Tag Archives: DryTheory2JucyReality

Playing for #FlumeFriday

Yesterday, we’ve had four rotating tables operating simultaneously, for three different experiments. The one that everybody is gathering around in the picture above is our favourite experiment: a slowly rotating tank with cooling in the middle that shows a nice 2D circulation instead of an overturning as we would expect in a non-rotating system.

A second group was doing an Ekman spiral experiment similar to this one.

If you are interested in observing the bottom boundary layer of a tank, it might look a bit weird to people who don’t know what you are up to…

And the other two experiments were the planetary Rossby wave experiments that I’ve written about so much before that it doesn’t really matter that I didn’t take any pictures this time round.

New rotating table on #FlumeFriday! Welcome to the family!

In addition to our four DIYnamics-inspired rotating tanks, we now have a highly professional rotating table with SO MANY options! And also so much unboxing and constructing and trouble-shooting to do before it works. But we finished the first successful test: wanna see some rotating coffee in which milk is added? Then check this out!

Luckily Torge is patient enough to deal with me bossing him around, but it took forever to get the whole thing to work and I wanted my movie ;-)

Before we got to that point, though, did I mention that we had a lot of unboxing and constructing to do? But it was a bit like Christmas… And I can’t wait to play with every last piece of equipment! So many new and fun options for experiments I’ve always been wanting to do!

Happy #FlumeFriday! :-)

Rotating tank experiments on a cone

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?

Thermal forcing in a non-rotating vs rotating case: Totally different results

On Thursday, I wrote about the thermally driven overturning circulation experiment that Torge and I did as past of our “dry theory 2 juicy reality” experiments, and mentioned that it was a non-rotating experiment in a class about rotating fluid dynamics.

I showed you the rectangular tank, but we also used a cylindrical tank with cooling in the middle that is a rotational symmetric version of the “slice” in the rectangular tank. In both cases we see the same: Cold water sinks and spreads at the bottom and is then replaced by warmer water.

But when we start turning the cylindrical tank with the cooling in the middle, cool things start to happen. I’ve blogged about that experiment before, but here is a pic of the circulation that develops. Instead of an overturning, we now get heat transport via eddies!

This is actually a really nice way to show again how hugely important the influence of rotation is on the behaviour of the ocean and atmosphere!

Salt fingers in my overturning experiment

You might have noticed them in yesterday’s thermally driven overturning video: salt fingers!

In the image below you see them developing in the far left: Little red dye plumes moving down into the clear water. But wait, where is the salt? In this case, the “double” in double diffusion comes from heat and dye which are diffusing at different rates. As temperature’s molecular diffusion is about 100x faster than that of salt (or other things that have to physically change their distribution, rather than just bump into each other to transfer energy), the red and clear water quickly have the same temperature, but then the red dye makes the red water more dense, hence it sinks.

Over time, those fingers become more and more clearly visible…

Until after a couple of minutes, we see that they are really contributing to mixing between the two layers.

Even though double diffusive mixing happens in the ocean, too, the scaling of these fingers is of course totally off if we think of this tank as for example the northern half of the Atlantic. But then so is the density stratification… But it’s always good to keep in mind that while this experiment is showing some things quite nicely, there are also things that are artefacts of the way the experiment is set up and that aren’t analogous to how things work in the ocean.

A really nice and very new-to-me way of observing them is from above:

This is a picture that was taken fairly early in the experiment, when the layers hadn’t propagated far yet and the salt fingers weren’t being pulled back by the shear between the layers. But it’s nice to see how the dye is concentrated in those downward moving fingers, isn’t it?

Thermally driven overturning circulation

Today was the second day of tank experiments in Torge’s and my “dry theory 2 juicy reality” teaching innovation project. While that project is mainly about bringing rotating tanks into the theoretical teaching of ocean and atmosphere dynamics, today we started with the non-rotating case of a thermally driven overturning circulation.

Very easy setup: A rectangular glass vase filled with luke-warm water. A frozen cool pack for sports injuries draped over one end (which we’ll think of as the northern end) provides the cooling that we need for deep water formation. The deep water is conveniently dyed blue with food dye. Red food dye is warmed up and added to the “southern end” of the tank, and voilà! An overturning circulation is set up.

Watch the sped-up movie to see what happens:

As you will notice, this circulation won’t last for a very long time. Since we are adding neither warming nor mixing, the cold water will eventually fill up the tank. But it’s still quite a nice experiment!

(And should you have noticed the “salt fingers” forming towards the end of the movie, I’ll write about those tomorrow)

And here is the nice group of students that humoured me and posed for this picture. It’s fun with such a motivated group that comes up with new things to try all the time! :-)

If one rotating table is awesome, four rotating tables are…?

I’m actually at a loss for words. Amazing? Spectacular? So much fun? All of that!

Today was the first time Torge and I tried our four DIYnamics-inspired rotating tables in teaching. (Remember? We want to use 4 rotating tables simultaneously so students can work in small groups rather than watching us present experiments, and also so we could quickly see how slightly different conditions might lead to different results. Having 4 tanks running at the same time cuts down on a lot of spin-up wait time! And we wanted affordable rotating tables so a) we could afford them and b) students would really just be able to play without them, or us, being afraid that they might break something). And it went even better than we had hoped, and we were already pretty convinced that it would be awesome!

It all started out, even before class started, with one of the students asking if it was me who had done the recent takeover of Kiel University’s Instagram account with the awesome tank experiments in Bergen. Yep, that was me, and it was great that she remembered she had seen the experiments and even recognized me! Made me very happy. If I had needed convincing that social media is awesome, here it was!

But then the students started playing, and they got really into it. We started out with just tanks filled with water on the Lazy Susans, and the students moved them by hand to get a feel for how water behaves under rotation. We looked at deformation of surfaces, how confetti as tracers behaved on the surface and on the bottom, all the good stuff. Already with such simple experiments there is so much physics to discuss!

And then we moved on to turbulence in a non-rotating and rotating system. Look at the cool vortex rings you can make with food coloring :-)

And then we moved on to turbulence in the rotating system. Our final tanks haven’t arrived yet, so we made do with whatever we had at hand (see the green bowl as tank below…). Students also started improvising to include a topography and other modifications that we hadn’t planned for. This is so great if students are so keen to figure things out that they take the initiative to make it happen themselves!

Judging from what I could observe, students were really enjoying themselves and got into deep discussions, trying to connect their observations to the theory they had learned. Additionally, there were lots of “oh wow!”s and “coooool”s everywhere. And I overheard this one exchange between two students: “careful, don’t drop the phone into the tank!” “oh, it’s ok, it’s waterproof” “I don’t care about the phone, I don’t want you to mess up the experiment!” :-D

Btw, note below the small Lego motor that drives the Lazy Susan. That’s really the whole setup. Speaking of affordable and easy. And portable. And all-around awesome!

And it was great fun for Torge and me, too, to observe what the students were up to, and to discuss with them. There were already several curious questions as to what experiments we are planning to do throughout the course. The next sessions, Torge will connect the experiments we did today to theory, and start on the theory we need for the next set of experiments we are planning to run, but I can’t wait to continue working with the tank experiments with such a motivated group of students! :-)

Planetary Rossby waves on Beta-plane. A super easy tank experiment!

This is seriously one of the easiest tank experiments I have ever run! And I have been completely overthinking it for the last couple of weeks.

Quick reminder: This is what we think hope will happen: On a slope, melt water from a dyed ice cube will sink, creating a Taylor column that will be driven down the slope by gravity and back up the slope by vorticity conservation, leading to a “westward” movement in a stretched, cyclonic trajectory.

We are using the DIYnamics setup: A LEGO-driven Lazy Susan. And as a tank, we are using a transparent plastic storage box that I have had for many years, and the sloping bottom is made out of two breakfast boards that happened to be a good size.

Water is filled to “just below the edge of the white clips when they are in the lower position” (forgot to take measurements, this is seriously what I wrote down in my notes. We didn’t really think this experiment would work…)

The tank is then rotated at the LEGO motor’s speed (one rotation approximately every 3 seconds) and spun into solid body rotation. We waited for approximately 10 minutes, although I think we had reached solid body rotation a lot faster. But we had a lot of surface waves that were induced by some rotation that we couldn’t track down and fix. But in the end they turned out to not matter.

To start the experiment, Torge released a blue ice cube in the eastern corner of the shallow end. As the ice cube started melting, the cold melt water sank down towards the ground, where it started flowing towards the bottom of the tank. That increased the water column’s positive relative vorticity, which drove it back up the slope.

This was super cool to watch, especially since the ice cube started spinning cyclonically itself, too, so was moving in the same direction and faster than the rotating tank.

You see this rotation quite well in the movie below (if you manage to watch without getting seasick. We have a co-rotating setup coming up, it’s just not ready yet…)

Very soon, these amazing meandering structures appear: Rossby waves! :-)

And over time it becomes clear that the eddies that are being shed from the column rotating with the ice cubes are constant throughout the whole water depth.

It is a little difficult to observe that the structure is really the same throughout the whole water column since the color in the eddies that were shed is very faint, especially compared to the ice cube and the melt water, but below you might be able to spot it for the big eddy on the left.

Or maybe here? (And note the surface waves that become visible in the reflection of the joint between the two breakfast boards that make up the sloping bottom. Why is there so much vibration in the system???)

You can definitely see the surface-to-bottom structures in the following movie if you don’t let yourself be distracted by a little #HamburgLove on the back of the breakfast boards. Watching this makes you feel really dizzy, and we’ve been starting at this for more than the 8 seconds of the clip below ;-)

After a while, the Taylor column with the ice cube floating on top starts visibly moving towards the west, too. See how it has almost reached the edge of the first breakfast board already?

And because this was so cool, we obviously had to repeat the experiment. New water, new ice cube.

But: This time with an audience of excited oceanographers :-)

This time round, we also added a second ice cube after the first one had moved almost all the way towards the west (btw, do you see how that one has this really cool eddy around it, whereas the one in the east is only just starting to rotate and create its own Taylor column?)

And last not least: Happy selfie because I realized that there are way too few pictures like this on my blog, where you see what things look like (in this case in the GEOMAR seminar room) and who I am playing with (left to right: Torge, Franzi, Joke, Jan) :-)

Taylor column in a rotating tank

For both of my tank experiment projects, in Bergen and in Kiel, we want to develop a Taylor column demonstration. So here are my notes on the setup we are considering, but before actually having tried it.

Since water under rotation becomes rigid, funny things can happen. For example if a current in a rotating system hits an obstacle, even if the obstacle isn’t high at all relative to the water depth, the current has to move around the obstacle as if it reached all the way from the bottom to the surface. This can be shown in a rotating tank, so of course that’s what we are planning to do!

We are following the Weather in a Tank instructions:

  • rotating our tank at 5rpm 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 little (they suggest as little as -0.1 rpm) so water moves relative to tank and obstacle, i.e. we have created a current flowing in the rotating system.

As the current meets the obstacle, columns of water have to move around the obstacle as if it went all the way from the bottom to the surface. This is made visible by the paper bits floating on the surface that are also moving around the area where the obstacle is located, even though the obstacle is far down at the bottom of the tank and there is still plenty of water over it.

In the sketch below, the red dotted line indicates a concentric trajectory in the tank that would go right across the obstacle, the green arrows indicate how the flow is diverted around the Taylor column that forms over the obstacle throughout the whole water depth.

Or at least that’s what I hope will happen! I am always a little sceptical with tank experiments that require changing the rotation rate, since that’s what we do to show both turbulence and Ekman layers, neither of which we want to prominently happen in this case here. On the other hand, we are supposed to be changing the rotation rate only very slightly, and in the videos I have seen it did work out. But this is an experiment that is supposedly difficult to run, so we will see…

I also came across about a super cool extra that Robbie Nedbor-Gross and Louis Dumas implemented in this demo: a moving Taylor column! when the obstacle is moved, the Taylor column above it moves with it. Check out their video, it is really impressive! However I think implementing this feature isn’t currently very high on my list of priorities. But it would be fun!

Rossby waves in a rotating tank — three different demonstrations

For both of my tank experiment projects, in Bergen and in Kiel, we want to develop a Rossby wave demonstration. So here are my notes on three setups we are considering, but before actually having tried any of the experiments.

Background on Rossby waves

I recently showed that rotating fluids behave fundamentally differently from non-rotating ones, in that they mainly occur in the horizontal and thus are “only” 2 dimensional. This works really well as long as several conditions are met, namely the water depth can’t change, nor can the rotation of the fluid. But this is not always the case, so when either the water depth or the rotation does change, the flow still tries to conserve potential vorticity and stay 2 dimensional, but now displays so-called Rossby waves.

Here are different setups for Rossby wave demonstrations I am currently considering.

Topographic Rossby wave

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. They use an annulus and introduce the ridge at a random longitude, we could also build one across the center of the tank all the way to both sides to avoid weird things happening in the middle (or introduce a cylinder in the middle to mimic their annulus)
  • spin up the tank to approximately 26 rpm (that seems very fast! But that’s probably needed in order to create a parabolic surface with large height differences)
  • wait for it to reach solid body rotation (ca 10 min)
  • 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
  • introduce dye upstream of the ridge, watch it change from laminar flow to eddies downstream of the ridge (they introduced dye at the inner wall of their annulus when the water was in solid body rotation, before slowing down the tank).

What are we expecting to see?

In case A, we assume that the rotation of the tank is slow enough that the surface is more or less flat. This will certainly not be the case if we rotate at 26rpm, but let’s discuss this case first, anyway. If we inject dye upstream of the obstacle, the dye will show that the current is being deflected as it crosses the ridge, to one direction as the water columns are getting shorter as they move up the ridge, then to the other direction when the columns are stretched going down the obstacle again. Afterwards, since the water depth stays constant, they would just resume a circular path.

In case B, however, we assume a parabolic surface of the tank, which we will have for any kind of fast-ish rotation. Initially, the current will move similarly to case A. But once it leaves the ridge, if it has any momentum in radial direction at all, it will overshoot its circular path, moving into water with a different depth. This will then again expand or compress the columns, inducing relative vorticity, leading to a meandering current and eddies downstream of the obstacle (probably a lot more chaotic than drawn in my sketch).

So in both cases we initially force the Rossby wave by topography at the bottom of the tank, but then in case B we sustain it by the changes in water depth due to the sloping surface.

My assessment before actually having run the experiment: The ridge seems fairly easy to construct and the experiment easy enough to run. However what I am worried about is the change in rotation rate and the turbulence and Ekman layers that it will introduce. After all, slowing down the tank is what we do create both turbulence and Ekman layers in demonstrations, and then we don’t even have an obstacle stuck in the tank. The instructions suggest a very slight reduction in rotation, so we’ll see how that goes…

Planetary Rossby waves on beta-plane

If we want to have more dramatic changes in water depth H than relying on the parabolic shape of the surface, another option is to use a rectangular tank and insert a sloping bottom as suggested by the Weather in a Tank group here. We are now operating on a Beta plane with the Coriolis parameter f being the sum of the tank’s rotation and the slope of the bottom.

Following the Weather in a Tank instructions, we plan to

  • fill a tank with a sloping bottom (slope approximately 0.5)
  • spin it at approximately 15 rpm until it reaches solid body rotation (15-20 minutes later)
  • place a dyed ice cube (diameter approximately 5 cm) in the north-eastern corner of the tank

What do we expect to see?

Ice cube and its trajectory (in red) on a sloping bottom in a rotating tank. Note: This sketch does not include the melt water water column!

Above is a simplified sketch of what will (hopefully!) happen. As the ice cube starts melting, melt water is going to sink down towards the sloping bottom, stretching the water column. This induces positive relative vorticity, making the water column spin cyclonically. As the meltwater reaches the sloping bottom, it will flow downhill, further stretching the water column. This induces more positive relative vorticity still, so the water column, and with it the ice cube, will start moving back up the slope until they reach the “latitude” at which the ice cube initially started. Having moved up the slope into shallower water, the additional positive vorticity induced by the stretching as the water was flowing down the slope has now been lost again, so rather than spinning cyclonically in one spot, the trajectory is an extended cycloid.

My assessment here (before having run it): I find this experiment a little more unintuitive because there are the different components of stretching contributing to the changes in relative vorticity. And from the videos I’ve seen, we don’t really get a clear column moving, but there are cyclonic eddies in the boundary layer that are shed. So I think this might be more difficult to observe and interpret. But I am excited to try!

Planetary Rossby wave on a cone (cyclical beta-plane?)

Following the Weather in a Tank instructions, we plan to also do the experiment as above but with cyclical boundary conditions, by using a cone in a cylindrical tank instead of a sloping bottom in a rectangular one.

The experiment is run in the same way as the one above (except they suggest a slightly slower rotation of 10 rpm). Physics are the same as before, except that now the transfer to reality should be a little easier, since we now have Rossby waves that can really run all the way around the pole. Also the experiment can be run for a longer time, since we don’t run into a boundary in the west if we are moving around and around the pole.

Ice cube and its trajectory (in red) on a cone in a rotating tank. Note: This sketch does not include the melt water column!

My assessment before actually having run the experiment: This shouldn’t be any more difficult to run, observe or interpret than the one above (at least once we’ve gotten our hands on a cone). Definitely want to try this!