Thermal forcing vs rotation tank experiments in more detail than you ever wanted to know

This is the long version of the two full “low latitude, laminar, tropical Hadley circulation” and “baroclinic instability, eddying, extra-tropical circulation” experiments. A much shorter version (that also includes the end cases “no rotation” and “no thermal forcing”) can be found here.

Several of my friends were planning on teaching with DIYnamics rotating tables right now. Unfortunately, that’s currently impossible. Fortunately, though, I have one at home and enjoy playing with it enough that I’m

1. Playing with it
2. Making videos of me playing with it
3. Putting the videos on the internet
4. Going to do video calls with my friends’ classes, so that the students can at least “remote control” the hands-on experiments they were supposed to be doing themselves.

Here is me introducing the setup:

Today, I want to share a video I filmed on thermal forcing vs rotation. To be clear: This is not a polished, stand-alone teaching video. It’s me rambling while playing. It’s supposed to give students an initial idea of an experiment we’ll be doing together during a video call, and that they’ll be discussing in much more depth in class. It’s also meant to prepare them for more “polished” videos, which are sometimes so polished that it’s hard to actually see what’s going on. If everything looks too perfect it almost looks unreal, know what I mean? Anyway, this is as authentic as it gets, me playing in my kitchen. Welcome! :-)

In the video, I am showing the two full experiments: For small rotations we get a low latitude, laminar, tropical Hadley circulation case. Spinning faster, we get a baroclinic instability, eddying, extra-tropical case. And as you’ll see, I didn’t know which circulation I was going to get beforehand, because I didn’t do the maths before running it. I like surprises, and luckily it worked out well!

Thermal forcing vs rotation

The first experiment we ever ran with our DIYnamics rotating tank was using a cold beer bottle in the center of a rotating tank full or lukewarm water. This experiment is really interesting because, depending on the rotation of the tank, it will display different regimes. For small rotations we get a low latitude, laminar, tropical Hadley circulation case. Spinning faster, we get a baroclinic instability, eddying, extra-tropical case. Both are really interesting, and in the movie below I am showing four experimentsm ranging from “thermal forcing, no rotation”, over two experiments which include both thermal forcing and rotation at different rates to show both the “Hadley cell” and “baroclinic instability” case, to “no thermal forcing, just rotation”. Enjoy!

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!

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!

Experiment: Eddy in a jar

Eddies, those large, rotating structures in the ocean, are pretty hard to imagine. Of course, you can see them on many different scales, so you can observe them for example in creeks, as shown below:

Eddies in the Pinnau river, and their dark “shadows”.

If you can’t really spot them in the image above, check out this post for clues and a movie.

So how can you create eddies to observe their structure?

Dye spiral caused by an eddy in a jar

I took a large cylindrical jar, filled it with water, stirred, let it settle down a little bit and then injected dye at the surface, radially outward from the center. Because the rotating body of water is slowed down by friction with the jar, the center spins faster than the outer water, and the dye streak gets deformed into a spiral. The sheet stays visible for a very long time, even as it gets wound up tighter and tighter. And you can see the whole eddy wobble a bit (or pulsate might be the more technical term) because I introduced turbulence when I stopped stirring.

Watch the movie below if you want to see more. Or even better: Go play yourself!

P.S.: This text originally appeared on my website as a page. Due to upcoming restructuring of this website, I am reposting it as a blog post. This is the original version last modified on November 27th, 2015.

I might write things differently if I was writing them now, but I still like to keep my blog as archive of my thoughts.

Of swirls, eddies and fairy dust

Similarly to last Friday’s Kelvin-Helmholtz instabilities, observing swirls and eddies made from green fairy dust is not really what we are in Grenoble for. But are they pretty!

And it is actually very interesting to observe the formation of eddies. If you look at the picture above and focus on the sharp edge “downstream” of the canyon, you see that there are some small instabilities forming there that detach as eddies. And in the picture below you see that there are more, and larger ones, a little while later.

And below you see how they have grown into larger eddies.

And in the gif below you see that the structures of those eddies inside the canyon are actually coherent throughout the uppermost three layers (which are the only ones in which the shelf is lit, for the lower three layers we can just observe what’s going on deeper than the depth of the canyon). So a nice and barotropic flow, just like we had hoped!

Don’t those eddies look just like phytoplankton patches observed from a satellite?

Creating eddies

I always love watching paddles in water, or ships in water, or ducks in water, or anything water, really, but on a wind-less day in Ratzeburg, Siska managed to create the beautiful eddies you see in the movie below, that survived well over half a minute out in the open lake! Beautiful.

Diving ducky and resulting eddies

My sister and I did a little sight-seeing tour in Hamburg the other day, and one of the most fascinating things I saw was — a diving duck. Now, that is not a reflection of how exciting the rest of Hamburg is, but if you don’t see it after watching the movie below, when you read the upcoming blog post on Friday, you’ll understand why this was so exciting to watch :-)

[vimeo 131966138]

I’ll give you a hint:

Diving duck :-)