Yesterday, we combined a thermally-driven overturning circulation with the effects of rotation, and thus created a Hadley cell circulation. And while the tank was turning faster than we would have liked, we still managed to create a circulation that largely resembles the sketch below: An axially-symmetric overturning circulation (with cold water, indicated by blue arrows, moving down near the cooling in the middle and then outwards, and warmer water moving up along the outer rim and then towards the middle of the tank) which induces the thermal wind flow (sketched in green: Fast surface current in the direction of rotation but even faster than the tank is rotating, and slow bottom flow in the opposite direction).
But what would happen if we increased the tank’s rotation rate? It would make the induced azimuthal flow, the thermal wind, faster too, until it eventually becomes unstable and breaks down into eddies. And then, the experiment (first blogged about a long time ago) looks similar to this one: Lots and lots of eddies that are now rigid vertically and move as Taylor columns!
Heat exchange between the cold core and the warmer areas towards the rim of the tank now doesn’t happen via overturning any more, but looks something like sketched below: We now have radial currents bringing warm water towards the middle (red) and cold water away from it (blue), and the eddies that create those currents are coherent over the whole depth of the tank.
This is actually a really nice demonstration of the circulation in mid- and high latitudes where the weather is determined by baroclinic instabilities, i.e. weather systems just like the eddies we are showing here.
Btw, having two different experiments both represent the same Hadley cell circulation isn’t a contradiction in itself: On Earth, the Coriolis parameter changes with latitude, but in the tank, the Coriolis parameter is the same throughout the tank. So depending on what latitude we want to represent, we need to change the tank’s rotation rate.
Here is an (old) movie of the experiment, and I can’t wait for our own tanks to be ready to produce a new one!
Setting up an overturning circulation in a tank is easy, and also interpreting the observations is fairly straightforward. Just by introducing cooling on one side of a rectangular tank a circulation is induced (at least for a short while until the tank fills up with a cold pool of water; see left plot of the image below).
But now imagine an axially symmetric setup where the cooling happens in the middle. What will happen to that overturning circulation if the tank is set into rotation (see right plot above)?
First, let’s check there is an overturning circulation. We can see that there is when we look at dye crystals that sank to the bottom of the tank: Dye streaks are moving outwards (and anti-clockwise) from where the crystals dropped on the ground, so at least that part of the overturning circulation is there for sure. If our tank were taken to represent the Hadley cell circulation in the atmosphere, this bottom flow would be the Trade winds.
Now, in addition to having water sink in the middle of the tank, spread radially outwards, and returning by rising near the outer edge of the tank and flowing back towards the middle, a secondary circulation is induced, and that’s the “thermal wind”. The thermal wind, introduced by the temperature gradient from cold water on the inside of the tank to warmer waters towards the rim, tilts columns that would otherwise stay vertically.
You see that in the image below: Dye dropped into the tank does not sink vertically, but gets swirled around the cold center in a helix shape, indicated in the picture below by the white arrows. In that picture, the swirls are tilted very strongly (a lot stronger than we’d ideally have them tilted). The reason for that is that we just couldn’t rotate the tank as slowly as it should have been, and the higher the rotation rate, the larger the tilt. Oh well…
So this is the current pattern that we observe: An overturning circulation (sketched with the red arrows representing warmer water and the blue arrows representing colder waters below), as well as the thermal wind circulation (indicated in green) with stronger currents near the surface (where the water is moving in the same direction as the rotating tank, but even faster!) and then a backward flow near the bottom. The velocities indicated here by the green arrows are what ultimately tilted our dye streaks in the image above.
The thermal wind component arises because as the overturning circulation moves water, that water carries with it its angular momentum, which is conserved. So water being brought from the rim of the tank towards the middle near the surface HAS to move faster than the tank itself the closer it gets to the middle. This flow would be the subtropical jets in the Hadley cell circulation if out tank were to represent the atmosphere.
Here is an old video of the experiment, first shown 5 years ago here. I’m looking forward to when Torge’s & my rotating tanks are ready so we can produce new videos and pictures, and hopefully being able to rotate the tank even more slowly than we do here (but that was the slowest possible rotation with the setup we had at that time). I promise you’ll see them here almost in realtime, so stay tuned! :-)
For our project “Ocean currents in a tank: From dry theory to juicy reality“, Torge, Joke and I are working on building affordable rotating tanks to use in Torge’s Bachelor class on ocean and atmosphere dynamics. When people ask what we need rotating tanks for, the standard answer is that rotation of the tank simulates rotation of the Earth. Which is of course true, but it is not really satisfying because it doesn’t really convey the profound effect that rotation has on the behaviour of the ocean and atmosphere, which is actually very easy to show in a quite dramatic way (at least I think it’s dramatic ;-)).
Imagine a cylindrical tank filled with fresh water. In its middle, we place a (bottom-less) cylinder filled with dyed, salty water. When we lift the cylinder out of the tank, the blue dye is released into the freshwater. And depending on whether the tank is rotating or not, the blue water behaves very differently.
The picture below shows top views and side views of a non-rotating and a rotating experiment, taken after similar amounts of time after the “release” of the blue water.
Let’s focus on the top view first. In the non-rotating experiment, a dipole of two counter-rotating eddies develops within seconds of the central dense column being released, spreading blue water pretty much all throughout the tank. In the rotating experiment, after a similar amount of time, the dipole looks different: Even though the same amount of dyed water was released, the two eddies are much smaller and much more well-defined.
In the side view, the difference becomes even more clear. In the non-rotating experiment, looking at the boundary between the blue and clear water, we see eddies moving water in all directions, so in combination with the top view, we know that turbulence is three-dimensional.
In the rotating experiment, however, the boundary between blue and clear water looks very different. There is a clear separation between a blue column of water and the clear water surrounding it. From the side view, we don’t see any turbulence. We know, however, from the top view that there is turbulence in the horizontal plane. In the rotating case, turbulence is two-dimensional.
And this is the dramatic difference between rotating and non-rotating fluids: rotating fluids are rigid in a way that non-rotating fluids are not. And this means that they behave in fundamentally different ways: rather than developing in 3 dimensions, they only develop in 2 dimensions. So in order to simulate the atmosphere and ocean of the rotating earth correctly, we need to also rotate our water tank.
P.S.: Images for this post were originally posted in this post (and in other posts linked therein) 5 years ago. Hoping we’ll have new images soon when our new tanks are up and running! :-)
Ekman spirals — current profiles that rotate their direction over depth, caused by friction and Coriolis force — are really neat to observe in a rotating tank. I just found out that they are apparently (according to Wikipedia) called “corkscrew currents” in German, and that’s what they look like, too. I tend to think of Ekman spirals more as an interesting by-product that we observe when stopping the tank after a successful experiment, but they totally deserve to be featured in their own experiments*.
Ekman layers form whenever fluid is moving relative to a boundary in a rotating system. In a rotating tank, that is easiest achieved by moving the boundary relative to the water, i.e. by increasing or decreasing the rotation rate of a tank and observing what happens before the water has adjusted to the new rotation and has reached solid body rotation. Spinning the tank up or down creates high and low pressure systems, respectively, similar to atmospheric weather system.
Creating a low-pressure system: Slowing down the tank
In atmospheric low pressure systems, air moves towards the center of the low pressure system, where it rises, creating the low pressure right there. This situation can probably easiest be modelled by stirring a cup of tea that has some tea leaves still in it. As the surface deforms and water bunches up at the sides, an overturning circulation is set into motion. Water sinks along the side walls and flows towards the center of the cup near the bottom. From there it rises, but any tea leaves or other stuff floating around get stuck in the middle on the bottom because they are too heavy to rise with the current. So there you have your low pressure system!
You can observe the same thing with a rotating tank, except now we don’t stir. The tank is filled with water and spun up to solid body rotation on the rotating table. When the water is in solid body rotation, a few dye crystals are dropped in, leaving vertical streaks as they are sinking to the ground (left plot in the image below).
Then the tank is slowed down. The resulting friction between the water body and the tank creates a bottom Ekman spiral. The streaks of dye that were left when the dye crystals were dropped into the tank move with the water when the tank is slowed down. In the upper part of the tank, the dye stripes stay vertical. But at the bottom, within the Ekman layer, they get deformed as the bottom layer lifts up, and thus show us the depth over which the water column is influenced by bottom friction (see black double arrow in the right plot in the picture below). Again, we have created a low pressure system with a similar overturning circulation as we saw in the tea cup.
In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.
Looking into the tank with a co-rotating camera, we can also observe the Ekman depth, i.e. the depth that is influenced by the bottom: We see a clear distinction between the region where the dye streaks from the falling crystals are still vertical and the bottom Ekman layer, where they are distorted, showing evidence of the friction with the bottom.
So this was what happens when water is spinning relativ to a slower tank (or a non-rotating cup) — the paraboloid surface is adjusting to one that is more even or completely flat. But then there is also the opposite case.
Creating a high-pressure system: Spinning up the tank
If we take water that is at rest and start spinning the tank (or spin a moving tank faster suddenly), we create a high pressure system until we again reach solid body rotation.
Again, we dropped dye crystals when the water was in solid body rotation (or in solid body without rotation) before we start the spinup, as we see in the left plot below.
Now the sudden spinning of the boundaries relative to the body of water creates a high pressure system with the bottom flow outward from the center, which again we see in the deformation of the dye streaks. The Ekman depth is again the depth over which the dye streaks get bent, below the water column that isn’t influenced by friction where they still have their original vertical shape.
In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.
Here is what this experiment looks like in a movie:
So here we have it. High pressure and low pressure systems in a tank!
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?
Turns out building a rotating table isn’t as easy as we had hoped, because my Lazy Susan’s axle is unfortunately really off centre (how did I never notice before?), which makes it pretty difficult to drive it with a grinding wheel, and the LEGO motor we were using only has one speed (which would have to be regulated by changing the diameter of the gears). That makes it really difficult to spin up a tank at rest if you go at it zero to full force…
But we got it to spin! Look at the cool paraboloid surface!
Next issue, though: my awesome glass vase which looks like it should work well as a tank has a really irregular bottom, which makes it very difficult to have anything stand in the centre without too much of a wobble. Also, for the Hadley Circulation experiment we were trying to set up here, when do you add in the cooling in the center? Would be best to do it after the tank is spun up, but that is such a pain to do! And I messed up the dye here, too.
But at least you can see a little bit of what it will be like when we are done, right?
better Lazy Susan
think about how to film it, therefore either have a co-rotating camera or a white background
And then it will be almost ready to be used in teaching. Well, almost…
Funny how tank experiments that you think should be quick and easy to set up & run always take sooo much longer than expected. But it’s so much fun that I really don’t mind! :-)
Can you do a bottom Ekman layer demonstration without a rotating table? That’s the kind of challenge I like :-)
The way I’ve previously showed bottom Ekman layers is by spinning up a cylindrical tank on the rotating table until it reaches solid body rotation, adding dye crystals to visualise the circulation later, and then stopping the tank to create friction at the bottom (and the sides, but we are mainly interested in the bottom since we want a bottom Ekman layer) as the water continues moving but comes under the influence of friction. But what if we just invert the whole thing?
Move the “bottom”, not the water
My initial idea was to use a Lazy Susan (you know, the kind of tray on a swivel base that you can use for your jam and honey etc on your breakfast table, but which you shouldn’t turn too rapidly (ask me how I know)) and to have a cylindrical vase sit on it, which will then be put in rotation and will rotate around and under the (initially still stagnant) water. The friction with the moving vase will then lead to a bottom-intensified circulation.
Problem here: While I have a Lazy Susan at home as well as a vase that would work as “tank”, I am currently in Bergen where I don’t have access to my own equipment. Instead, though, I have access to a rotating table in GFI’s basement which I used to simulate my Lazy Susan idea (Cool, eh? Simulating a non-rotating-table situation on a rotating table ;-)).
The physics themselves obviously work in this setup. However, they will be really difficult to observe for several reasons:
Scales. A small dish (like the one I used; for comparison see the usual tank in the background in the picture above) makes it a lot more difficult to see what’s going on, and in my case the circulation is quickly influenced by the sides of the dish (which is obviously not what we wanted).
Rotation. It’s not difficult to set a Lazy Susan into rotation, but I imagine it will be quite difficult to keep it at a constant rotation for any length of time. But you will only see the nice spiral for as long as you keep the rotation constant. As soon as it changes, so will your currents and that will be clearly visible in the dye (which is why you put it in in the first place).
Documentation. If you want to document your experiment, if want to have your cameras co-rotating with the Lazy Susan, it’s going to be quite difficult to install them (but maybe you would just want one that sits stationary above the center of rotation? That would obviously be easy to do with a tripod)
So all in all: it was a nice idea, but either I haven’t thought it through well enough, or it is a whole lot easier to do with a rotating table. I would imagine that it’s quite hard to observe when you don’t know very well what you are looking for, so it is unfortunately not useful as a demonstration to introduce people to the topic. What do you think? Any suggestions on how to improve this and make it work at home?
You know I like tank experiments, but what I am lucky enough to witness right now is NOTHING compared to even my wildest dreams. Remember all the rotating experiments we did with this rotating table back in Bergen?
Those were awesome, no question about that. But the rotating tank I am at now? 13 meters diameter.
In any case, don’t miss the opportunity to see what is going on in a tank this size:
Yes, they are both INSIDE the tank. Elin (on the left) is sitting on the tank’s floor, Nadine (on the right) is climbing on the topography representing Antarctica. For more details, head over to the blog!