Tag Archives: tank experiment

Lee waves with an asymmetrical “mountain”

How will lee waves look differently if we are using the asymmetrical mountain instead of the symmetric one? And is symmetry actually important at all or are we just looking at different slopes downstream while the upstream slope doesn’t have an influence on the wave field?

After admitting I had only ever used the symmetrical mountain to generate lee waves in the long tank in the GFI basement, I had to try the asymmetrical one!

There are a couple of reasons why I had not done that before:

  • It’s longer (1.5 m instead of the 1 m of the other mountain), therefore the tank is, relatively speaking, shorter. And since being close to the ends of the tank leads to weird interferences, this limits the distance over which observations can be made
  • Since it’s asymmetrical, pulling one way or the other would likely show different wave fields, so you couldn’t just run it back and forth and have students observe the same thing several times in a row

But then it would be really interesting to see what the difference would be, right?

I tried two different stratifications.

Weak stratification, shallow water

Since I just wanted a quick idea of what this mountain would do, I used leftover water I had prepared for the moving mountain experiment. Since there wasn’t a lot left, I ended up with 11.5 cm fresh water, but only 4 cm salt water at approximately 20 psu (since I stretched the 35 psu a little).

What I noticed: A LOT more mixing than with the other mountain! Stratification is pretty much destroyed after the first run, usually we run back and forth a lot. This can be for several reasons:

  • The water is very shallow, meaning mixing is happening over the whole water column. It might not actually be more mixing than in the other case, but since it’s affecting the whole water column, it might just seem like more because no clearly visible stratification is left above and below the layer which is mixed by the mountain?
  • The left side of the mountain was bent up a little (as in 2 or 3 cm), meaning that especially on the way back it was flapping up and down on the upstream side, doing a lot of mixing that wasn’t due to the shape of the mountain, just of bits of it being loose.

And the shape of the “reservoir” that is being built up upstream of the mountain is different to what I have observed before: Running in either direction, the reservoir didn’t built up smoothly, but as a hump that was pushed in front of the mountain. Maybe because the internal wave speed in this case was very close to the speed of the mountain, something like 7cm/s, so the disturbance created by the mountain couldn’t propagate upstream. Is that an upstream hydraulic jump we are seeing there?!

What’s also cool: Lee waves are now not only happening as internal waves, but you see a very clear signature in surface waves! Usually all we see are surface convergences and divergences, adjusting the surface layer to the internal waves underneath. That we now see surface waves is, I am assuming, mainly due to the shallow water relative to the height of the obstacle.

Since I was not satisfied with this at all, I ran a second experiment:

Strong stratification, deep water

First, I tried to set up the same stratification as for this lee wave experiment with the symmetrical mountain because I thought that would be easiest to compare. But I aborted that after having moved the mountain just a little because it was mixing so much that there stratification was destroyed completely and nothing could be seen. I ended up putting more dense water in and ended up with 12 cm pink (35 psu) and 4 cm clear freshwater. And this is what this looked like:

You now see a wave train with wave lengths longer than in the symmetrical case. Probably due to the longer length of the obstacle (even thought the waves are still shorter than the obstacle)? Or what sets the wavelength?

This time, with a faster internal wave speed of around 10cm/s while the mountain is still pulled with 7cm/s, we don’t see the “hump” in the upstream reservoir — the signal can propagate faster than the mountain and thus smoothes out.

So that is what I think is going on here. While the first experiment mainly showed effects of the stratification compared to previous experiments, the second one might provide some insight on the different slopes of the mountain, although I am not sure in what way. Do you see something I didn’t observe? How would you expect the different slopes to influence the lee waves?

I am so glad I tried this and I’m looking forward to thinking about this more! :-) Any insights you’d care to share with me?

Instructions: Lee wave demonstration in the GFI basement

This blog post is meant as guideline if someone other than me might have to set up this demonstration at some point… Have fun! :-)

Lee waves

Lee waves are the kind of waves that can be observed downwind of a mountain in the clouds, or downstream of an obstacle in a current as a series of undulations with crests parallel to the disturbance.

Why move the mountain?

Students sometimes find it hard to imagine that a moving mountain should be equivalent to flow across a ridge. It helps to discuss how it would be really difficult to set up a flow in a tank: A huge amount of water would need to be moved without too much turbulence. Instead, it’s a lot easier to imagine the water is moving by moving a mountain through the tank, so the water is moving relative to it if not relative to the lab.

Dimensions

The size of the tank is 60×1.5×5 dm, so it can hold a total of 450l of water.

The mountain we use is 10.5 cm high and 1 m long and it’s symmetric, so pulling it either way shows similar lee waves (which is why I’ve always used it). There is a second, asymmetrical mountain on the shelf that I have never used*.

Setting up the stratification

The stratification that we’ve found works well is 10 cm at 35 psu (here dyed pink) and 9 cm at 0 psu. This leads to an internal wave speed of approximately ~11cm/s.

Prepare the dense water in a barrel that sits high enough so gravity will bring the water down into the tank (see picture below). For the 80l barrel, you need 2.8kg of salt and 1/3 tea spoon of dye MAX.

Elin's GEOF213 class observing lee waves

Elin’s GEOF213 class observing lee waves

You achieve the stratification by filling in the fresh water first through the bottom left inlet, moving the mountain over it, and filling in the dense water. That way the mixing is contained to the volume underneath the mountain which will be a lot better for your nerves (believe me!).

Moving the mountain

The system that pulls the mountain can go at two speeds: “fast” and “slow”, “slow” meaning 5m in 1:11min (7cm/s) and “fast” meaning 5m in 0:36min (14cm/s).

Here is where you run the mountain from:

Troubleshooting if the mountain doesn’t move:

  • you might be trying to pull the mountain in the wrong direction (into the wall)
  • the mountain might not be located on the sledge well. There is a tongue on the sledge that needs to sit in the groove in the mountain
  • the mountain might not be sitting well in the tank so an edge digs into the side
  • the belt that pulls the tank might not be tight enough (always make sure the two weights at both ends of the tank are actually hanging down to put tension on the belt!)
  • the belt might have come off the axle that drives it (the white plastic above the left end of the tank)
Elin's GEOF213 class observing lee waves

Elin’s GEOF213 class observing lee waves

Observations

As you see in the pictures above (or the movie below), there is a lot to observe!

  • Lee waves (not one, but a whole train!)
  • Different flow regimes: supercritical shooting down the lee side of the mountain, then a hydraulic jump, and then a normal flow
  • The reservoir upstream of the mountain that builds up as the mountain is moving
  • Even after the mountain has stopped, you see waves travelling through the tank and being reflected at the ends
  • Turbulence!

Movie

Here is a movie of the lee wave experiment. Feel free to use it in teaching if you like! And let me know if you need the movie in a higher resolution, I am happy to share!

*Yes, this was true at the time of writing. But I am setting up that experiment as we speak. Write. Read. Whatever. Will post movies tomorrow!

Accidental double-diffusive mixing

When setting up the stratification for the Nansen “dead water” demo (that we’ll show later today, and until then I am not allowed to share any videos, sorry!), I went into a meeting after filling in layer 4 (the then lowest). When I came back, I wanted to fill in layer 5 as the new bottom layer. For this experiment we want the bottom four layers to have the same density (so we would actually only have one shallow top layer and then a deep layer below [but we can’t make enough salt water at a time for that layer, so I had to split it into four portions]), and I had mixed it as well as I could. But two things happened: a) my salinity was clearly a little fresher than the previous layer, and b) the water in the tank had warmed up and the new water I was adding with layer 5 was cold tap water. So I accidentally set up the stratification for salt fingering: warm and salty over cold and fresh! Can you spot the darker pink fingers reaching down into the slightly lighter pink water? How cool is this??? I am completely flashed. Salt fingering in a 6 meter long tank! :-D

 

Observing waves in a tank

So you thought filling water into a tank was boring? Not on my watch!

This is how we fill up the tank: Through a hole at the bottom. Which leads to a very nice fountain that slowly submerges as the water level rises:

…and to tons of nice waves, which are great to observe!

Propagation of waves

Below you see waves propagating. Can you spot the water’s orbital movement, i.e. water particles moving in circles, even though the wave phase is propagating from left to right?

Standing waves

After a while, waves are reflected at the end of the tank and propagate back, setting up a different, very cool, pattern:

Now the wave phase does not seem to travel any more! Instead, there are fixed points in space where water levels oscillate between maximum and minimum, and in between there are other points where the water level stays more or less the same. How cool is that?!

…And this is just filling the tank. Just wait how cool it gets when we are actually running our demonstrations! :-)

Experiment: Double-diffusive mixing (salt fingering)

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:

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 occuring 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)

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 method (as in: I wanted to show something completely different, but then I saw the salt fingers and was hooked):

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.

IMG_9084

Self-portrait with salt fingers :-)

In my experience, the best salt fingers happen when you use hot water with dye (as the warm and salty top layer) and cold fresh water below. Salt fingers develop quickly, you don’t have the hassle of hitting the exact temperatures or salinities to make the density stratification statically stable, yet unstable in salinity, and it ALWAYS works.

 

IMG_9079

Double-diffusive mixing. Scale at the bottom is centimeters.

 

IMG_9054

Salt fingering in a tank. Scale at the bottom is centimeters.

And look at how beautiful it looks! Do you understand why I LOVE double diffusion?

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 4th, 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.

Tank experiment: Lee waves in a fancy density (and dye) stratification

Did you seriously think we’d stop tank experiments with only 2-layer systems? Nooo!

Today, the plan was to set up a continuous stratification, which I have been planning to do for many years. After fiddling with the setup all morning (do you have any idea how many fittings on all kinds of hoses are needed to get that to work well?), reality set in and we ended up doing a quasi-continuous stratification, i.e. 12 density layers dyed in 6 different colors*.

And this is what it looks like when you tow a mountain through that stratification (and try to ignore the excited audience being reflected in the tank): Still very nice lee waves and surprisingly little turbulence!

*We set up the tank to contain the same amount of salt as our 2-layer system yesterday, so instead of one big density jump from about 1000g/l to 1026g/l, this now happened in 5 smaller, more or less regular, jumps. And here is how we did it in the end: Two large reservoirs (unfortunately of different diameters), one containing freshwater, the other one filled up to the same height, containing as much salt as we had in our experiment yesterday. Now the height of the reservoirs was divided in 12 equal dzs, and for each dz that went out of the “freshwater” tank into the experimental tank, we added salt water of the same dz to the “freshwater” tank, which thus continued to increase in salinity. The water that we mixed that way went through a hose and entered the experimental tank through the bottom of the tank through a hole over which we had put the mountain (to contain mixing to a small volume and also so we didn’t have to watch water shooting out of that hole in our nice stratification). So as the water we added became increasingly dense, it nicely layered itself underneath the other water in the tank. And we just had to add more and more dye for the color gradient. Easy peasy :-)

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… ;-)

Dead water — the fancy experiment including Nansen himself

Now that we do have a really awesome 12-layer 6-color stratification, we obviously had to do the dead water experiment again. This time we chose to include a not-too-happy-looking Nansen on the ship, too!

I love this even more than the one we did yesterday!

“Dead water” or: ship-generated internal waves

And here is another experiment that can be done with the same stratification as the lee waves: Towing a ship to explore the phenomenon of “dead water”!

Dead water is well known for 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 of 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)

Finding the explanation for this phenomenon took a little while, but in 1904, Vilhelm Bjerknes explained that “in the case of a layer of fresh water resting on the top of salt water, a ship will not only produce the ordinary visible waves at the boundary between the water and the air, but will also generate invisible waves in the salt-water fresh-water boundary below” — a lot of the ship’s work is now going towards generating the internal waves at the interface rather than for propulsion.

It’s hard to imagine how a ship will generate waves somewhere in the water below, so we are demonstrating this in the tank:

Isn’t it fascinating to think about how far oceanography has come in only a little over a hundred years? And despite all the extremely powerful instrumentation and modelling that we have available now, how cool are even such simple demonstrations in a tank? These are the moments where I know exactly why I went to study oceanography in the first place, and why it’s still the most fascinating subject I can think of…

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…. ;-)