Tag Archives: DryTheory2JucyReality

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!

Spin down — lots of shear instabilities in our tank!

When you stop a rotating tank, lots of stuff happens and it is usually very impressive to watch. Sometimes we stop tanks on purpose to show for example the development of Ekman layers, but sometimes we are just done with an experiment and then get to see cool stuff to see just as part of cleaning up.

Like below: When the tank stops, the water inside continues to spin, but friction with the sides and the bottom of the tank starts slowing the water down, inducing shear. Shear in turn produces turbulence and the structures cause smaller and smaller eddies. Very cool to watch!

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

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!

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

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

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! :-)