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.

Involuntary #dropphotography today

When I decided that I was going to stop under a tree for a while to let the shower of rain pass before heading home, the weather looked like this.

Not even half a minute later, I was very happy I had stopped! Because the wave watching got a lot better as the wind drove larger wave over the lake, and also because the rain got a lot heavier and I was semi-dry under the tree. But that makes for some fun drop photography!

All those little wave rings look so cool!

And it’s impressive how a little wind quickly changes the wave field on the lake, too.

Foggy morning in Kiel and thoughts on the accessibility of the images I post

I don’t want to do the actual statistics, but it feels like most of what I post is completely dependent on people being able to see the images I post. Of course, that’s kind of the idea of the wave watching that I do: To show you waves the way you might encounter them, too, and then explain what you see.

But a foggy morning run and my dad’s recent eye surgery have made me think about accessibility of my blog posts, and that it must be extremely dissatisfying to just read / listen to a constant “See? And look here! See here?” without having any idea of what is going on.

In the image below, for example, you see Kiel fjord on a foggy morning, and it’s not really clear where the grey water changes into grey sky. The other shore can kind of be guessed in the right side of the picture, but all the landmarks that you would typically see, like the light house at Falckenstein or the Memorial thingy in Laboe, are swallowed up in the fog.

Or even more dramatic on the next picture: We see the sea front road on one side of the picture and the sea on the other, and both vanish into fog. The whole naval port is missing because it’s so foggy. There are two cars appearing out of the fog, and a cyclist about to be swallowed.

So I have decided that I need to work on my blog’s accessibility, and I am telling you this hoping that you will hold me accountable. And I am hoping for your input on this: I know that the alt text options on both blogs as well as Twitter and Instagram are there for accessibility reasons. But do people really use those, or would it be as helpful to write good figure captions going forward? Is using the same text in both the figure caption and alt text a good option or is that really annoying to people using a screen reader, because they now have to listen to it twice? What’s the best practice that you’ve seen?

Lüneburg — how a few centimetres in distance separate two seemingly completely different bodies of water

Sightseeing is best when it involves a little water watching, like for example last weekend in Lüneburg.

Doesn’t it look intriguing below, the change from a calm, mirror-like surface to something a lot less regular on the other side of the bridge?

Take it in: so peaceful! Although, judging by the plants growing in the water and by how they look like someone took a rake and put them in order, there must be a substantial current going through underneath the bridge.

And turns out there is: The bridge is a weir and there is a waterfall on the other side!

I find it so fascinating how the appearance of water can change literally over the distance of a few centimetre. So calm on one side, and boiling, spraying, turbulent on the other!

And then just a couple meters further downstream, we are back to mainly calm and only a few bubbles floating along give you an indication of what just happened upstream…

And again, no matter how peaceful everything looks here, the water plants tell us that there is still a lot of water moving, bending the leaves with it.

Do you look at this kind of things when sightseeing, too?

Understanding ocean physics using different senses: Making waves in a sandpit

For me, participating in the Science in Public conference was so inspiring! Not only because of the conference itself, but also because of the people I met there.

In a conversation about wave watching and how it can be done with kids, Felipe suggested to ask the kids to make wave models for them to discover waves with different senses and also build more defined mental models. Also these models could act well as conversation pieces to discuss different features that different kids might include.

I think he initially envisioned clay models, but I immediately saw the effect that would have on my flat (no! I cannot have every surface covered in clay wave models that I make or people give me!) and thought about sandpits instead. Easily available on most playgrounds, the “sculptures” don’t invite to be kept and stored, and also handling is very quick and easy.

So this morning, I set out to do a pilot.

Here is my first attempt of waves approaching the shore, getting steeper and steeper and finally breaking.

What this model doesn’t include, which I should really include next time, but this time I got chased away by tons of little kids: How the wave length gets shorter as the waves get higher.

Which you see, for example, when you look at waves that approach a shallow beach and get refracted towards it (see my model of that below).

Another phenomenon that worked really well in the sandpit: Interference of waves. Below you see the model (my feet for scale). Here I first made the horizontal lines just using my fingers, and then for the second wave field, I let some sand trickle through my fingers to have equal amounts of sand deposited over distance along the lines perpendicular to the first wave field.

And if you look at this from a smaller angle, you see that the areas where wave crests meet are highest — the typical interference pattern of waves.

But even with less effort, cool things can happen: See below my “ring waves radiating out from a point source” model.

This was definitely fun and actually a lot more educational than I would have expected, even for me as someone who has been thinking about waves a lot over the years. When representing wave fields, there are so many things to consider and you actually need to observe fairly carefully (or understand the physics really well) to be able to represent a snapshot of a moving water surface. So I see tons of potential here (especially since you don’t even have to do it in a sandpit, you could do it at the beach where you can observe waves simultaneously!), now I just need to figure out how I want to include it in a bigger concept. But such a cool idea, thanks Felipe!

What are you thinking about now? Do you want to start doing your scicomm in a sandpit, too? Any suggestions for me or ideas that might inspire new things?

Seeing the world with different eyes

My not-so-new-anymore job, GEO-Tag der Natur,’s goal is to help people see nature around us through different eyes. In order to enrich people’s lives, but also in order to encourage and empower people to protect nature, for which a necessary first step is to start noticing everything that is there and worth protecting. We do that by providing opportunities for interactions between laypeople and experts (my personal favourite biologists? Definitely @nena_weiler & @fraubioke!), who then engage in some sort of activity related to biodiversity together.

And we see positive effects of all these interactions all the time within the project, but now it has also invaded my personal life: Instead of focussing the picture (or even my attention!) on the waves like I usually do, I climbed where I should probably not have been climbing and took pictures of a butterfly! And another insect! And more butterflies!

And even though I am still more interested in waves and physics than in critters, I love how seeing the world with different eyes is enriching my life and making me take different kinds of pictures than what I am used to. It’s nice to see that my project does have these kinds of effects, not only on our intended audience, but also on myself (and, self-reportedly, also my colleagues!), and I can’t wait to get into creating an even more awesome event for next year!

Walk to & visit at GEOMAR as wave watching occasion

These very long and regular wave crests were caused by a ship — they are one side of the V of a ship’s wake that’s about to reach the sea wall here.

I love how well defined the wave crests are — on one side you see the reflection of the bollards and the bright sky, on the other side the reflection of the dark sea wall.

Below you can see the waves approaching the sea wall and then their reflection:

And I realized that it’s a very good thing I didn’t own a smartphone when I was still working at GEOMAR, otherwise you’d be completely fed up by these kinds of pictures by now :-)

For the rest of this post: More pictures of more wakes as seen from the roof top terrace, which very nicely show you the V-shape…

I just love how you see the “feathers” that, together, make up the V-shaped wake.

And several wakes on top of each other…

And below you see the turbulent wake in the middle of the V as a lighter line where the surface appears smooth due to turbulence.

 

 

Lake District #wavewatching

The first wave watching during our vacation in the Lake District (which I am only writing about now because I had to post about the amazing stuff at the coast first, like the Arnside tidal bore or general wave watching in Arnside) happened on the drive to our first hike when we had to stop because I get car sick on narrow, windy roads, especially driving on the wrong side of the road. So we stopped at this lake to see this wave pattern:

One thing is clear: Those waves are wakes. You see this from how long the wave crests are, how they trace each other, how there isn’t a spectrum of similar wavelengths but just that one wave field and then much much shorter wind waves.

But I wasn’t able to figure out why they looked the way they do until I saw what caused them: Someone trying to pull someone else on water skis, except the second person kept falling in and letting go of the leash, the first person then slowing down, circling back, handing the leash over, and all starting over again.

I’m showing you this just because sometimes wave watching isn’t easy at all, even though the wave field looks very well defined…

But moving on to lakes we saw during our hike, and wave watching on those. Actually, mainly showing you landscape, but there are always at least some waves in the pictures, which I will point out to you.

Below, in the lower left of Loughrigg Tarn, you see a swan’s wake!

And another one!

And below, you see wave rings radiating from where kids are playing in the water.

Below, a very cool W-shaped wake. Usually we have V-shaped wakes, but in this case, the swimmer turned around and went back, so a W developed. Very cool, I don’t think I have seen something like this before!

Below there is a swimmer’s V-shaped wake, and then the ring waves from someone playing in the water.

Another wake by a duck…

And another one!

And in the picture below I just love the calm surface in the left and then the turbulence downstream of the obstacles!

More pretty turbulence…

And below we see wave rings made by water striders.

And another wake on another “can we please take a break, I am not feeling 100% in the car….” break. And that was that day :-)

Crabs in the grass — tides in Ulverston

I hope you saw my post on the Arnside tidal bore and are well aware of the awesome tides in Morecombe Bay (if not, check it out here!), so here is a little more about them.

This is what the bay looked like at the beginning of our picknick.

40 minutes later, see how there is a sand bank that appeared out of nowhere? Well, out of the water to be precise.

Tides make for really interesting beach finds. Not only are there crabs in the grass everywhere (and salt marshes are totally confusing to me. I am used to the tidal areas being muddy. Why is there grass growing in spots that are flooded with salt water twice a day?), there is also deceased jellyfish art to be found!

This is such a pretty area, and I love thistles.

Yep, more thistles. (And if there is one typical kind of picture I take over and over it’s this: sea sides with a little greenery on one side in the foreground…)

And I really liked this art!

Wake watching at Ratzeburger Segelschule

The waves that ducks (or ships, or anything else moving through water) make are called “wakes”. And wake watching is so much fun! A wake is pretty much the Mach cone in 2D — waves from the duck can’t propagate faster than the leading edge of the wake. When a wake passes by, that’s the moment you would hear the supersonic boom of an aircraft in the Mach cone analogy. That explains why the wake develops as a feathery V with the duck at its tip. Or several ducks at the tips at several Vs, as in the picture above. How awesome is that?

But wake watching is usually more complicated than just Vs with stuff at their tips. See for example below — two ducks with Vs, two row boats also with Vs, but with the additional eddies where their oars pushed through the water.

See how different the two pairs of wakes look?

Or here, we have wakes again, but they are now occurring on a lake surface that shows more different waves: The half circles that my feet tapping on the water made! And, if you look closely, you can spot algae growing in the lake in the foreground of the picture.

Isn’t it fascinating how you see the algae in the foreground, but the further you look towards the other shore of the lake, the more you see the reflection of the sky or the other shore instead?

That’s due to a phenomenon called “total internal reflection“: For light that hits the interface between two different materials (air and water in this case), there are angles at which it can cross the interface (at steep angles we can look from the air into the water and see the algae), and others where it can’t (at small angles, we cannot look into the water, light gets reflected at the lake’s surface and we see the opposite shore instead). This fascinates me time and time again!

Note how the duck in the image above doesn’t actually have a wake? That’s because it’s swimming too slowly for the wake to develop — it is just radiating ring waves in all directions.

Below, this is kind of a boarder line wake — we can see the V developing, but se also still see the ring waves in the spot where the duck first started swimming.

But of course, wakes are only straight Vs when the ship is driving in a straight line, too, otherwise it will get deformed like below.

And just because I love this picture so much: Here is a wake coming across the lake