpm to produce 1g of centripetal acceleration on the inner surface, and then we wait for everything to reach some sort of equilibrium-ish state.

The tangential velocity at the outer radius is ~630km/hr (nearly 400 miles/hour), whereas at the axis it's nil.

Because the spin gravity is fictional, acceleration is only imparted to the atmosphere by frictional interactions with the inner surface of the cylinder. Let's assume it's not smooth, but populated with short buildings (probably two or three stories, max), small trees, people, etc.

So, near the inner surface, you have the outer edge of a vortice of atmosphere spinning at ~400mph, and a relatively calm eye at the axis.

There are a lot of oddities about this vortice though. I'm imagining it like a smoothie in a blender, except the whole blender is spinning, with paddles extending from the walls of the blender instead of a blade at one end.

Because there's no true gravity, the air molecules are just hanging out in space until they interact with the inner surface and are imparted with a tangential velocity. The outer edge of the vortice will end up moving at roughly the same tangential velocity as the inner surface, so just like you don't notice the air in your car moving with you at 60mph, the residents shouldn't be bothered by super-hurricane-force winds. But if you consider how ballistic trajectories work in this system, I think there'll be the sensation of a steady "downward"/spinward breeze as the accelerated mass of air meets the curve of the ground.

Then we have to consider thermal transfer and convection, but again, the gravity is fictional, so I'm not sure we can think about this system in the same way we'd think about atmosphere on Earth. Normally you would think of hot air rising, and cooler air sinking, but without real gravity, that goes out the window.

Instead you have the frictional interaction at the outer edge of the atmosphere imparting linear velocities to masses of air. If the blender analogy applies, I think there's going to be some significant amount of pressure differential between axis and outer radius, but I have no idea how much.

So because of the pressure differential, you'd still have warm air "rising" as the higher pressure system seeks a lower pressure environment, and I think you'd have masses of cooler air "sinking" back into the higher-pressure outer radius, with all the weird apparent deflections that you get in a rotating reference frame: anything moving in toward or out from the axis will appear to be deflected anti-spinward.

Then there's the wind shear to account for: going from a theoretically-calm axis to 400mph winds at radius will be no joke.

So between denser, cooler air masses deflecting anti-spinward as they make their way out from the axis, and that steady spinward breeze from frictional linear accelerations at the surface level, it definitely seems like we're going to at least have buffeting spinward and antispinward breezes at the surface. Unless I have any signs reversed in my very-provisional mental modeling! :)

As for thermal inputs, you have radiative insolation through the windows, you have conductive heat transfer through the shell, and you have heat generated by the friction between atmosphere and the inner walls, buildings, trees, etc. (In another question Carlos Zamora suggests convective systems developing between the windows and the land purlins, but he may not be taking the "blender effect" into consideration...)

My question: what in the world is this crazy weather system going to be like, experientially, for shirtsleeve humans living on the surface? There's certainly going to be some crazy wind shear as you move from axis to radius (no human gliders in this scenario, I think, and no fluffy white clouds). I think the surface would be habitable, even if it might always be good kite-flying weather.

The harder the science you can appeal to in the answer, the better, but I don't think anybody has actually studied this question with any amount of rigor, so I'll happily take flights of fancy and imagination as well. :D

I've read all the discussions I could find about atmospheres in one of these contraptions. I see lots of suggestive hints, lots of questionable assumptions, but no clear answer:

• Prevailing winds on a rotating space habitat This is a very similar question, but encompasses everything from sealed cylinders to Ringworlds, and the drift of the conversation tends to a Ringworld scenario, whereas I'm interested solely in the much smaller O'Neill cylinder. Carlos Zamora provides a fascinating answer outlining the pattern of convection from warm land to cold windows, with a stagnant hot zone at the axis, but I'm not sure that he's taking pressure differential and wind shear into consideration.
• What would happen to air flow and fires in an O'Neill cylinder? Another similar question, with an interesting answer about how smoke would propagate. However, that question is labelled hard-science and so doesn't get much help because of the lack of hard research.
• What conditions would make rain possible in an O'Neill Cylinder? There's a very suggestive comment by Loren Pechtell that got me thinking about this.
• Radial variation of atmospheric pressure in rotating O'Neill cylinder-like ship? This suggests that there wouldn't be much variation between the pressures at the axis and radius of an O'Neill cylinder.
• Can birds fly inside an O'Neill cylinder? and also Flying helicopters on Rama
• What would determine the interior temperature of a large space station? Tangential (ha!) discussion of temperature management for a space colony. Summary: let the engineers figure it out. They'll be fine.

Update: @Matthew makes a really good point about convection: it's just various densities of gas seeking an equilibrium. When I first was preparing the question, I was weirding myself out switching between the two reference frames and considering the transition from rest to spinning. As the habitat hits its target angular velocity and the contents come to equilibrium, velocities are transferred from walls to nearby gasses via friction, and then knock-on until everything near the walls is moving in a relatively orderly fashion along with the walls, so everything close to the walls is acting more or less as if they were under gravity, with convection currents and the whole nine yards.