# Tilting frontal surface under rotation / cylinder collapse

Torge and I are planning to run the “tilting of a frontal surface under rotation / cylinder collapse” experiment as “remote kitchen oceanography” in his class on Thursday, so I’ve been practicing it today. It didn’t work out quite as well as it did when Pierre and I were running it in Bergen years ago, so if you are looking for my best movie of that experiment, you should go read the old blog post.

The idea is that a density front is set up by spinning up a tank in which a bottom-less cylinder contains a denser fluid, set up into a less dense fluid. Once the tank is spun up, the cylinder is removed, releasing the denser fluid into the less dense one. In contrast to the non-rotating case, where the dense water would sink to the bottom of the tank and form a layer underneath the less dense water, here the cylinder changes its shape to form a cone that retains its shape. The slope of the front is determined by both the rotation rate and the density contrast.

What I can show you today is what it looks like on my DIYnamics rotating table in my kitchen (and it’s pretty cool that all these different experiments can be run on such a simple setup, isn’t it?!). This is from two weeks ago:

And a second attempt done today (I’m not showing you all the failed ones in between, and since I’m a little sick, I’m also not showing you what I look like, and spare you the sound of my incoherend explanations ;-)). But: Now everything is set up so I can use my right hand to pull out the cylinder to introduce fewer disturbances (spoiler alert: didn’t work out — see all the waves on the tank after I remove the cylinder?)

Check out the flower “floats” — the ones on the remains of the cylinder are rotating in the same direction as the tank, only faster! That’s something we didn’t show in Bergen and that I think is really neat.

What I learned about how to set up the experiment: I filled the cylinder with ice cubes and then filled water into the donut outside of the cylinder. That way, water pressure would push water through the petroleum jelly seal at the bottom of the cylinder inside, but the dye of the melting ice cubes would not seep out (very much). Also, the cold melt water would make the water inside the cylinder denser (make sure to stir!). The whole fancy “get water out and refill using a syringe” stuff sounds nice but just isn’t feasible in my setup…

In this case, having a larger tank would be really helpful, because the disturbances introduced in either case are probably more or less the same, but the smaller the tank, the larger the relative effect of a disturbance… Also, my tripod was making it really difficult for me to reach into the tank without hitting it, both for filling the tank and for removing the cylinder. I guess if we didn’t need a top view, things would be a lot easier… ;-)

# Front-spotting in muddy waters

On a recent flight from Hamburg to London City Airport, I ended up on one of the tiniest planes I’ve ever been on. Which meant that we flew super low, I took tons of pictures out of a not-very-clean window, and all my pictures have at least one propeller blade in them.

But look at what we saw!

For example in the picture below, a plume of muddy water coming from some canal into a river (and I should probably know where this is, but I have no idea. Somewhere between Hamburg and London?). I’m not sure whether the inflowing water itself was muddy to begin with, but I would guess that it is stirring up mud from the bottom of the river since it seems to be low tide and the inflowing water is maybe moving a lot faster than the water in the river itself?

Closer to England we flew across this wind farm, where turbines have mud stripes in their lee. Also pretty interesting. Maybe they change direction with tides?

And then coming to the mouth of the River Thames, there is quite a clear front between outflow and muddy North Sea water.

Going upstream on the River Thames, boats stir up a lot of mud!

So you can clearly see where they went for a pretty long time.

On this flight, I sat next to a professional photographer who rolled his eyes at me taking pictures pretty much non-stop. And yes, they might not be the best quality. But at least you see what I saw, right?

# 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.

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.

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.

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: