From wind-driven capillary waves to gravity waves on a calm lake

The picture above I thought was too pretty to not put on my blog (because my blog’s main function to me is still my personal brain dump), but the picture below is actually interesting from a physics point of view.

In the middle of the lake, the surface looks a lot rougher and crumpled than the water surrounding it. That’s because there the light breeze is generating small capillary waves, whose restoring force is surface tension. But if we look closely towards the lower edge of the “crumpled” area, we see that the water isn’t as calm and the surface isn’t as flat as they appeared to be on first glance — there are longer waves propagating out of the crumpled area. Those waves are gravity waves, and they can propagate for longer distances without having constant new energy input by the wind.

But why doesn’t the crumpled area that is directly influenced by the wind extend all the way to the shore? Of course, on one side of the lake it would be sheltered from the wind by the trees and other things growing there. But on the other side, it’s in a way sheltered by the trees, too, even though the mechanism there is different. There, we don’t have wind until the very edge of the lake, because the current of air is deflected upwards by the trees, so an area of low velocity is formed, kind of like the area surrounding a stagnation point in an idealized model.

Morning and evening #wavewatching in Ratzeburg, including sun dogs!

I’m super excited to be back in Ratzeburg, but before I start on all the new pictures I will be taking over the next couple of days, let’s get some old pictures out of the pipeline, all taken either in the morning when the lake is still calm, or in the evening, when it’s calm again.

I love, for example as shown in the picture above and below, how paddling with my feet dangling from the pier creates this beautiful pattern of waves that radiate for such a long distance over the lake. And I love how we see that there is wind somewhere further out — the surface roughness is higher and the lake appears a darker blue — but that there is an area with very little wind, where we can see the dark reflection of the forest on the shore across the lake.

Looking into the water at a steeper angle, how creepy are those water plants growing there? The water depth is larger than 2.5 meters here and they still almost reach the surface! Did I mention I like my water without any biology in it? ;-)

Depending on the light, it can look even more creepy, like below…

Good things there are other views to be had, too, when you do a tour around the island. Like here, all those waves coming through the narrow inlet and spreading over the calm pond! Such a pretty sight!

Or a different corner of the small pond — so fascinating how there are the different reflections, shadows and insights into the water happening simultaneously!

And the picture below just makes me happy. Doesn’t it evoke feelings of promise and a new day? (Although it must have been taken in the evening if the sun is on that side. But anyway, all that spring green! :-))

Another thing I observed on two evenings in a row: Sun dogs! Can you spot one in the image below?

Or in this one? Below there should even be two sun dogs (but maybe that’s mainly due to my active imagination…)

Combining rotation of a water tank with a temperature gradient: A Hadley cell circulation demo!

Yesterday, we combined a thermally-driven overturning circulation with the effects of rotation, and thus created a Hadley cell circulation. And while the tank was turning faster than we would have liked, we still managed to create a circulation that largely resembles the sketch below: An axially-symmetric overturning circulation (with cold water, indicated by blue arrows, moving down near the cooling in the middle and then outwards, and warmer water moving up along the outer rim and then towards the middle of the tank) which induces the thermal wind flow (sketched in green: Fast surface current in the direction of rotation but even faster than the tank is rotating, and slow bottom flow in the opposite direction).

But what would happen if we increased the tank’s rotation rate? It would make the induced azimuthal flow, the thermal wind, faster too, until it eventually becomes unstable and breaks down into eddies. And then, the experiment (first blogged about a long time ago) looks similar to this one: Lots and lots of eddies that are now rigid vertically and move as Taylor columns!

Heat exchange between the cold core and the warmer areas towards the rim of the tank now doesn’t happen via overturning any more, but looks something like sketched below: We now have radial currents bringing warm water towards the middle (red) and cold water away from it (blue), and the eddies that create those currents are coherent over the whole depth of the tank.

This is actually a really nice demonstration of the circulation in mid- and high latitudes where the weather is determined by baroclinic instabilities, i.e. weather systems just like the eddies we are showing here.

Btw, having two different experiments both represent the same Hadley cell circulation isn’t a contradiction in itself: On Earth, the Coriolis parameter changes with latitude, but in the tank, the Coriolis parameter is the same throughout the tank. So depending on what latitude we want to represent, we need to change the tank’s rotation rate.

Here is an (old) movie of the experiment, and I can’t wait for our own tanks to be ready to produce a new one!


Combining a slowly rotating water tank with a temperature gradient: A thermal wind demonstration!

Setting up an overturning circulation in a tank is easy, and also interpreting the observations is fairly straightforward. Just by introducing cooling on one side of a rectangular tank a circulation is induced (at least for a short while until the tank fills up with a cold pool of water; see left plot of the image below).

But now imagine an axially symmetric setup where the cooling happens in the middle. What will happen to that overturning circulation if the tank is set into rotation (see right plot above)?

First, let’s check there is an overturning circulation. We can see that there is when we look at dye crystals that sank to the bottom of the tank: Dye streaks are moving outwards (and anti-clockwise) from where the crystals dropped on the ground, so at least that part of the overturning circulation is there for sure. If our tank were taken to represent the Hadley cell circulation in the atmosphere, this bottom flow would be the Trade winds.

Now, in addition to having water sink in the middle of the tank, spread radially outwards, and returning by rising near the outer edge of the tank and flowing back towards the middle, a secondary circulation is induced, and that’s the “thermal wind”. The thermal wind, introduced by the temperature gradient from cold water on the inside of the tank to warmer waters towards the rim, tilts columns that would otherwise stay vertically.

You see that in the image below: Dye dropped into the tank does not sink vertically, but gets swirled around the cold center in a helix shape, indicated in the picture below by the white arrows. In that picture, the swirls are tilted very strongly (a lot stronger than we’d ideally have them tilted). The reason for that is that we just couldn’t rotate the tank as slowly as it should have been, and the higher the rotation rate, the larger the tilt. Oh well…

So this is the current pattern that we observe: An overturning circulation (sketched with the red arrows representing warmer water and the blue arrows representing colder waters below), as well as the thermal wind circulation (indicated in green) with stronger currents near the surface (where the water is moving in the same direction as the rotating tank, but even faster!) and then a backward flow near the bottom. The velocities indicated here by the green arrows are what ultimately tilted our dye streaks in the image above.

The thermal wind component arises because as the overturning circulation moves water, that water carries with it its angular momentum, which is conserved. So water being brought from the rim of the tank towards the middle near the surface HAS to move faster than the tank itself the closer it gets to the middle. This flow would be the subtropical jets in the Hadley cell circulation if out tank were to represent the atmosphere.

Here is an old video of the experiment, first shown 5 years ago here. I’m looking forward to when Torge’s & my rotating tanks are ready so we can produce new videos and pictures, and hopefully being able to rotate the tank even more slowly than we do here (but that was the slowest possible rotation with the setup we had at that time). I promise you’ll see them here almost in realtime, so stay tuned! :-)

Why do we need a rotating tank to study ocean and atmosphere dynamics? A demonstration

For our project “Ocean currents in a tank: From dry theory to juicy reality“, Torge, Joke and I are working on building affordable rotating tanks to use in Torge’s Bachelor class on ocean and atmosphere dynamics. When people ask what we need rotating tanks for, the standard answer is that rotation of the tank simulates rotation of the Earth. Which is of course true, but it is not really satisfying because it doesn’t really convey the profound effect that rotation has on the behaviour of the ocean and atmosphere, which is actually very easy to show in a quite dramatic way (at least I think it’s dramatic ;-)).

Imagine a cylindrical tank filled with fresh water. In its middle, we place a (bottom-less) cylinder filled with dyed, salty water. When we lift the cylinder out of the tank, the blue dye is released into the freshwater. And depending on whether the tank is rotating or not, the blue water behaves very differently.

The picture below shows top views and side views of a non-rotating and a rotating experiment, taken after similar amounts of time after the “release” of the blue water.

Let’s focus on the top view first. In the non-rotating experiment, a dipole of two counter-rotating eddies develops within seconds of the central dense column being released, spreading blue water pretty much all throughout the tank. In the rotating experiment, after a similar amount of time, the dipole looks different: Even though the same amount of dyed water was released, the two eddies are much smaller and much more well-defined.

In the side view, the difference becomes even more clear. In the non-rotating experiment, looking at the boundary between the blue and clear water, we see eddies moving water in all directions, so in combination with the top view, we know that turbulence is three-dimensional.

In the rotating experiment, however, the boundary between blue and clear water looks very different. There is a clear separation between a blue column of water and the clear water surrounding it. From the side view, we don’t see any turbulence. We know, however, from the top view that there is turbulence in the horizontal plane. In the rotating case, turbulence is two-dimensional.

And this is the dramatic difference between rotating and non-rotating fluids: rotating fluids are rigid in a way that non-rotating fluids are not. And this means that they behave in fundamentally different ways: rather than developing in 3 dimensions, they only develop in 2 dimensions. So in order to simulate the atmosphere and ocean of the rotating earth correctly, we need to also rotate our water tank.

P.S.: Images for this post were originally posted in this post (and in other posts linked therein) 5 years ago. Hoping we’ll have new images soon when our new tanks are up and running! :-)

Tidal mixing on a (fjord’s) sill

A pink swirl going across a styrofoam block underneath a layer of yellow water? What’s going on here?

The picture was taken in a water tank, simulating the circulation of water masses in a fjord. A fjord is a long and narrow bay, usually with a sill that is separating the bay from the open ocean. And those sills play an important role in on the one hand preventing water exchange between the fjord and the open ocean (because everything below sill depth has a really hard time getting across the sill) and on the other hand mixing water masses inside and outside of the fjord (which we see visualized with the pink dye).

And here is why the sill is so important: Every time the tide goes in or out of the fjord (so pretty much all the time), the sill acts as an obstacle to the water that wants to go in or out. And flow across a ridge tends to create mixing downstream of the ridge.

In the picture below, we see a sketch of the situation in an outgoing tide, which is what we also see represented in the photo above: Water wants to push out of the fjord and has to accelerate to get through the much smaller cross section where the sill is located. This leads to strong currents and strong mixing “downstream” of the obstacle.

Except that “downstream” is on the other side of the sill only a couple of hours later, when the tide is pushing water into the fjord, but is again hindered by the sill.

So what is happening is this: The tidal current goes in and out, and mixing occurs on one or the other side of the sill. So the situation looks like this:

This is what that looks like in our tank (the “tidal waves” are generated by lifting the right end of the tank and then just slushing back and forth):

Of course, in reality we don’t see pink swirls, and the surface layer isn’t a different color from the deep layer, either. But that’s why tank experiments are so cool: They show us what’s going on deep below the waves, that we can otherwise only deduce from complicated measurements of temperatures, salinities or mixing rates, which require highly specialized equipment, a research ship, and lots of technical know how to process and analyse and display. Which, of course, is also being done, but this demonstration gives a quick and easy visual representation of the processes at play at sills all around the world.

P.S.: The photos in this blog post were taken when I ran the fjord circulation experiment with Steffi and Ailin at GFI earlier this year. I am posting about this again now because I wanted to use the picture for other purposes and realized that I never actually wrote about this feature in as much detail as it deserves!


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?