Im “eMagazin für aktuelle Themen der Hochschuldidaktik” der Uni Kiel ist der Artikel “Praxisnähe dank digitaler Versuchsküche” von Phil Mertsching über Torge’s und mein Projekt “Dry Theory 2 Juicy Reality”, insbesondere die Umsetzung im letzten Jahr mit den Zoom-Konferenzen aus meiner Küche, erschienen, zusammen mit vielen anderen spannenden virtuellen und hybriden Formaten. Es lohnt sich, da mal rein zu gucken!
We’ve become quite experienced with remotely-controlled rotating tank experiments, but the current lockdown brought us into yet another new-to-us situation: We had plans to film and live-stream tank experiments from Geomar, but not being employed there, I am currently not allowed in the building! So what happened this morning is that Torge and I met up on Zoom and I watched from home as he had all the fun.
It all started out quite well — camera tests worked well, water was in the tank, I was having fun taking screenshots. Well, and I was wishing I was there, playing, rather than watching and occassionally interrupting with instructions or unsolicited advice!
When we were done setting things up, students joined in for their exercise session (no, it’s not me three times in the meeting below, I just edited that in for privacy because we didn’t ask students for permissions to use their pictures), and a lively discussion ensued. Topic of the day were eddies in the ocean, and it was all leading up to the Taylor column experiment that we had only recently figured out.
The Taylor column experiment basically shows that rotating flows cannot just flow across an obstacle, they have to stay 2D and thus move around it. Which worked out beautifully! The blue dye started out upstream of the obstacle and got deformed into these beautiful filaments as it is moving around the hockey puck and the Taylor column on top of it (The puck is only blocking the lower part of the water column, above it there is just water!).
It all went super well until we fell into the trap we’ve been falling in ever since we started working with the tank: The co-rotating camera switches off when the power to the rotating table is switched off, which is the easiest way for the rotation to be switched off. So yeah. Below you see Torge trying to save the day by holding his laptop above the tank to give students a look into the tank after it stopped. Oh well…
But all in all, it worked super well and it’s great to see how virtual teaching and learning can be a really good substitute for in-person classes. But we are still looking forward to the times when we can all play together again!
I have a slightly complicated history with Taylor column experiments — even though the experiments look fine compared to all other videos I’ve found online, I somehow always had higher expectations.
But now I’ve tried doing the experiment in a rheoscopic fluid (approximately 2cm of it over the hockey puck) and it looks a whole lot better in person than in these pics!
Here is a movie of the experiment. The Taylor column is created by first spinning up the tank to (almost, or in my case not quite because I didn’t have enough time but really wanted to try this) solid body rotation, and then slightly reducing the rotation rate (and then slightly increasing it again) in order to create a flow relative to the obstacle.
In the movie it becomes quite clear that while in the very beginning a lot of fluid gets advected across the puck, this does not happen when the fluid is (close to) solid body rotation. Then, there is a column of fluid (the Taylor column) spinning on top of the obstacle.
But there are other cool features visible in the movie, like the shear instabilities around the puck, and the lee waves downstream of it.
Can’t wait to spin this up to full solid body rotation on Thursday and try again!
Torge and I are planning to run the “tilting of a frontal surface under rotation / cylinder collapse” experiment as “remote kitchen oceanography” in his class on Thursday, so I’ve been practicing it today. It didn’t work out quite as well as it did when Pierre and I were running it in Bergen years ago, so if you are looking for my best movie of that experiment, you should go read the old blog post.
The idea is that a density front is set up by spinning up a tank in which a bottom-less cylinder contains a denser fluid, set up into a less dense fluid. Once the tank is spun up, the cylinder is removed, releasing the denser fluid into the less dense one. In contrast to the non-rotating case, where the dense water would sink to the bottom of the tank and form a layer underneath the less dense water, here the cylinder changes its shape to form a cone that retains its shape. The slope of the front is determined by both the rotation rate and the density contrast.
What I can show you today is what it looks like on my DIYnamics rotating table in my kitchen (and it’s pretty cool that all these different experiments can be run on such a simple setup, isn’t it?!). This is from two weeks ago:
And a second attempt done today (I’m not showing you all the failed ones in between, and since I’m a little sick, I’m also not showing you what I look like, and spare you the sound of my incoherend explanations ;-)). But: Now everything is set up so I can use my right hand to pull out the cylinder to introduce fewer disturbances (spoiler alert: didn’t work out — see all the waves on the tank after I remove the cylinder?)
Check out the flower “floats” — the ones on the remains of the cylinder are rotating in the same direction as the tank, only faster! That’s something we didn’t show in Bergen and that I think is really neat.
What I learned about how to set up the experiment: I filled the cylinder with ice cubes and then filled water into the donut outside of the cylinder. That way, water pressure would push water through the petroleum jelly seal at the bottom of the cylinder inside, but the dye of the melting ice cubes would not seep out (very much). Also, the cold melt water would make the water inside the cylinder denser (make sure to stir!). The whole fancy “get water out and refill using a syringe” stuff sounds nice but just isn’t feasible in my setup…
In this case, having a larger tank would be really helpful, because the disturbances introduced in either case are probably more or less the same, but the smaller the tank, the larger the relative effect of a disturbance… Also, my tripod was making it really difficult for me to reach into the tank without hitting it, both for filling the tank and for removing the cylinder. I guess if we didn’t need a top view, things would be a lot easier… ;-)
A very common misconception when looking at atmosphere & ocean dynamics in a rotating tank is that the center of the tank represents one of the poles and the edge of the tank the equator. And there is one experiment that — I fear — might reinforce that misconception, and that is the one we love to show for rotation vs thermal forcing, baroclinic instabilities (fast
rotation), Hadley cell circulation (slow rotation).
When we do this experiment, the tank looks like a polar stereographic view of the Earth, with the pole (represented by the blue ice in the picture below) in the center and the equator at the edge of the tank. And when we then talk about the eddies we see as representing weather pattern, it’s all too easy to assume that the Coriolis parameter also varies throughout the tank similarly as it would on Earth, only projected down into the tank. Which is not the case!
But the good news is that it’s super easy to drive this experiment by heating rather than cooling in the center of the tank. The physics are exactly the same, only the heat transport is now happening radially outward rather than radially inward. And that it’s now not the easiest assumption any more that we are looking down at the pole.
Also: Heating in the middle is a lot easier to do spontaneously than cooling using ice — no overnight stay in the fridge required, just a kettle! :-)
What are other misconceptions related to rotating tanks that you commonly come across? And do you have any advice on how to prevent these misconceptions or elicit, confront, resolve them?
I had so much fun playing with rotating tank experiments on a cone this afternoon! And with Torge Martin (who I have the awesome #DryTheory2JuicyReality project with) and Rolf Käse (who got me into tank experiments with an amazing lab course back in 2004, that I still fondly remember). We tried so many different things, that I will at some point have to describe in detail, but for now I just need to share the excitement ;-)
Here, for example, a blue fish-shaped ice cube. This experiment is pretty much the topographic Rossby wave experiment described here, except now we aren’t on an inclined plane, but on a cone. Which is basically an infinitely long inclined plane — the ice cube doesn’t encounter a boundary as it travels west, it just goes round and round the tank until it melts. And look at the cool Rossby waves!
Then we did another one of our favourite experiments, the Hadley cell circulation. What was really fascinating to observe was how turbulence the turbulence that was introduced by dripping dye into the tank changed scales. At first, we had the typical 3D pattern with plumes shooting down. But over time, the pattern became more and more organized, larger, and 2D. See below: The blue dye had been in the tank for a little longer than the red dye, so the structures look completely different. But interesting to keep that in mind when interpreting structures we observe!
Here is another view of the same experiment. Since we are cooling in the middle and rotating very slowly (about 3 rotations per minute), the eddy structures aren’t completely 2D, but they are influenced by an overturning component.
This looks even cooler when done on a cone. Can you see how there is both an overturning component (i.e. the plumes running down the slope) and then still a strong column in the middle?
This just looks so incredibly beautiful!
And one last look on the eddies that develop. We saw that there are cyclonic eddies happening in the center of the tank and anti-cyclonic eddies at the edge. Since we are on a cone, I could imagine that it’s just due to conservation of vorticity. Stuff that develops near the center and moves down the slope needs to spin cyclonically since the columns are being stretched, and on the other hand things that develop near the edge must move up the slope, thus columns being compressed. What do you think? What would be your explanation?
I was super keen on trying the Taylor column experiment, but maybe I expected things to look too much like my sketch below, or my technique isn’t quite perfect yet, but in any case, the results don’t look as good as I had hoped.
This is the setup I was aiming for:
- put ice hockey puck (two in our case), ca 1/5th water depth, ca 1/4 diameter of tank
- rotating our tank at 5rpm (ca 7 on GFI’s large tank’s display) with the obstacle in the water until solid body rotation is reached (We know that solid body rotation is reached if paper bits distributed on surface all rotate at same rate as the tank).
- change the rotation rate a tiny little bit so water moves relative to tank and obstacle, i.e. we have created a current flowing in the rotating system.
And here is what happened.
- tank was rotating way too fast
- tank wasn’t in solid body rotation because it wasn’t level
- one of the hockey pucks didn’t stay in place but moved to the edge of the tank as the tank (slowly!) accelerated
- more confetti on the surface!
But! We see that there is clearly something happening around the hockey puck that seems to deform the curtain of blue dye.
- Stopped too rapidly / bumpy
Even though the blue dye curtain moves over the pucks initially, we see that they develop a wake or something, deforming the dye.
Accidentally deleted the movie, so we will have to make do with a couple of pics I took while the experiment was running.
Slowing down worked a lot better this time round. We clearly see that the dye curtains are deformed around the Taylor columns and don’t move over the pucks.
I think I am finally accepting that this way of introducing dye as a tracer isn’t working as I had hoped…
And this is when my camera decided to stop working…
Back to the basics: Confetti floating on the surface.
Before slowing down, the field of confetti looked like this.
Then, the tank was slowed down and the field got deformed. Some confetti went over the puck, but there is an eddy downstream of it that catches confetti.
And the confetti that went over the puck seem to be stuck there.
Final attempt (for now).
More confetti. This is the situation before slowing down the tank:
Confetti distribution is influenced by the puck similarly to what we saw in the dye: Some confetti are slowed down upstream, some move around the puck.
Eventually, most confetti end up in the puck’s wake.
Next attempt at the topographic Rossby wave! This time with following the geosci.uchicago.edu instructions more closely…
…and then the tank had hickups, so we did get waves, but a lot more diffusive than we had hoped, because the tank slowed down a lot more and in a more bumpy fashion than I had planned…
Setup of the topographic Rossby wave experiment
For a demonstration of topographic Rossby waves, we want the Coriolis parameter f to stay constant but have the depth H change. We use the instructions by geosci.uchicago.edu as inspiration for our experiment and
- build a shallow ridge into the tank, from a cylinder in the middle to the outer wall. My solution: Take a 1.5 cm (outer) diameter hose, tape it to the bottom of a tank to achieve a ridge with smooth edges
- 7 cm water depth
- spin up the tank to approximately 26 rpm
- wait for it to reach solid body rotation (ca 10 min)
- introduce dye all around the cylinder in the middle
- reduce rotation slightly, to approximately 23 rpm so the water inside the tank moves relative to the tank itself, and thus has to cross the ridge which is fixed to the tank
- watch it change from laminar flow to eddies downstream of the ridge. Hopefully ;-)
I ran my new favourite experiment again, the planetary Rossby waves. They work super well on the DIYnamics table we built in Kiel and they also worked really well the other day in Bergen.
I mainly ran it today because I wanted to get an idea of how robust the experiment is, i.e. what to prepare for when running it with students in terms of weird results that might have to be explained.
Here is a side view of the square tank with a sloping bottom. The blue ice cube is melting. The melt water is forming a Taylor column down to the bottom of the tank. Some of it then continues down the slope.
Here we are looking at the slope and see the same thing (plus the reflection at the surface). Note how the ice cube and its meltwater column have already moved quite a bit from the corner where I released it!
When the blue ice cube had crossed half the width of the tank and the blue melt water had almost reached the other edge, I released a green ice cube. Sadly the dye wasn’t as intense as the blue one. But it’s quite nice that the wave length between the individual plumes going down the slope stays the same, for all the blue plumes as well as for the new green ones.
Here in the side view we see the columns of the blue and green ice cube, and we also see that each of the plumes going down the slope still has Taylor columns attached at its head.
Here is an accelerated movie of the experiment, 20x faster than real time. Not sure why there is still sloshing in the tank (this time I made sure it was level), but it’s very nice to see that the ice cubes are spinning cyclonically, faster than the tank! As they should, since they are sitting on Taylor columns…
I think next time I really want to make a side view movie of the Taylor columns and plumes. Not quite sure yet how I will manage the lights so they don’t get super annoying…
And here is my new favourite experiment again: Planetary Rossby waves! This time filmed with a co-rotating camera.
We have a square tank with a sloping bottom at solid body rotation (except this annoying slogging because the rotating table wasn’t levelled out [meaning: I didn’t level it before starting the experiment…]). We then release a blue ice cube in the eastern corner of the shallow end of the tank and watch as the melt water column stretches down to the bottom, and is driven back up the slope to conserve vorticity. A planetary Rossby wave develops and propagates westward!
Above, we are looking at the tank east-to-west. Note the sloping bottom with the deep side on the left. And just look at all these beautiful eddies!
This is what it looks like in motion:
Watch the full experiment here if you are still curious after seeing the 1.5 minutes above :-)