# 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:

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.

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

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! :-)

# When water doesn’t seek its level

Last week we talked about misconceptions related to hydrostatic pressure, and how water always seeks its level. Today I’m gonna show you circumstances in which this is actually not the case!

We take the fat separator jug we used last week. Today, it is filled with fresh water, to which we add very salty water through the jug’s spout. What is going to happen? Watch the movie and find out!

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.

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

Do you see the opportunities for discussions this experiment provides? If we knew the exact volumes of fresh water and salt water, and the exact salinity, we could measure the difference in height of the water levels and try to figure out how much mixing must have taken place when the fresh water was added to the jug. Or we could use the difference in height to try and calculate the density difference between fresh water and salt water and then from that calculate salinity. So many possibilities! :-)

# 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 an experiment that Martin and I ran at the JuniorAkademie this summer, but since I posted soooo much back than (just look for the tag “JuniorAkademie” to get an impression of what we did) I feel it never got the attention it deserves. So here we go again! :-)

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 to force mixing through the wind stress. After about a minute, the tank was fully mixed.

In the second experiment, we created a salt 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. We then added the wind stress.

After a minute, the surface layer was well mixed, but there was no mixing penetrating into the bottom layer. 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!).

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 been expecting to see a difference, but we were really surprised that the difference was so large. I started the experiment an hour before a meeting we had to attend, but then obviously couldn’t leave on time, because I could neither stop the experiment (seriously! How could I have stopped?) nor leave the hair dryer running while I wasn’t in the room.

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

# Creating a continuous stratification in a tank, using the double bucket filling method

Because I am getting sick of stratifications not working out the way I planned them.

Creating stratifications, especially continuous stratifications, is a pain. Since I wanted a nice stratification for an experiment recently, I finally decided to do a literature search on how the professionals create their stratifications. And the one method that was mentioned over and over again was the double bucket method, which I will present to you today.

Two reservoirs are placed at a higher level than the tank to be filled, and connected with a U-tube which is initially closed with a clamp. Both reservoirs are filled with fresh water. To one of the buckets, salt is added to achieve the highest desired salinity in the stratification we are aiming for. From this bucket, a pump pumps water down into the tank to be filled (or, for the low-tech version: use air pressure and a bubble-free hose to drive water down into the tank as shown in the figure above!); the lower end of the hose rests on a sponge that will float on the water in the tank. When the pump is switched on (or alternatively, the bubble-free hose from the reservoir to the tank opened), the clamp is removed from the U-tube. So for every unit of salt water leaving the salty reservoir through the hose, half a unit of fresh water flows in to keep the water levels in both reservoirs the same height. Thus the salt water is, little by little, mixed with fresh water, so the water flowing out into the tank gets gradually fresher. If all goes well, this results in a continuous salinity stratification.

Things that might go wrong include, but are not limited to,

• freshwater not mixing well in the saline reservoir, hence the salinity in that reservoir not changing continuously. To avoid that, stir.
• bubbles in the U-tube (especially if the U-tube is run over the top edges of the reservoirs which is a lot more feasible than drilling holes into the reservoirs) messing up the flow. It is important to make sure there is no air in the tube connecting the two reservoirs!
• water shooting out of the hose and off the floating sponge to mess up the stratification in the tank. Avoid this by lowering the flow rate if you can adjust your pump, or by floating a larger sponge.

P.S.: For more practical tips for tank experiments, check out the post “water seeks its level” in which I describe how to keep the water level in a tank constant despite having an inflow to the tank.

# Mixing in a non-stratified and in a stratified tank

A wind stress is applied to the surface to cause mixing.

This is an experiment that I have been wanting to do for a long time, but somehow it never worked out before. But last night Martin and I finally ran it!

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 to force mixing through the wind stress. After about a minute, the tank was fully mixed.

In the second experiment, we created a salt 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. We then added the wind stress.

After a minute, the surface layer was well mixed, but there was no mixing penetrating into the bottom layer. To fully mix the whole depth, the wind forcing ran for 86 minutes.

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

# Forced internal waves in a continuous stratification

Plus all kinds of dyes. (deutscher Text unten)

Using the continuous salinity stratification created yesterday, Rolf and Daniel conducted a really cool experiment: They forced internal waves and watched them develop. I’ve converted their movie into a time-lapse; watch it below.

Mit der kontinuierlichen Salzschichtung, die Daniel und Rolf gestern gebastelt haben, haben sie danach noch weiter experimentiert. Sie haben einen durch einen kleinen Motor angetriebenen Stempel in die Schichtung eingeführt und auf und ab bewegt. Das Wellenfeld, das sich dadurch entwickelt hat, sieht man im Film oben im Zeitraffer (einige kurze Abschnitte zwischendurch zeigen auch Echtzeit). Farbkristalle, die nachträglich hinzugefügt wurden, helfen, die Strömungen zu visualisieren.

# Why we absolutely need toy boats at the JuniorAkademie

Luckily I’m not the only one believing that we absolutely need remotely controlled boats! – Zum Glück bin ich nicht die Einzige, die findet, dass wir ferngesteuerte Boote brauchen!

Mein Boot hat Hochkonjunktur. D. kann es in einem Tank wenden, der nur etwa 1.5 mal so breit ist wie das Boot lang! Das kann man im Film unten bewundern. Der Film zeigt eine der ersten Wendungen, mittlerweile wendet er ohne die Ränder zu berühren. Ich hingegen komme nur um die Kurve wenn ich mit Bande spiele, und auch dann nur mit Mühe…

Und dann ist da ja noch das U-Boot. Was wir heute in Schichtung ausprobiert haben. Interne Wellen anzuregen war nicht so einfach, aber Vermischung ist doch auch was schönes!

Und dann bekam ich heute morgen von meinen Eltern das Foto unten geschickt mit dem Kommentar “Eins ist für uns”. Offensichtlich haben sie erkannt, dass man wirklich ferngesteuerte U-Boote braucht! Sind meine Eltern super oder sind meine Eltern super?

# Salt fingering – DIY

How to easily set up the stratification for the salt fingering process.

Setting up stratifications in tanks is a pain. Of course there are sophisticated methods, but when you want to just quickly set something up in class (or in your own kitchen) you don’t necessarily want to go through the whole hassle of a proper lab setup.

For double diffusive mixing, there are several methods out there that people routinely use.

For example the hose-and-funnel technique, where the less dense fluid is filled in the tank first and then the denser fluid is slid underneath with the help of a hose and a funnel. And a diffuser at the end of the hose. And careful pouring. And usually a lot more mixing than desired.

Or the plastic-wrap-to-prevent-mixing technique, where the dense fluid is put into the tank, covered by plastic wrap, and then the lighter fluid is poured on top. Then the plastic wrap is removed and by doing so the stratification is being destroyed. (No video because I was frustrated and deleted it right away)

Or some other techniques that I tried and didn’t find too impressive. (No videos either for the same reason as above)

But then accidentally I came across this one:

Granted, this is not a realistic model of an oceanic stratification. But as you can see towards the end of that movie, that turns out to be a blessing in disguise if you want to talk about the process in detail. As you see in the movie, the salt fingers inside the bottle are much smaller than the salt fingers outside the bottle. Because, clearly, inside the bottle the warm water is cooled both at the interface with the cold water inside the bottle, and by heat conduction through the walls of the bottle, since the water is surrounded by cold water. The warm water that flowed out of the bottle and up towards the water’s surface is only cooled at the interface with the water below (the air above is warmer than the cold water). So this gives you the perfect opportunity to discuss the scaling of salt fingers depending on the stratification without having to go through the pains of actually preparing stratifications with different gradients in temperature or salinity.

# Diffusive layering. Or: This is not a trick question!

The “other” double-diffusive mixing process.

After having talked extensively about double diffusive mixing in my courses, I tend to assume that students not only remember that there is such thing as double-diffusive mixing, but that they also remember our discussions on how the process works, and that they would be able to transfer this to processes other than salt fingering.

So in two courses (at different universities) I asked students in the exam to describe what would happen in a stably stratified body of water, where cold and fresh water overlies warm and salty water. And in both courses I have been surprised (read: shocked) by the responses I got.

The by far most common response goes along these lines: “Cold water is denser than warm water, so it will sink to the bottom and the warm water will rise”.

What I find frustrating about this (besides the fact that they didn’t notice that I clearly stated in the question that the stratification was stably stratified) is that whenever I talked about density, I mention how density depends on both temperature and salinity.

The next most common response is then this: “Heat diffuses a factor 100 faster than salt. Hence, salt fingers will form at the interface”. This answer then continues on describing salt fingering and never even mentions that the stratification I described in the question was actually the opposite one to the one they are assuming. So here, students clearly jumped to the conclusion that if I bothered describing a stratification, it clearly had to be the one for my favorite process (even though during those discussions I made sure to mention diffusive layering, too, but without talking it through in as much detail as salt fingering).

But then there are always students (usually the ones who don’t have a lot of confidence in their oceanography skills) who take the questions I ask at face value. Those are the students who go on to write something like this (numbering referring to the sketch below):

1) The initial stratification is stable in density, with cold and fresh water over warm and salty water. This means that the salinity stratification outweighs the temperature stratification in terms of density.

2) Since temperature diffuses a factor 100 faster than salinity, a thin layer with an intermediate temperature will form around the interface in salinity, that will persist for a while.

3) Focussing above the interface now, we have a stratification where cold and fresh water overlies lukewarm and fresh water. This stratification is hence unstable in temperature and convective overturning will occur. Below the interface, a similarly unstable layer has formed: lukewarm and salty water over warm and salty water. Again, convective overturning will occur.

The thickness of those layers depends on the initial temperature stratification and on how quickly temperature exchange happens during the overturning. In the end, two new temperature interfaces will have formed.

Sketch of the diffusive layering process. The red shading indicates warmer temperatures, the black dots indicate higher salinities.

And yes – that is exactly the response I wanted to hear!

So why do only so few students answer this question correctly? Don’t they understand that when I talk about salt fingering it is only an example of a double-diffusive process and not the only double-diffusive process there is? That was my initial thought after I saw the exams in the first class. So for the second class, I made sure to mention diffusive layering even more, and to explicitly say that I was talking through only one of the processes and that it might be helpful if they went through the other one on their own. Yet in the exams, the results did not change. And I have no idea. Do you? Then please let me know!

# Salt fingering

How to show my favorite oceanographic process in class, and why.

As I mentioned in this post, I have used double-diffusive mixing extensively in my teaching. For several reasons: Firstly, I think that the process is just really cool (watch the movie in this post and tell me that it isn’t!!!) and that the experiments are neat and that everybody will surely be as excited about them as I am. Secondly, because it shows that understanding of small processes can be really important in order to understand the whole eco- and even climate system. And thirdly, because it helps to demonstrate a way of thinking about oceanography.

When I introduce salt fingering, I talk students through the process in very small steps. It goes something like this (Numbering is referring to the sketch below):

1) Initially, you have a stratification where warm and salty overlies cold and fresh water. This stratification is stable in density (meaning the influence of the temperature stratification on density outweighs that of the salinity stratification).

2) Since molecular diffusion of temperature is about a factor 100 faster than that of salinity (we will talk about why that is in a later blog post), the interface in salinity is initially basically unchanged, whereas a temperature exchange is happening across that interface, and a layer of medium temperature is forming.

3) At the salinity interface, we now have a stratification that is no longer stable in density: while the water now has the same temperature in a thin layer above and below the interface, it is still more salty on top and less salty below the interface. This means that the saltier water in this thin layer is denser than the less salty water below. This leads to finger-shaped instabilities at the interface: The salty water will sink and the fresh water will rise.

The individual salt fingers now have a much larger surface than the original interface, hence molecular diffusion of salt will happen much more efficiently and eventually the salinity inside and outside of the salt fingers will be the same, hence the growth of the fingers will stop.

At the depth where the salt fingers stopped, a new interface has formed. This new interface can also develop salt fingering, leading to a staircase-like structure in temperature and salinity.

After salt fingering has been introduced, there are usually several other occasions where it, or its effects, can be pointed out, like for example when showing this experiment (see picture below), when talking about the hydrographic properties in the area of the Mediterranean outflow or the Arctic, or when talking about nutrients in subtropical gyres.

This is a zoom in on one of the bottles shown in this experiment: In the warm bottle, the red food dye acts as salt to form salt fingers!

While talking about salt fingering, since I focus so much on the process, I have always been under the illusion that students actually understand the reasoning behind it and that they can reproduce and transfer it. Reproduce they can – transfer not so much. Stay tuned for the next post discussing reasons and possible ways around it.