How to simulate tidal currents on an O'Neill Cylinder

At a guess? Try placing the cylinder in orbit around a suitably sized planetary body at the appropriate distance and have the cylinder rotate so that each ends moves first closer to then father away from the larger body.

Other than that pumps and weirs and power driven hydro mechanics. If you can build an O'Neil cylinder electric power shouldn't be a problem

Add a different kind of spin.

An object can have only one axis of rotation as I learned here:

https://physics.stackexchange.com/questions/322200/how-many-different-axes-of-rotation-can-coexist

But for ease of thinking let us think about 2 axes, realizing in our hard physics heart that there can be only one.

The cylinder spins along its long axis to simulate gravity. Yes, yes. Left image. Your left, not the images left.

Now let us also spin the cylinder along its short axis, like a propeller. Right image. This propeller spin is much slower than the long axis "gravity" spin. The effect of this gentle slow spin is to produce a vector force out towards the ends of the cylinder.

One could imagine this centrifugal force to simulate a change in altitude. Now it is "downhill" from the cylinder center to the ends. Water will tend to flow out towards the cylinder ends.

The cylinder ends admit more radiation than the central cylinder. Possibly a lot more. Water that reaches the end heats up and hot gases rise. The hot gases from the cylinders end will rise because of the same forces that pulled the water to the edges - gases are also pulled by this force, and hot, less massive gases will float atop cold. The evaporated water will make its way back to the relatively cool cylinder center and fall as rain.

I'm wondering how much energy it would cost to just ebb + flow the spin of the whole cylinder once per day.

Let's see:

The moon is $7.34 times 10^{22}$ kg in mass, and perigee is 362,300 km from the center of the Earth. Deduct the radius of the Earth (6,371 km) to get the "feel" at the surface and $a = {{GM} over {r^2}}$ the moon exerts a change of ${{6.67 times 10^{-11} 7.34 times 10^{22}} over ({355,929,000})^2 } = 3.86 times 10^{-5}$ m/s/s. Or, in context of centrifugal spin producing 9.8 m/s/s of "force", a 0.000004% change in cylinder spin.

Now, you actually get the drop for free. You can use regenerative braking, braking the rotational energy into a flywheel, that you can then re-provide during spin-up. You could design-in the friction drop to occur smoothly over the course of 12-hours, and then computer control the spin-up over the next 12-hours.

As El Duderino pointed out in the comments, having a global change in the "centrifugal" force won't produce a tide. Tides are caused by uneven dynamic forces (tidal effect is weakest directly under the moon, a spot that moves constantly as the world turns).

I wonder if this can still work, however, with the radial part of the acceleration causing clockwise and counter-clockwise "tides"; helped a little by the reduction (or increase) in the ground-pulling force.

• $ E = mgh = sqrt{(ma_{perp}h)^2 + ({{1 over 2} mv_{parallel}^2})^2}$
• $a_{parallel} = alpha r$
• $a_{perp} = {omega}^2 r = {alpha t}^2 r$

The mass of the ocean and the height don't change, so m and h can be dropped. The change in g we're looking for is $3.86 times 10^{-5}$

• $3.86 times 10^{-5} = sqrt{({alpha t}^2 r)^2 + ({{1 over 2} ({alpha r t})^2)^2}}$

You can still use regenerative braking to catch most of the braking energy for recycling into spinning back up. However, it's not quite like tides work on Earth.

Cost:

• Consumes the least possible energy and resources : costs you nothing you weren't going to have to spend already to keep the cylinder spinning (although perhaps you had even lower-friction spinning; maybe costs you that).
• Can be built in as many kinds of places as possible : the "tidal" effect is global; merely need to add water.
• Would be the least expensive to build in the first place : only costs a few lines of software putting some timing into the re-spin schedule.

You need currents for two main purpose:

• oxygenate the water
• recirculate the nutrients

Waterfalls and artificial rain can help you with the first one, while thermal circulation can help you with the second and also in distributing the oxygenated waters. You can use the dump heat from the activities hosted in the cylinder to create a density differential in the water bodies, which then following the gravity will induce flow in the water itself.

Inside the cylinder you are free to arrange the hydrography as you like, so a couple options are:

1. Make the water run in a circuit and use wave pool mechanisms to keep it circulating.

Wave pools replicate the movement of the ocean one of two ways, depending on the size of the pool and the size of wave desired. In small wave pools, pressurized air is blown onto the surface of the water, or a paddle creates force in the water, creating small ripple-like waves. Other techniques utilize an "accordion mechanism" which opens and closes in order to suck water into its belly (opening) and push it out (closing) to cause waves. However, in high-volume wave pools, a large volume of water is quickly allowed into the far end of the pool, forcing the water to even out, generating a sizeable wave. In these large wave pools, the excess water is removed by being channeled through a return canal where it can be used again to generate another wave.

Make gentle waves that all flow in the direction of the circuit, and you will have an artificial current. The waves may be used for surfing too, which gives more options for leisure and fitness to the crew and passengers.

If you make the whole machinery run at really, really gentle levels you can even turn it into a lazy river, but that is not as much fun:

A lazy river is a water ride found in water parks, hotels, resorts, and recreation centers, which usually consists of a shallow (2½ ft. to 3½ ft.) pool that flows similarly to a river.[1] There is generally a slow current, usually just enough to allow guests to gently ride along lying on rafts. There may also be scenic elements added, such as small waterfalls on the edge of the river. Some connect or lead into swimming pools or wave pools, while others are self-contained courses that simply complete a circuit.

A torrent river, or wave river, is a related concept. Torrent rivers feature wave machines similar to those that are in wave pools; the waves then push riders (who are on rafts, as they are in a regular lazy river) around the river faster than they would be traveling in a regular lazy river.