## Fictitious forces (1/5): Record players and Coriolis deflection

An experiment showing how seemingly straight trajectories can be transformed into curly ones.

One of the phenomena that are really not intuitive to understand are fictitious forces. Especially relevant in oceanography: The Coriolis force. The most difficult step in understanding the Coriolis force is accepting that whether or not a trajectory appears straight or curved can depend on the frame of reference it is observed from.

Or to say it with John Knauss in his Introduction to Physical Oceanography: “Even for those with considerable sophistication in physical concepts, one’s first introduction to the consequences of the Coriolis force often produces something analogous to intellectual trauma”.

One way to show that the apparent change of shape is really due to different frames of reference, is to take a trajectory that is objectively AND subjectively straight and watch it being transformed into something curly.

We did this at JuniorAkademie by taping a piece of paper on a record player, putting it into motion and then, at as constant a speed as possible, drawing along a ruler’s edge straight across. (if you don’t have a record player or rotating table at your disposal, you could also use a Lazy Susan and turn it as uniformly as possible).

Of course, this approach has a lot of potential pitfalls. For example, if you change the speed while you draw, you get kinks in your curls (as the child drawing in the video below points out when it happens). Also, by drawing on a flat paper rather than a spherical Earth, this isn’t completely equivalent to the Coriolis force.

And, more importantly, I think this experiment is only helpful for an audience that doesn’t “know” about fictitious forces yet. A problem we have experienced with oceanography students is that they “know” that moving objects should be deflected, and that they “see” a deflection even when there is none (for example when they are watching, from a non-rotating frame of reference, an object move across a rotating table). In that case, sliding the pen along the ruler might be perceived as forcing an otherwise curly trajectory to become a straight line, hence cheating by preventing a deflection that should occur.

## The effects of rotation on a collapsing column

Comparing a rotating and non-rotating dipole.

I just realized that I never explicitly showed the difference between rotation and no rotation, even though I do have the footage to do so: Two experiments set up to create a monopole, which both turned dipole.

In the non-rotating experiment (which was, by the way, set up carefully in preparation for a rotating experiment, but then the v-belt on the rotation table failed [but luckily this was on the last night of the JuniorAkademie, so we had otherwise run everything we had been planning to run], so we ended up with a non-rotating experiment), the dipole shown below develops within seconds of the central dense column being released.

In the rotating experiment, however, this is what the dipole looks like after a similar amount of time:

And we see that in the non-rotating case, the eddies are spreading to fill the whole width of the tank within seconds, whereas in the rotating case the eddies mainly stay confined into their respective columns. This is the often quoted phenomenon of conservation of vorticity in a rotating system, where movements happen mostly in the horizontal plane, whereas in non-rotating system, vertical movements happen easily, too (i.e. the dense water from the upper part of the initial dense column can sink to the bottom of the tank in this case, which it could not do in the rotating case), and turbulence can hence develop in 3D and not only 2D.

For videos of both experiments, please check out the posts on the rotating case and the non-rotating case.

## Simulations of hetonic explosions

Because sometimes it’s easier to control a computer than rotation, salinity, water and dye.

After looking at a non-rotating cylinder collapse the other day, it is time to look at proper hetonic explosions (you know? The experiment on the rotating tank where a denser column of water at the center of the tank is released when the whole tank has reached solid body rotation). In Bergen, we used to show this experiment as a “collapsing column” experiment, the tilting of a frontal surface under rotation. For those cases, all the parameters of the experiment, e.g. the rotation rate, the density contrast, the water height, the width of the cylinder, were set up such as to ensure that one single column would persist in the middle of the tank. At JuniorAkademie, we’ve also run it in other setups, to form dipoles or quadrupoles. For a real hetonic explosion, we would typically go for even more eddies than that.

But if you read through all those posts then, you might remember that I’ve been complaining about how it is really difficult to set up an experiment in such a way that you have total control over the amount of vortices that form. Firstly, because the system is inherently chaotic, but let’s forget about that for a minute. But then because the calculations aren’t that easy for school kids to do, and then even when everything is calculated correctly, water has to be prepared with the correct salinity, the rotation has to be set to the correct period, the cylinder has to be completely centered in the tank, the water level has to be just right and when the cylinder is pulled up, this has to happen with a swift movement as to add as little disturbance as possible. Not an easy task, especially when there is a camera mounted on the tank!

To show us what to expect, Rolf did some model simulations for us. This is what a monopole looks like:

Shown is an isoline in density, separating the dense water below from the lighter water above. Superimposed are the horizontal velocities, so you get a sense of the rotation.

For more advanced experimentalists to recreate, here a dipole:

As for the monopole, you see chimneys that are open on top. That is because the density is higher than the one of the isoline inside the eddy, so you get the impression that you can look inside.

But the picture is different for quadrupoles, here the four eddies (that form when the central column breaks up) do not reach the water surface any more, hence they appear closed in the visualization below.

Btw, the time is of course not measured in weekdays, that’s just a glitch in the visualization that we didn’t fix.

Seeing the simulated situations for the three cases above was quite comforting  after having run this experiment a couple of times. When you run the experiment in a tank, there is always a lot of turbulence that you wish wasn’t there. But it really helps to keep your expectations in check when you see that in the simulation there are always little vortices, trying to break away from the main ones, too, and that that is how it is supposed to be.

So now for an attempted experimental monopole, which turned out as a dipole due to turbulence introduced when removing the cylinder, similarly to what happened to us in the no-rotation collapsing column experiment.

When you watch the side views closely, you can see that the tank appears to be wobbling (which we usually can’t see, because this is the only time we taped a camera to the side of a tank – usually when filming from the side, I film from outside the rotating system, holding the camera in my hand). You see it most clearly when the yellow dye crystals are added – the water is sloshing back and forth, and that is most definitely not how it is supposed to be. Oh, the joys of experimentation! But what is pretty awesome to see there is how the vertical dye streaks get pulled apart into sheets as they get sucked into the vortices. Reminds me of Northern Lights! :-)

## Collapsing column

Or: This is what happens to a hetonic explosion experiment without rotation.

I’ve posted a lot while at JuniorAkademie a while back, so it is hard to believe there are still experiments from that time that I haven’t shown you. But I’ve probably only shown you about half the experiments we’ve done, and there are plenty more in the queue to see the light of day on this blog!

Today I want to talk about hetonic explosions (you know? The experiment on the rotating tank where a denser column of water at the center of the tank is released when the whole tank has reached solid body rotation). In Bergen, we used to show this experiment as a “collapsing column” experiment, the tilting of a frontal surface under rotation. For those cases, all the parameters of the experiment, e.g. the rotation rate, the density contrast, the water height, the width of the cylinder, were set up such as to ensure that one single column would persist in the middle of the tank. At JuniorAkademie, we’ve also run it in other setups, to form dipoles or quadrupoles. For a real hetonic explosion, we would typically go for even more eddies than that.

Today I want to show you this experiment under very special conditions: The no rotation case!

For all of you oceanographers out there who know exactly what that experiment will look like, continue reading nevertheless. For all of you non-oceanographers, who don’t know why some oceanographers might be disappointed by this experiment, continue reading, too!

You see, one of the fundamental assumptions we often make when teaching is that what is exciting to us, the instructor, is exciting to the students, too. And the other way round – that experiments that we might find boring will be boring the students, too. But I often find this to be completely wrong!

In case of the hetonic explosion experiment with no rotation, the experts know what will happen. We pull out the cylinder containing the denser water, so the denser water column will collapse and eventually form a layer of denser water underneath the rest of the water. We know that because we are aware of the differences between rotating and non-rotating systems. However, many students are not. And if you don’t have a strong intuition of how the water will behave, i.e. that in this case you will eventually have two layers, rather than a dense column surrounded by lighter water, it is not terribly exciting when you finally do the rotating experiment and – contrary to intuition – the dense water does not end up below the lighter water. So in order to show you in my next post what to be excited about, today I am showing you the normal, non-rotating experiment:

[vimeo 105481230]

But note that the experiment is not nearly as boring as you might have thought! We had put a lot of vaseline at the bottom of the cylinder to prevent the denser water from leaking out, so when the cylinder was pulled up, it gave an impulse to the dense column, which ended up splitting up into a dipole upon hitting the wall of the tank. Still looks pretty cool, doesn’t it? And for this to be a good teaching video, I really should have continued filming until the layers had settled down. In my defense I have to say that we had a second experiment set up at the other rotating table that we wanted to run, so I had to get the cameras over to the other table… And you’ll see those movies in my next post!

## Double overflow

Because sometimes one overflow simply isn’t enough.

Finn’s group came up with – and ran – an overflow experiment with many different densities and even more colors. While the movie didn’t turn out too well, the idea was pretty awesome.

Rolf went ahead and modeled the experiment right away. And because the plume didn’t go across the second ridge in a dramatic enough fashion, he did the same experiment again, this time with a higher density contrast.

If you compare those two figures, you notice that the second one is a lot more diffusive than the first one. To test whether the model was doing well, we obviously had to run both experiments in the tank, too. Watch the movie below to see how they turned out:

Turns out that also for us, the run with the higher density contrast is a lot more diffusive. Kelvin-Helmholtz-instabilities develop on the first down slope of the first ridge, and generally a lot more mixing is going on. To get an impression of the regions of high mixing and recirculation, rather than guessing from the diffusing salinities, Rolf displayed the horizontal velocity:

Notice the high mixing whenever the plume is running down a slope, and then the recirculations in the valleys. Pretty awesome, huh?

## Cylinder collapse on a cone

Water running uphill during spin-down – how much more awesome can it get?

After hours, when all but the most curious students had left, Rolf and I ran another collapsing cylinder experiment, this time on Rolf’s old disk player turned rotating table.

Rolf has a cone-inset for the round tank, and we set a cylinder on top of the cone and filled it with dyed salt water. The rest of the tank was filled with fresh water and the whole system spun up into solid body rotation. Then the cylinder was pulled out and here is what happened:

The column sat right on top of the cone! And stayed there, and stayed there, and stayed there. Slowly a bottom boundary layer started creeping down the slope, so we decided to add more color.

Nice to see that, for a change, we calculated all the parameters correctly! But then The Boss himself had done the calculations this time round…

But the most fascinating thing happened during spin-down when we had stopped the tank: The column slowly withdrew up the slope again! Our two fascinated students were absolutely wowed (and that’s saying something – they were really impressed with the salt fingers earlier already).

Watch the movie below for some impressions of the experiment.

## Tagebuch – Tag 7

Von Carolin und Marie

Am heutigen Tage wurden auch das Salz, die Dichte und die Wellen endgültig überführt. Das, was jetzt noch alles abschließt, ist die morgige Gerichtsverhandlung.

Darauf haben sich alle Detektive genauestens vorbereitet und sie haben sich überlegt, wer welche Beweise im Gerichtssaal vorstellt. Genauere Details werden aber Morgen noch geklärt.

Die Salzüberführung erfolgte, indem die zugeteilte Lehrlingsgruppe herausfand, wo das Salz seine Finger mit im Spiel hatte. Dieses Experiment nannten sie Salzfinger.

Langsam wurden die drei mutigen Lehrlinge, die schon die ganze Zeit die geheimen Versuche der Meisterdetektive beobachtet hatten, ungeduldig. Als sie den Meisterdetektiven ein weiteres Mal zugeschaut hatten, durften sie sogar selbst Hand anlegen.

Bald müssen sie sich jedoch verabschieden und ihren eigenen Weg durch das gefährliche, aber spannende Leben gehen. Sie werden noch viele weitere hundert Male mit Schiffen zum Tatort reisen und auch noch viele weitere Täter schnappen.

Das war`s für Heute und bis Morgen,

Eure Berichterstatter.

## Salt fingering

My absolute favorite experiment ever: salt fingering.

I know I’ve said it before about another experiment, even today, but this is my absolute favorite experiment and I still get endlessly fascinated. I’ve written about salt fingering before, and given tips on run the experiment, but today we tried a different setup.

We used the same tank as in the “influence of salinity and temperature on density“, put warm, dyed water on the one side of the dam and cold fresh water on the other side.

Contrary to Rolf’s advice, we didn’t aim for specific temperatures and salinities to hit the density ratio in a specific way, but just went for really hot and really cold.

We pulled the parting out, and after a couple of minutes, salt fingers started to develop.

Unfortunately, they are really difficult to take pictures of.

But a lot of students watched and will hopefully remember what they saw.

And even if not – I thought it was awesome and Rolf said they were the best salt fingers he had seen yet – even though we just winged it ;-)

## Hetonic explosion

Trying to tweak conditions to force a set number of vortices.

We’ve done the hetonic explosion again. This time the group was super careful to calculate the Rossby radius correctly, and then to set up the experiment accordingly. We aimed for a single column like in our tilting of a frontal surface under rotation experiment.

We did manage to create one main vortex, but we saw at least two additional smaller vortices. And since we know how vortices are created, it is pretty likely that there were four in total.

But never mind, it is still a very nice experiment that we are happy to do over and over again!

Movies will come up once I have time to actually write the posts – we do have numerical simulations that we want to compare our experiments with. Stay tuned!

## Thermally driven circulation

One of my all-time favorite experiments.

The salt group got a bit bored from watching ice cubes melt, so I suggested they look at temperature differences for a change, and they ran the “leaking bottles” experiment.

Watch a movie combining their four different setups below!