Tag Archives: double-diffusive mixing

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.

IMG_5958_DL

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.

IMG_4233_sehr_klein

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.

Double-diffusive mixing

On the coolest process in oceanography.

My favorite oceanographic process, as all of my students and many of my acquaintances know, is double-diffusive mixing. Look at how awesome it is:

[vimeo 83429427]

Double-diffusive mixing happens because heat and salt’s molecular diffusion are very different: Heat diffuses about a factor 100 faster than salt. This can lead to curious phenomena: Bodies of water with a stable stratification in density will start to mix much more efficiently than one would have thought.

In the specific case of a stable density stratification with warm, salty water over cold, fresh water, finger-like structures form. Those structures are called “salt fingers”, the process is “salt fingering”.

IMG_4233_sehr_klein

Salt fingering happening with the red food dye acting as “salt”.

Even though salt fingers are tiny compared to the dimensions of the ocean, they still have a measurable effect on the oceanic stratification in the form of large-scale layers and stair cases, and not only the stratification in temperature and salinity, but also on nutrient availability in the subtropical gyres, for example, or on CO2 drawdown.

Over the next couple of posts, I will focus on double diffusive mixing, but less on the science and more on how it can be used in teaching. (If you want to know more about the science, there are tons of interesting papers around, for example my very first paper)