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.

A dipole created by releasing a column of dense water in the middle of a non-rotating tank.

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.

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Students watching the experiment shown below. We put paper on the outside of the tank because all the feet swiping past are kind of distracting on the movie later, but that is obviously really annoying for live observers. But in our defense – we only did this once for one experiment late one evening, and didn’t expect so many people to be interested in the experiment! Plus they got to watch on the tablet which showed the top-camera’s view via WiFi… ;-)

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! :-)

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 setting up the experiment

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:

Column sitting on top of the cone!

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.

Still only one column on top of the cone

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…

The column creeping back up the slope during spin-down

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.

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!

Hadley cell circulation – slow rotation

In order to not be in the eddying regime, this time we are rotating our tank as slowly as possible.

Since we ran the Hadley cell experiment the other day, I’ve been obsessed with running it again, this time with the slowest rotation possible in order to visualize a different flow regime – one were the heat transport happens through an overturning circulation rather than through eddies.

Unfortunately the camera we had mounted above the tank only started up halfway through the experiment (no idea how that happened!), so today you’ll only get snippets of this experiment. But all the more reason for us to run it again soon!

And I promise you’ll get a discussion of the differences between this and the Hadley cell experiment with the higher rotation rate soon. I just don’t have the time or mental space to write more than a couple of incoherent sentences while I’m still at the JuniorAkademie

Hetonic explosion

Or, an experiment on this blog often known as “slumping column”. (deutscher Text unten)

If you don’t scale your tilting of frontal surfaces under rotation experiment correctly, you get a phenomenon called “hetonic explosion”: the formation of a cloud of baroclinic point vortices. From the densities, the rotation rate, the dimensions etc you can calculate the Rossby radius and determine how many eddies you will generate. In our case, though, the calculation went wrong by a factor 10 (9.81, to be precise) and what we ended up getting is shown below.

Watch the movie below for the whole experiment (though most of it in time lapse).

Heute haben wir ein sehr spannendes Experiment gemacht. In einem Drehtank hatten wir in der Mitte einen Zylinder mit gefärbten Salzwasser und außen herum klarer Süßwasser ins Gleichgewicht gedreht. Dann wurde der Zylinder entfernt und die Säule blauen Wassers musste ein neues Gleichgewicht finden.

Im Film oben zeigen wir das Experiment – zum Teil allerdings im Zeitraffer. Viel Spaß!

Tilting of a frontal surface under rotation

Eddy in a rotating tank.

This is an experiment that Pierre and I ran two years ago in Bergen but that – as I just realized – has not been featured on this blog before. Which is a pity, because it is a pretty cool experiment.

Under rotation, vertical fronts with different densities on either side can persist for a long time without leading to the density-driven adjustment shown in the non-rotating Marsigli experiment. This is what we demonstrate with this experiment.

In a not-yet-rotating tank, dyed salt water is filled into a centered cylinder while, at the same time, fresh water is filled in the tank outside of the cylinder.

This setup is then spun up for approximately half an hour. Then, the cylinder can be carefully removed and the column of dense water can adjust to the new conditions.

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The rotating tank just as the cylinder is being removed

When the cylinder is being removed, disturbances are being introduced. Hence, several columns with sloping fronts develop in the rotating system.

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Dense columns developing towards an equilibrium state in the rotating system.

This is what the rotating tank looks like from the side several minutes after the cylinder has been removed.

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Side view of the sloping front around the dense column

Here are a couple of movies of this experiment. First a top view (note how you can see the deformation of the surface when you focus on the reflection of the ceiling lights on the water’s surface!):

Then a side view:

And finally (just because it’s fun) this is what it looks like when you switch off the rotation of the tank when you are done with the experiment: