# 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

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

# 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!

# 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!

# 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…. ;-)

# Wake of a house.

Am I weird for noticing that kind of stuff?

When I posted that picture of the fountain in the last post, it very strongly reminded me of a breakfast my sister and I had in Shetland in 2009, where the flags on the two poles outside the window were blowing towards each other (clearly caught in the wake of the house). I remember me mentioning it to her and taking pictures of it then, but even though I have looked through hundreds of pictures from that epic holiday, I can’t find the pictures that I remember taking through the window. But what I found instead is that I took pictures of the phenomenon from the outside. On three different days!

Day 1.

Shetland flags outside a youth hostel in Lerwick, Shetland.

Day 2.

Same house, same flags, different day.

Day 3.

Same house, same flags, third day.

Do you see what I mean? How weird and fascinating is that??? (And how weird and slightly disturbing is it that I vividly remember those flags that we saw 5 years ago?)

But seriously. Doesn’t that make you wonder what the story behind those flag poles might be? Did they put up one and then noticed after a while that it never showed the wind direction that the flags down at the harbor showed, so they put up the second one on the other side of the house? Did they realize right away that flags on the lee side of a house were going to do something weird, so in order to show that they put two poles? Is there a hidden camera somewhere, waiting to capture people’s reaction to the flags? So many questions…

# Details of lee waves in the tank.

A movie focusing on details of the lee waves in the tank.

In this post, we investigated lee waves in a tank in a general way. Here, I want to show a detail of those lee waves:

In this movie, the concept of hydraulic control becomes visible. On the upstream side of the mountain, the dense water layer forms a reservoir which is slightly higher than the mountain. On top of the mountain and towards its lee side, the layer of denser water is stretched thin and has a smooth surface until about half way down the mountain, where waves start to form. In this thin, smooth layer, flow speeds are higher than the wave speeds, hence disturbances of the interface are flushed downstream and cannot deform the interface. Only about halfway down the mountain, the phase speed becomes equal to the flow speed, hence waves can both form and stay locked in place relative to the mountain.

For more information on internal waves, check out these posts [which are scheduled to go online over the next couple of days]:

# Surface imprints of internal waves

How internal waves in the ocean can be spotted on the surface.

Under certain conditions, internal waves in the ocean can be spotted at the ocean’s surface due to changes in surface roughness or to the movement of floating foam or debris. They can be spotted if half their wavelength is longer than the distance between the interface on which the internal wave is traveling and the water surface, so that the orbital movement caused by the internal waves reaches the water surface. In the tank, they can also be seen – for example by adding small floating particles to the water surface.

Internal wave in a tank. Seen from the side due to different coloring of the two layers, and on the surface in the distribution of floating tracer.

In the movie below, you can see the interface between water layers of different densities and the water surface with particles on it. The particles make it easy to spot how the water surface is being stretched and squeezed as internal waves travel through underneath.

For more information on internal waves, check out these posts [which are scheduled to go online over the next couple of days]:

# Internal (lee) waves in a tank.

Lee wave experiment in a large tank with a moving mountain.

In this previous post, we talked about internal waves in a very simple experiment. But Geophysical Institute has a great tank to do lee wave experiments with that I want to present here (although it doesn’t seem to be clear what will happen to the tank when the remodeling of the main building starts in November – I hope we’ll be able to save the tank!). I think it has originally been used for real research, but these days the GEOF130 lab is the only time this tank gets used.

Tank for internal lee wave experiments – a “mountain” is moved through the tank and generates internal waves.

In this tank, a “mountain” can be moved all the length of the tank through more or less stagnant water, thereby simulating a current going over a non-moving mountain (which might be a slightly more realistic setup). At the lee of the mountain, lee waves form on the interface between two water layers of different density.

For more information on internal waves, check out these posts [which are scheduled to go online over the next couple of days]: