Baroclinic instabilities / Hadley cell circulation in a tank

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The DIYnamics-inspired turntable that Torge and myself have been working on for our “dry theory to juicy reality” project is finally working well!

This is what the setup now looks like (how simple is that?!) and we had an exciting morning testing different experiments!

The one experiment that we have been using as test case in all our previous sessions is the Baroclinic Instability / Hadley cell circulation. There are sketches of the setup and the expected circulation in this blogpost, so just a quick reminder: We place a cold core in the center of our tank (here a glass with blue ice in it), spin the tank (at approximately 20rpm) into solid body rotation, and introduce dye (blue towards the center, red towards the outer edge of the tank).

And what happens then is just beautiful: We get 2D instabilities that transport cold (blue) water outwards and warmer (room-temperature, red) water towards the center of the tank.

We’ve run the experiment three times with different water levels (and once with Southern Hemisphere rotation just for fun) and it worked beautifully each time.

I find it always fascinating how there is hardly any mixing between the red and blue curtains (and there shouldn’t be any because rotating flows become 2D (as shown here)).

Just look at how the dye curtains form when we first add the blue dye…

And then a little later added some red dye…

And then let the field develop.

So I think we’ve got this experiment down and can run it with the students once the semester starts up again in October! :-)

Vorticity and Rossby waves

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Usually when we talk about waves on this blog, we talk about surface- or sometimes internal waves, but my waves almost always oscillate vertically. Today, we’ll mix things up a little: Rossby waves are waves in the horizontal plane. They exist for example as oscillations on the atmosphere’s jet stream. In order to understand what causes them, we need the concept of vorticity, which I will go over first before giving examples for Rossby waves.

Vorticity

Vorticity is a measure of how much a fluid is rotating. Generally speaking, once a fluid is in rotation, it wants to keep rotating (as we saw for example with the bottom Ekman layers in a rotating tank, where the water inside kept on rotating after the tank was stopped, until it was slowed down by friction). There are several components that are at play here — the rotation that we see when looking at eddies, the rotation of the Earth, and others — which I will go over in the following.

Relative vorticity

The easiest way to imagine what “vorticity” is (and the only one that I’ve talked about on this blog, see here), is to think of a little float in a flow. In a vorticity-free flow, that little float will always keep its orientation (see below). However if there is shear in the flow, i.e. the flow field carries vorticity, it will start to turn.

vorticity1

Flow fields without vorticity (top) and with vorticity (bottom). 

Relative vorticity is what we see for example when looking al leaves swirling in rivers.

Planetary vorticity

Since the Earth is turning (and all the water on it with it), the water also carries planetary vorticity, i.e. the rotation of the Earth, which is the Coriolis parameter. The Coriolis parameter is largest at the poles and zero at the equator, meaning the rotation changes with latitude.

The rotation of the Earth is clearly important enough for us to want to spin our tanks to simulate its effects on ocean currents.

Absolute vorticity

The sum of relative and planetary vorticity is called absolute vorticity: This is how much any fluid column is rotating in total, including all possible components of rotation (which are only the two mentioned above, but still…).

Potential vorticity

One more factor that can influence the rotation of a fluid parcel is the water depth. When water depth increases, columns of water get expanded vertically (since, for continuity reasons, they still have to go all the way from surface to bottom, even if the distance is now larger) or, if water depth decreases, squished. Similarly to figure skaters that stretch or crouch to increase or decrease their rotation, the expansion of a column of water leads to a change in its rotation.

Potential vorticity is defined as absolute vorticity over water depth.

Conservation of potential vorticity leads to waves

Potential vorticity is conserved, so if water depth, planetary vorticity changes or relative vorticity changes, something else has to change to compensate. And if water changes how much it is rotating, this leads to meanders in currents, i.e. waves.

Depth is constant, but latitude changes: Planetary Rossby waves

Planetary vorticity changes with latitude, therefore if a water parcel moves in north-south direction over constant water depth, its relative vorticity needs to change in order for potential vorticity to be conserved. This leads to so-called planetary Rossby waves, where currents in the ocean or the atmosphere start oscillating in north-south direction (see figure below).

At position 1, a fluid parcel gets for any random reason pushed northward. As it moves north, its planetary vorticity increases and its relative vorticity therefore has to decrease to compensate (2). This leads to southward movement, but the initial latitude (3) is overshot a little (4). This again leads to a change in relative vorticity (4), which brings the water parcel back to its initial latitude (5), but it overshoots again… So this mechanism leads to a wave-like motion in the horizontal plane, with the phase of the wave propagating westward.

This can happen at any latitude, even at the equator where “equatorial planetary Rossby waves” occur. At the equator f=0, but as soon as the water column has moved slightly north or south from the equator, f kicks in and drives the water column back to the equator (where it then overshoots, is turned back, overshoots again…….).

Latitude is constant but depth changes: Topographic waves

If a current encountered a ridge, the water depth changes and the current thus gets deflected. This motion is called topographic wave: When a water column gets stretched, it gains relative vorticity, making it rotate cyclonically. When it runs into shallower water, it loses relative vorticity and starts turning the other way.

I’m hoping to set up demonstrations for both types of Rossby waves soon. Stay tuned! :-)

New role: Associate Editor at Frontiers for Young Minds!

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When I meet new people and am asked the compulsory “and what do you do?” question, I sometimes struggle to answer. I am wearing so many different hats! Depending on the context, I might be in the role of programme manager of GEO-Tag der Natur, a consultant in Higher Education and/or Science Communication, a science communicator with my own projects like kitchen oceanography or wave watching, initiator of #scicommchall, facilitator of networking events, and many more. And while I enjoy each of those hats, people are usually not patient enough to listen to me listing all of those, and yet omitting one (or more) doesn’t feel right.

But lately, things seem to be falling into place. With GEO-Tag der Natur’s focus on “seeing nature with different eyes”, this programme’s goal aligns very much with the goals I am pursuing with, among others, my wave watching activities. And facilitating excellent science communication by using my theoretical background, practical experience and amazing network seems to become a more and more prominent part of my endeavours.

I am super excited to be strengthening that strand of my “personal brand” even further, and am honoured to say that I have taken on the role as Associate Editor on the editorial board of “Understanding the Earth and its Resources“, a specialty section of Frontiers for Young Minds. I am looking forward to inviting scientists in writing articles for — and supporting the article’s peer-review process by — kids. I published two articles with Frontiers for Young Minds earlier this year (on the formation of sea ice, and on density driven ocean currents), and I enjoyed the experience so much that It was really very easy to decide to dedicate time and energy towards this project.

By specifically creating articles for children, on both scientific core concepts and cutting edge science, Frontiers for Young Minds is building an amazing collection that is accessible to anyone in the world. Since the articles are written by the scientists themselves and then peer-reviewed by children, they are both factually correct and at the same time understandable by the target audience. And from my own experience as an author, this is such an enriching experience!

One role in the peer-review-by-kids process that isn’t as prominently visible, but that is crucial for the success, is the “science mentor“. Science mentors are the middle persons between the journal side (i.e. myself, how exciting to say this!) and the kids. They work with the kids to read, understand and critique the articles, to formulate the reviews and to submit them via the system. And if you are still reading this, I think you might be destined to become a science mentor (I am specifically thinking of you, Elin and Joke ;-)), but anyone else, too: If you are interested in getting involved, please be in touch!

Observing the shape of shallow water waves on a beach

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When I go wave watching back home in Kiel, I tend to be drawn to other places than this particular one, but sometimes you find gold in the places you least expect it. And then, what is usually a really nice and easy to explain kind of wave — shallow water waves — acts up and becomes difficult. You win some, you lose some…

In these pictures, we see these very weirdly-shaped waves in very shallow water. When the water is shallow enough, waves don’t even have a “proper wave shape” any more, they look more like pool noodles that are being pushed towards the beach, but in a very inefficient, sideways manner.

When the water is shallow enough, the waves also change their behaviour in that usually we can just add two incoming wave fields and get a good idea of what the resulting wave field will look like, but in very shallow water, things become very nonlinear and messy.

Do you see how wave crests seem to start clinging together, resulting in weird X and Y shapes?

Usually we can easily calculate the velocity of shallow water waves just from the water depth, but here in this picture, all kinds of weird and wonderful things are happening and I don’t actually have a clue what’s going on.

A little bit further along, some other surprising wave watching: A wake is running onto the shallow beach.

What i find really interesting here is the one long, straight wave crest that runs all the way across the picture, and then how different the waves look on either side of the draining pipe (actually, I don’t know what’s going into Kiel fjord there, although now I am curious…).

On the left side of the picture, the wave crest hits the shore and that’s the end of waves on that side. On the right side, though, wave crests continue on in shallow water for quite some time before they end up on the shore, and here we see how they get bent by the changing water depth (Remember? Phase velocity of shallow water waves should only depend on water depth, so the deeper the water, the faster the wave). The wave crests get slowed down a lot faster on towards the shallow water on the left than towards the deeper water on the right, thus the right side starts overtaking the left, bending the whole wave crest around.

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

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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!

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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!

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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!

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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

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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

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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!