# Ekman layers in my kitchen

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 Ekman layers. 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 stopping a tank that was spun up into solid body rotation, to watch a bottom Ekman layer develop. Follow along for the whole journey:

Now. What are you curious about? What would you like to try? What would you do differently? Any questions for me? :-)

# Demonstrating Ekman layers in a rotating tank: High pressure and low pressure systems!

Ekman spirals — current profiles that rotate their direction over depth, caused by friction and Coriolis force — are really neat to observe in a rotating tank. I just found out that they are apparently (according to Wikipedia) called “corkscrew currents” in German, and that’s what they look like, too. I tend to think of Ekman spirals more as an interesting by-product that we observe when stopping the tank after a successful experiment, but they totally deserve to be featured in their own experiments*.

Ekman layers form whenever fluid is moving relative to a boundary in a rotating system. In a rotating tank, that is easiest achieved by moving the boundary relative to the water, i.e. by increasing or decreasing the rotation rate of a tank and observing what happens before the water has adjusted to the new rotation and has reached solid body rotation. Spinning the tank up or down creates high and low pressure systems, respectively, similar to atmospheric weather system.

# Creating a low-pressure system: Slowing down the tank

In atmospheric low pressure systems, air moves towards the center of the low pressure system, where it rises, creating the low pressure right there. This situation can probably easiest be modelled by stirring a cup of tea that has some tea leaves still in it. As the surface deforms and water bunches up at the sides, an overturning circulation is set into motion. Water sinks along the side walls and flows towards the center of the cup near the bottom. From there it rises, but any tea leaves or other stuff floating around get stuck in the middle on the bottom because they are too heavy to rise with the current. So there you have your low pressure system!

You can observe the same thing with a rotating tank, except now we don’t stir. The tank is filled with water and spun up to solid body rotation on the rotating table. When the water is in solid body rotation, a few dye crystals are dropped in, leaving vertical streaks as they are sinking to the ground (left plot in the image below).

Then the tank is slowed down. The resulting friction between the water body and the tank creates a bottom Ekman spiral. The streaks of dye that were left when the dye crystals were dropped into the tank move with the water when the tank is slowed down. In the upper part of the tank, the dye stripes stay vertical. But at the bottom, within the Ekman layer, they get deformed as the bottom layer lifts up, and thus show us the depth over which the water column is influenced by bottom friction (see black double arrow in the right plot in the picture below). Again, we have created a low pressure system with a similar overturning circulation as we saw in the tea cup.

In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.

Looking into the tank with a co-rotating camera, we can also observe the Ekman depth, i.e. the depth that is influenced by the bottom: We see a clear distinction between the region where the dye streaks from the falling crystals are still vertical and the bottom Ekman layer, where they are distorted, showing evidence of the friction with the bottom.

So this was what happens when water is spinning relativ to a slower tank (or a non-rotating cup) — the paraboloid surface is adjusting to one that is more even or completely flat. But then there is also the opposite case.

# Creating a high-pressure system: Spinning up the tank

If we take water that is at rest and start spinning the tank (or spin a moving tank faster suddenly), we create a high pressure system until we again reach solid body rotation.

Again, we dropped dye crystals when the water was in solid body rotation (or in solid body without rotation) before we start the spinup, as we see in the left plot below.

Now the sudden spinning of the boundaries relative to the body of water creates a high pressure system with the bottom flow outward from the center, which again we see in the deformation of the dye streaks. The Ekman depth is again the depth over which the dye streaks get bent, below the water column that isn’t influenced by friction where they still have their original vertical shape.

In the bottom right corner of the image above, we see a top view of the tank with the trajectory the dye is taking from the spot where it rested on the ground before the rotation of the tank changed.

Here is what this experiment looks like in a movie:

So here we have it. High pressure and low pressure systems in a tank!

*Which I actually did before, both in a rotating tank as well as on a Lazy Susan.

# Bottom Ekman layer without a rotating table

Can you do a bottom Ekman layer demonstration without a rotating table? That’s the kind of challenge I like :-)

The way I’ve previously showed bottom Ekman layers is by spinning up a cylindrical tank on the rotating table until it reaches solid body rotation, adding dye crystals to visualise the circulation later, and then stopping the tank to create friction at the bottom (and the sides, but we are mainly interested in the bottom since we want a bottom Ekman layer) as the water continues moving but comes under the influence of friction. But what if we just invert the whole thing?

# Move the “bottom”, not the water

My initial idea was to use a Lazy Susan (you know, the kind of tray on a swivel base that you can use for your jam and honey etc on your breakfast table, but which you shouldn’t turn too rapidly (ask me how I know)) and to have a cylindrical vase sit on it, which will then be put in rotation and will rotate around and under the (initially still stagnant) water. The friction with the moving vase will then lead to a bottom-intensified circulation.

Problem here: While I have a Lazy Susan at home as well as a vase that would work as “tank”, I am currently in Bergen where I don’t have access to my own equipment. Instead, though, I have access to a rotating table in GFI’s basement which I used to simulate my Lazy Susan idea (Cool, eh? Simulating a non-rotating-table situation on a rotating table ;-)).

That worked quite well, didn’t it?

This, btw, is what the setup looked like:

# So how would that work as kitchen oceanography without an actual rotating table?

The physics themselves obviously work in this setup. However, they will be really difficult to observe for several reasons:

• Scales. A small dish (like the one I used; for comparison see the usual tank in the background in the picture above) makes it a lot more difficult to see what’s going on, and in my case the circulation is quickly influenced by the sides of the dish (which is obviously not what we wanted).
• Rotation. It’s not difficult to set a Lazy Susan into rotation, but I imagine it will be quite difficult to keep it at a constant rotation for any length of time. But you will only see the nice spiral for as long as you keep the rotation constant. As soon as it changes, so will your currents and that will be clearly visible in the dye (which is why you put it in in the first place).
• Documentation. If you want to document your experiment, if want to have your cameras co-rotating with the Lazy Susan, it’s going to be quite difficult to install them (but maybe you would just want one that sits stationary above the center of rotation? That would obviously be easy to do with a tripod)

So all in all: it was a nice idea, but either I haven’t thought it through well enough, or it is a whole lot easier to do with a rotating table. I would imagine that it’s quite hard to observe when you don’t know very well what you are looking for, so it is unfortunately not useful as a demonstration to introduce people to the topic. What do you think? Any suggestions on how to improve this and make it work at home?