Tag Archives: solid body rotation

Working on our own affordable rotating table for oceanographic experiments!

Inspired by the article “Affordable Rotating Fluid Demonstrations for Geoscience Education: the DIYnamics Project” by the Hill et al. (2018), Joke, Torge and I have been wanting to build an affordable rotating table for teaching for a while now. On Saturday, we met up again to work on the project.

This post is mainly to document for ourselves where we are at and what else needs to happen to get the experiments working.

New this time: New rotating tables, aka Lazy Susans. After the one I’ve had in my kitchen was slightly too off-center to run smoothly, we bought the ones recommended by the DIYnamics project. And they work a lot better! To center our tank on the rotating table and keep it safely in place, we used these nifty LEGO and LEGO Duplo contraptions, which worked perfectly.

We also used a LEGO contraption to get the wheel close enough to drive the rotating table. The yellow line below shows where the rim of the rotating table’s foot needs to sit.

And this is how the engine has to be placed to drive the rotating table.

First attempt: Yes! Very nice parabolic surface! Very cool to see time and time again!

Now first attempt at a Hadley cell experiment: A jar with blue ice is placed at the center of the tank. Difficulties here: Cooling sets in right away, before the rotating tank has reached solid body rotation. That might potentially mess up everything (we don’t know).

So. Next attempt: Use a jar (weighted down with stones so it doesn’t float up) until the tank has reached solid body rotation, then add blue ice water

Working better, even though the green dye is completely invisible…

We didn’t measure rotation, nor did we calculate what kind of regime we were expecting, so the best result we got was “The Heart” (see below) — possibly eddying regime with wavenumber 3?

Here is what we learned for next time:

  • use better dye tracers and make sure their density isn’t too far off the water in the tank
  • use white  LEGO bricks to hold the tank in place (so they don’t make you dizzy watching the tank)
  • measure the rotation rate and calculate what kind of regime we expect to see — overturning or eddying, and at which wave number (or, even better, the other way round: decide what we want to see and calculate how to set the parameters in order to see it)
  • use white cylinder in the middle so as to not distract from the circulation we want to see; weigh the cylinder down empty and fill it with ice water when the tank has reached solid body rotation
  • give the circulation a little more time to develop between adding the cold water at the center and putting in dyes (at least 10 minutes)
  • it might actually be worth reading the DIYnamics team’s instruction again, and to buy exactly what they recommend. That might save us a lot of time ;-)

But: As always this was fun! :-)

P.S.: Even though this is happening in a kitchen, I don’t think this deserves the hashtag #kitchenoceanography — the equipment we are using here is already too specialized to be available in “most” kitchens. Or what would you say?

Water not in solid body rotation yet

Confusing students even more by discussing how momentum is being transferred from the tank to the water.

As you remember, we are preparing for the Ekman experiment and need to spin up the tank to solid body rotation.

We had started discussing how, when observed from the co-rotating camera, particles seem to be slowing down relative to the coordinate system underneath the tank as we are approaching solid body rotation.

And this is where I usually confuse the students even more, because I start talking about how momentum is being transferred from the tank to the water. For that, I point out how when observing the tank from the non-rotating framework, the particles further away from the center are moving faster than the ones closer towards the center…

(and on the screen: particles closer to the center are moving faster than the ones further away).

Why is that?

Well, for exactly the same reason we can use this setup to simulate Ekman spirals: Because when the tank is sped up or slowed down, this initially creates friction with the water inside. And as the layer that is in direct contact with the tank is brought to the same speed as the tank, it changes its velocity relative to the next layer, which creates friction and influences the movement of this second layer. And so on and so forth.

I think that it is really useful to point this out, and in some of the groups students jump at it and understand where I am going right away, but in other groups I just cannot phrase it in a way that they understand me. Or maybe they are just not as fascinated as I am by being able to see how friction inside water propagates momentum and hence don’t get excited? Who knows.

[Thanks, Pierre, for your help with the filming!]

Water in solid body rotation.

Spinning up a tank until all water particles move with the same angular velocity.

Before running the Ekman spiral experiment, the tank needs to be spun up to solid body rotation. Even though the concept itself is not difficult, it seems to be difficult to determine when a body of water has reached the point where it rotates as a solid body. So here is my attempt to sort my thoughts well enough to explain it better next time I teach this experiment.

Firstly: Solid body rotation of water in a tank basically means that every water molecule is at rest relative to the tank (neglecting thermal movement). This means that over any given period of time, particles that started out on a straight line going radially outwards from the centre will still be on straight line going radially outwards from the centre, with the same radii as initially.

But since we are usually not rotating with the tank, this is pretty hard to observe from a non-rotating frame. Enter the mounted camera rotating with the tank (and, I think, the confusion).

When we start up the rotation of the tank, the water is initially at rest in the frame of the lab. This means that for a counter-clockwise rotating table, particles on the water surface appear to be moving clockwise when observed on the screen.

As time goes by, the water inside the tank starts spinning with the tank, and with it the particles on its surface. On the screen, this appears as though the particles are slowing down.

When the particles don’t move any more relative to the coordinate system underneath the tank, the water is moving with the same speed as the tank and solid body rotation has been reached.

Part 2 will shortly be uploaded, looking into how momentum is being transferred from the tank to the water.