Tag Archives: DryTheory2JucyReality

Parabolic surface shape of a tank of water in solid body rotation

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One of the first exercises Torge and I plan on doing with the students in our “dry theory to juicy reality” project is to bring a water-filled tank to solid body rotation and measure rotation, surface height at the center of the tank and the sides, as well as water depth before rotation, and then have them put those together according to theory.

Setup of the experiment as we did it using a glass vase my mom gave me as tank (diameter 24.5 cm). The non-rotating water depth was 9.2 cm. Once we rotated the tank with 10 rotations per 8.6 seconds, the maximum water level at the outside edge of the tank was approximately 10.8 cm, and the minimum 7.9 cm.

Seeing how difficult it is to “measure” the surface heights while the tank is rotating (we chose to draw circles on the outside of the tank at the heights where we thought the water levels were, in order to measure them later on a non-rotating tank), we were quite pleased with those results once we plugged them into the equations.

Calculating the resting water level as arithmetic mean between the rotating maximum value at the rim and the minimum value in the center, we are only off by 0.1 cm, so not too shabby!

And calculating the height difference between resting water level and rotating maximum level from the tangential velocity and radius of the tank, we are only off by 0.4 cm. So all in all, that’s working well!

Btw, below you see the resting water level and above the mark for the rotating maximum value. Quite impressive difference, isn’t it?

Anyway, looking at rotational surfaces and volumes and stuff this way is a lot more fun than doing it the dry theoretical way only! At least that’s what I think ;-)

Rotating vs non-rotating turbulence — now with movie!

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Lots of demonstrations being prepared for Torge’s and my “dry theory to juicy reality” project. Shown here today: rotating vs non-rotating turbulence. Because the only way to really appreciate how amazing rotating flows are is to compare them with non-rotating ones. And not everybody does have a clear idea what non-rotating flows would even look like.

So here we are dropping dye into a non-rotating tank. Top view shows it forming tons of small eddies and spreading to the sides.

Side view shows that most of the dye sank to the bottom of the tank and is spreading there, showing 3-dimensional turbulence.

Now, for comparison, the rotating case!

Top view shows one single, clean eddy.

And side view shows that the structure is coherent all the way from surface to bottom. Now doesn’t this look really fascinatingly different from the non-rotating case?

To show the difference even more clearly, check out the movie below. Speed of both movies is the same!

 

Spinning dye curtain — when a tank full of water has not reached solid body rotation yet

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With all the rotating tank experiments I’ve been showing lately, one thing that comes up over and over again is the issue of solid body rotation.

On our DIYnamics-inspired turntable for our “dry theory to juicy reality” project, Torge and I came up with a fun way to illustrate the importance of full body rotation in tank experiments, again inspired by the DIYnamics team, this time their youtube channel.

For the spinning dye curtain experiment, we start up the rotating table, and then pretty much immediately add in some dye. Below, you see what happens when you add in the dye too late (we waited for 2 minutes here before we added it): The water is so much in solid body rotation already, that we only form columns and 2D flow.

But if we add in the dye right away after starting up the tank, we form these spirals where the water further away from the center is spinning faster than the water right at the center, thus distorting the dye patches into long, thin filaments (Btw, I’ve shown something similar in my “eddies in a jar” experiment earlier, where instead of starting up a turntable I just stirred water in a cylindrical tank).

But as the tank continues to spin up, the eddies eventually stop spinning and the tank turns into solid body rotation. If new dye is added now, only columns form, but they stay intact as if they were, indeed, solid bodies.

But seeing the behaviour of a fluid change within half a minute or so is really impressive and something we definitely want to do in class, too!

Baroclinic instabilities / Hadley cell circulation in a tank

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The DIYnamics-inspired turntable that Torge and myself have been working on for our “dry theory to juicy reality” project is finally working well!

This is what the setup now looks like (how simple is that?!) and we had an exciting morning testing different experiments!

The one experiment that we have been using as test case in all our previous sessions is the Baroclinic Instability / Hadley cell circulation. There are sketches of the setup and the expected circulation in this blogpost, so just a quick reminder: We place a cold core in the center of our tank (here a glass with blue ice in it), spin the tank (at approximately 20rpm) into solid body rotation, and introduce dye (blue towards the center, red towards the outer edge of the tank).

And what happens then is just beautiful: We get 2D instabilities that transport cold (blue) water outwards and warmer (room-temperature, red) water towards the center of the tank.

We’ve run the experiment three times with different water levels (and once with Southern Hemisphere rotation just for fun) and it worked beautifully each time.

I find it always fascinating how there is hardly any mixing between the red and blue curtains (and there shouldn’t be any because rotating flows become 2D (as shown here)).

Just look at how the dye curtains form when we first add the blue dye…

And then a little later added some red dye…

And then let the field develop.

So I think we’ve got this experiment down and can run it with the students once the semester starts up again in October! :-)

Combining rotation of a water tank with a temperature gradient: A Hadley cell circulation demo!

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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!

 

Combining a slowly rotating water tank with a temperature gradient: A thermal wind demonstration!

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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! :-)

Why do we need a rotating tank to study ocean and atmosphere dynamics? A demonstration

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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! :-)

Demonstrating Ekman layers in a rotating tank: High pressure and low pressure systems!

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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!

*Which I actually did before, both in a rotating tank as well as on a Lazy Susan.

Funded! “Ocean currents in a tank: from dry theory to juicy reality”

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Remember how Joke, Torge and I were working on building an affordable, home-made rotating tank to use in ocean dynamics teaching only last weekend? That session was inspired by a proposal that Torge submitted a while back, and which now got funded by PerLe, Kiel University’s project for successful teaching and learning (German abstract here). This is really exciting, it not only gives us official permission to play (well, someone will have to build the rotating tables and test the experiments, right?), it will also fund the collaboration and materials. Exciting!

We are planning to add hands-on experiments to the Bachelor-level “atmosphere and ocean dynamics” course at GEOMAR over the next year, but since there is no rotating table available, we want to build several (!) so several student groups can work on them at the same time. And you know me — what we do there will be documented and shared online not only by myself, but also by the students. So stay tuned, I see a lot of rotating tank experiments in our future! :-)

This is the kind of stuff we are going for (picture below shows old Hadley cell experiments from 2014)… Not quite there yet, but we will get there!

Working on our own affordable rotating table for oceanographic experiments!

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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?