Tag Archives: stratification

Demonstration: Nansen’s “dead water” in a tank!

A ship that is continuously pulled with a constant force suddenly slows down, stops, and then continues sailing as if nothing ever happened? What’s going on there? We will investigate this in a tank! And in order to see what is going on, we have dyed some of the water pink. Can you spot what is going on?

The phenomenon of “dead water” is probably well known to anyone sailing on strong stratifications, i.e. in regions where there is a shallow fresh or brackish layer on top of a much saltier layer, e.g. the Baltic Sea, the Arctic or some fjords. It has been described as early as 1893 by Fridtjof Nansen, who wrote, sailing in the Arctic: “When caught in dead water Fram appeared to be held back, as if by some mysterious force, and she did not always answer the helm. In calm weather, with a light cargo, Fram was capable of 6 to 7 knots. When in dead water she was unable to make 1.5 knots. We made loops in our course, turned sometimes right around, tried all sorts of antics to get clear of it, but to very little purpose.” (cited in Walker,  J.M.; “Farthest North, Dead Water and the Ekman Spiral,” Weather, 46:158, 1991)

When observing the experiment, whether in the movie above or in the lab, the obvious focus is on the ship and the interface between the clear fresh water layer (the upper 5cm in the tank) and the pink salt water layer below. And yes, that’s where a large-amplitude internal wave develops and eats up all the energy that was going into propulsion before! Only when looking at the time lapse of the experiments later did I notice how much more was going on throughout the tank! Check it out here:

The setup for this experiment is discussed here and is based on the super helpful website by Mercier, Vasseur and Dauxois (2009). In the end, we ended up without the belt to reduce friction, and with slightly different layer depths than we had planned, but all in all it works really well!

Layered latte: A great real-life example of double-diffusive mixing!

Sometimes sitting in a café for a work meeting with #lieblingskollegin Julia can lead to unexpected discoveries of oceanographic processes — in my latte! It’s those little things that inspire blog posts…

“Kitchen oceanography” brings the ocean to your house or class room!

Oceanography is often taught in a highly theoretical way without much reference to students’ real life experience. Of course a sound theoretical basis is needed to understand the complexity of the climate system, but sometimes a little “kitchen oceanography” — doing experiments on oceanographic topics with household items — goes a long way to raise interest in the kind of processes that are not easily observed in the real world. I’ve previously written a lot about simple experiments you can perform just using plastic cups, water, ice cubes, and a little salt. But sometimes it’s even easier: Sometimes your oceanography is being served to you in a cafe!

Oceanic processes can be observed in your coffee!

Have you ever looked at your latte and been fascinated by what is going on in there? Many times you don’t just see a homogenous color, but sometimes you see convection cells and sometimes even layers, like in the picture below.

Layers in a latte.

Layers in a latte.

But do you have any ideas why sometimes your latte looks like this and other times it doesn’t?

When you prepare latte in the right way, many layers form

Layers forming in latte (and in the ocean or in engineering applications) are an active research field! In the article “laboratory layered latte” by Xue et al. (2017), the authors describe that the “injection velocity” of espresso into the warm milk has to be above a critical value in order for these pretty structures to form in a latte. They even provide a movie where you can watch the layers develop over a period of several minutes.

The homogeneous layers with sharp boundaries are caused by double-diffusive mixing

Double-diffusive mixing, which is causing the formation of these layers, is the coolest process in oceanography. In a nutshell, double diffusive mixing is caused by two properties influencing density having different rates of molecular diffusion. These different rates can change density in unexpected ways and an initially stable stratification (high density at the bottom, low density on top) can, over time, become statically unstable. And static instability leads to adjustment processes, where water parcels move in order to reach the position in the fluid where they are statically stable — the fluid mixes.

Layers in half a glass of latte.

Layers in half a glass of latte.

But there are more fascinating things going on with the latte. Would you expect this stratification to remain as clearly visible as it is in the picture above even though the glass is now half empty? I did not! And then check out what happens when you move the glass: Internal waves can travel on the boundaries between layers!

You can use this in class to teach about mixing!

Mixing in the ocean is mostly observed by properties changing over time or in space, and even though (dye) tracer release experiments exist, they are typically happening on scales that provide information on the large-scale effects of mixing and not so much on the mixing itself. And they are difficult to bring inside the classroom! But this is where kitchen oceanography and experiments on double-diffusive mixing come in. If you need inspiration on how to do that, I’ve recently published an article on this (unfortunately only in German), but there are plenty of resources on this blog, too. Or shoot me an email and we’ll talk!

P.S.: Even though the coffee company is displayed prominently in the pictures above, they did not pay for my coffee (or anything else). But if they’d be interested and make me a good offer, I’d definitely write up some fun stuff on learning oceanography with coffee for them ;-)

Waves in a density stratification. One of the most beautiful tank experiments I’ve ever seen.

It’s pretty impressive when a mountain moves through a stratification and generates lee waves. But what I find even more impressive: The waves that travel behind the mountain when the mountain is long gone. See here:

This kind of stuff looks more like a numerical simulation than something actually happening in a tank, doesn’t it? I am pretty stoked that we managed to set up such a nice stratification! Those are the things that make me really really happy :-)

(The setup of this experiment is the same as in this post)

The one where it would help to understand the theory better (but still: awesome tank experiment!)

The main reason why we went to all the trouble of setting up a quasi-continuous stratification to pull our mountain through instead of sticking to the 2 layer system we used before was that we were expecting to see a tilt of the axis of the propagating phase. We did some calculations of the Brunt-Väisälä frequency, that needs to be larger than the product of the length of the obstacle and the speed the obstacle is towed with (and it was, by almost two orders of magnitude!), but happy with that result, we didn’t bother to think through all the theory.

And what happened was what always happens when you just take an equation and stick the numbers in and then go with that: Unfortunately, you realize you should have thought it through more carefully.

Luckily, Thomas chose exactly that time to come pick me up for a coffee (which never happened because he got sucked into all the tank experiment excitement going on), and he suggested that having one mountain might not be enough and that we should go for three sines in a row.

Getting a new mountain underneath an existing stratification is not easy, so we decided to go for the inverse problem and just tow something on the surface rather than at the bottom. And just to be safe we went with almost four wavelengths… And look at what happens!

We are actually not quite sure if the tilting we observed was due to a slightly wobbly pulling of the — let’s use the technical term and go for “thingy”? — or because of us getting the experiment right this time, but in any case it does look really cool, doesn’t it? And I’ll think about the theory some more before doing this with students… ;-)

Lee waves in the tank

Did you guess what we needed the stratification for? Yes — we are moving mountains again! :-)

What we want to look at: How a current reacts to an obstacle in its way, especially a current in a stratification. But since it is really difficult to set up a current in a tank, let alone a stratified one, we are doing the next best thing: Moving the obstacle relative to the water rather than the other way round.

And this is what it looks like:

Et voilà: Beautiful lee waves!

And look at the paper bits floating on the surface and how they visualize convergences and divergences in the upper layer!

The three layers in the pink all have (more or less) similar densities, and are only dyed slightly differently because we had to make several batches of dyed salt water to be able to fill the tank. But look how well they show that the wave is really happening at the interface, and that the other layers are phase locked. What would happen if the stratification inside the pink layer was stronger? Just wait and see…. ;-)

Experiment: Influence of stratification on mixing

A wind stress is applied to the surface of a stratified and a non-stratified tank to cause mixing.

This is a pretty impressive experiment to run if you have a lot of time, or to watch the time-lapse of if you don’t. The idea is that a density stratification will make mixing harder than it would be in the unstratified case, because more energy has to be used to break up the stratification.

To look at this, we ran two experiments, one after the other.

In the first one, we took a tank full of freshwater, added dye droplets and switched on a hair dryer, set to blow pretty much along the surface of the tank, to force mixing through the wind stress. After about a minute, the tank was fully mixed.

In the second experiment, we created a density stratification: salt water with approximately 35 psu, and freshwater. We then added the dye droplets. The droplets never penetrated into the salty layer but instead layered in at the interface between the two layers. (See how there are internal waves on the interface, which is why the dye seems to penetrate much deeper on the right? If you watch the movie at the bottom of this page, you see the internal wave very clearly) We then added the hair-dryer wind stress.

After a minute, the surface layer was well mixed, but there was no mixing penetrating into the bottom layer. (We added blue dye at some point, which makes the picture below a little confusing.) To fully mix the whole depth, the wind forcing ran for 86 minutes (and I am proud to report that my hair dryer survived this ordeal! Don’t leave this experiment on its own, not every hair dryer might make this without catching fire!).

Mixing in a non-stratified tank (left) and in a stratified tank (right). See the stop watch at the bottom of the panels for an impression of the time scales involved!

This is a great demonstration of how mixing is inhibited by stratification. We had expected to see a difference, but we were really surprised that the difference was so large. Of course, the stratification in our tank was pretty harsh, but still.

Watch a short movie below and a movie containing the full time lapse even further down!

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.

“Laboratory layered latte” – combining latte and double diffusion. Easily my favourite paper ever!

My friends know me well. Especially A&I, which was proven again when they sent me the link to an article about two things that I am mildly obsessed with: Latte and double-diffusive mixing.

My obsession with latte is a fairly recent thing, but I have been known to blog about interesting convection pattern in it (for example here). The obsession with double-diffusive mixing, however, is well documented for more than the last 12 years (for example when I am writing experimental instructionspoems or scientific articles about it).

The double-diffusive process that I have been most concerned with is salt fingering, because it is oh-so-pretty, and also fool-proof to create for teaching purposes (when you know how to do it).

Diffusive layering I seem have to be a little frustrated with, at least in teaching (but reading back this post now, it turns out that that was entirely my own fault and not my students’. Oh well, you live and learn! Isn’t this exactly the kind of stuff that makes for great teaching portfolios? ;-)).

And it also turns out that I did the experiments themselves all wrong. According to the article “laboratory layered latte” by Xue et al. (2017). I should not have been trying to carefully stratify a tank in order to see diffusive layering. Instead, I should just have quickly poured the lower density fluid into the higher density one, and layers would have formed by themselves!

So there is one thing that you won’t see any time soon:

Yep. Me drinking latte from any kind of vessel that doesn’t let me look at the stratification! I don’t know how I could ever have fallen into the trap of missing out on observing fluid dynamics while having my early morning coffee in the office. Now I urgently need a nice glass mug!

And you should go check out the article, it’s a really nice read. My new ambition in life: Write a fluid dynamics research article that applies the FD to some really cool, yet mundane, every day thing. Are you in, Elin? :-)

Xue, Nan and Khodaparast, Sepideh and Zhu, Lailai and Nunes, Janine K. and Kim, Hyoungsoo and Stone, Howard A., Laboratory layered latte. Nature Communications 8(1), 2017

Observe a fresh water layer (with your eyes, not a CTD!)

Sometimes you actually see fresh water layers (see with your eyes, not a CTD or some other instrument) floating on top of denser waters, not only in your kitchen and with the help of dye, but for real. In this case, you see the layers because the shadow of a pole appears twice — once on the surface itself, and once on the interface between the layers.

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See below: Shadow on the surface between the red lines, on the interface between green lines, and the reflection on the surface between blue lines.

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I took these pictures on a trip to Husum with my sister and her family.

Taking the hydrostatic paradox to the next (water) level

How well do people understand hydrostatics? I am preparing a workshop for tomorrow night and I am getting very bored by the questions that I have been using to introduce clickers for quite a lot of workshops now. So I decided to use the hydrostatic paradox this time around.

The first question is the standard one: If you have a U-tube and water level is given on one side, then what is the water level like on the other side? We all know the typical student answer (that typically 25% of the students are convinced of!): On the wider side the water level has to be lower since a larger volume of water is heavier than the smaller volume on the other side.

Clearly, this is not the case:

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However, what happens if you use that fat separator jug the way it was intended to be used and fill it with two layers of different density (which is really what it is intended for: to separate fat from gravy! Your classical 2-layer system)?

Turns out that now the two water levels in the main body of the jug and in the spout are not the same any more: Since we filled the dense water in through the spout, the spout is filled with dense water, as is the bottom part of the jug. Only the upper part of the jug now contains fresh water.

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The difference in height is only maybe a millimetre, but it is there, and it is clearly visible:

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Water level 1 (red line) is the “main” water level, water level 2 (green line) is the water level in the spout and clearly different from 1, and water level 3 is the density interface.

We’ll see how well they’ll do tomorrow when I only give them levels 1 and 3, and ask them to put level 2 in. Obviously we are taking the hydrostatic paradox to the next (water) level here! :-)