I love how below you see the sharp edges of where the bridge’s shadow makes it possible to look into the water, when it is impossible to see anything where the sky is being reflected. But you see the equally sharp edge of the reflection of the mountains on the other side where you can’t look into the water. Isn’t physics just amazing?
Also I don’t know what it is, but I really like this perspective on the bridge :-)
The geometric shape of Lille Lungegårdsvannet makes for perfect wave watching conditions. Not only when wanting to look at waves from all sides, but also when you are just fascinated by reflections and geometric wave pattern.
And also by rainbows. Am I the only one who, when the sun is out and at a good angle, walks around Lille Lungegårdsvannet to see the rainbow that you know must be there?
I was super keen on trying the Taylor column experiment, but maybe I expected things to look too much like my sketch below, or my technique isn’t quite perfect yet, but in any case, the results don’t look as good as I had hoped.
This is the setup I was aiming for:
put ice hockey puck (two in our case), ca 1/5th water depth, ca 1/4 diameter of tank
rotating our tank at 5rpm (ca 7 on GFI’s large tank’s display) with the obstacle in the water until solid body rotation is reached (We know that solid body rotation is reached if paper bits distributed on surface all rotate at same rate as the tank).
change the rotation rate a tiny little bit so water moves relative to tank and obstacle, i.e. we have created a current flowing in the rotating system.
And here is what happened.
tank was rotating way too fast
tank wasn’t in solid body rotation because it wasn’t level
one of the hockey pucks didn’t stay in place but moved to the edge of the tank as the tank (slowly!) accelerated
more confetti on the surface!
But! We see that there is clearly something happening around the hockey puck that seems to deform the curtain of blue dye.
Stopped too rapidly / bumpy
Even though the blue dye curtain moves over the pucks initially, we see that they develop a wake or something, deforming the dye.
Accidentally deleted the movie, so we will have to make do with a couple of pics I took while the experiment was running.
Slowing down worked a lot better this time round. We clearly see that the dye curtains are deformed around the Taylor columns and don’t move over the pucks.
I think I am finally accepting that this way of introducing dye as a tracer isn’t working as I had hoped…
And this is when my camera decided to stop working…
Back to the basics: Confetti floating on the surface.
Before slowing down, the field of confetti looked like this.
Then, the tank was slowed down and the field got deformed. Some confetti went over the puck, but there is an eddy downstream of it that catches confetti.
And the confetti that went over the puck seem to be stuck there.
Final attempt (for now).
More confetti. This is the situation before slowing down the tank:
Confetti distribution is influenced by the puck similarly to what we saw in the dye: Some confetti are slowed down upstream, some move around the puck.
Eventually, most confetti end up in the puck’s wake.
Anyway, when I went there a couple of days ago, things were different. And while I still love visiting ruins of industrial buildings, especially in great weather, the water was … flat.
As in “flat as a mirror”. Below, you see the pillars that a bridge used to rest upon when the power plant was still in operation. And I have never been able to get this close to the funnel, whenever I have been here before, there were waves splashing everywhere and I wouldn’t have dared to go anywhere near that area.
Below you see the funnel that waves usually run up in and splash spectacularly. On the day we were there, we could walk up all the way to the funnel and even look down into it. See how the floor isn’t even wet in some places close to the funnel? The largest waves we saw were the size of the one below, just barely making it up into the mirror-like pond you saw in the picture above.
But luckily there is interesting stuff to watch there even when there are no waves, for example this happy fishy which just looks so content enjoying the view from the top of the cliff.
Or corroded steel rope. Did you know there is just ordinary rope in the middle? I did not. And how interesting that that middle bit is all that is left of the steel rope in places!
And also I always enjoy seeing different wave fields on bodies of water that are located close to each other, like here where the upper reservoir is sheltered from the wind whereas the lower isn’t.
So a nice trip all in all, just not quite the wave watching I had been hoping for! But I will be back! :-)
When Tor came to visit me in GFI’s basement lab a couple of days ago, he told me about an experiment he had seen in Gothenburg in the seventies. So Elin and I obviously had to recreate it on the spot. Therefore today, we are comparing phase- and group velocities in deep and shallow water!
Waves are excited by means of an oscillating, hand-helt beer can, curtesy of the beer brewing club at GFI. The experiments are filmed and wave lengths and phase velocities are determined from the videos, which is a lot easier than measuring them directly while the experiment is being run.
Shallow water waves
For shallow water, we are using a water depth of 10 cm. Waves are very easy to see and phase velocities are equally easy to measure.
There is another experiment on (standing) shallow water waves being run at GFI the year before students attend GEOF213, which I described back in 2013.
Deep water waves
For deep water waves, we use a water depth of 42.5 cm (the exact number only matters when the tank filling is also used to fiddle with the dead water experiment, as I had been when the idea for this experiment came up).
Typical wave lengths that are easy to do are between 10 and 25 cm (wave lengths obviously have to be short enough that the water is still “deep”, i.e. H>>wave length) — Elin’s instruction to me for the kind of waves she wanted was “Allegro!” :-D Elin, you are really the coolest and most fun person to play with tanks with!
In deep water, we now have the added difficulty that the phase speed is twice as fast as the group speed. This makes observing the whole thing a lot more difficult. Also amplitudes are a lot smaller now, since the tank was so full and we wanted to keep the water inside…
Here is t0 — Elin has just dipped the beer can into the water for the first time
t1 — can you see the wave signal has propagated up to where the red arrow is pointing to?
t2 — the signal has reached my thumb at the left edge of the picture.
From timing this, we can calculate the group speed. We can also measure the wave length on the video and then calculate a theoretical phase speed from that. For the experiments Elin and I did, the results were pretty good, as in phase speed was usually about twice as fast as group speed. And I am curious to hear how well this works out when the students run the experiment!
My friend Pierre, who I went to Saltstraumen with in 2012, wrote me a text about a year ago and asked me to remind him to tell me about 51 next time we met. We met and, as we do, geeked out about some hydrodynamics stuff. And he told me about 51. It turns out that on his way to work, Pierre crosses Straume Bru on the 51 almost daily, and watches the strong tidal currents and whirlpools that form there. But it wasn’t until a couple of days ago that we managed to take bus no 51 to this specific spot — Straume Bru — and geek out about it together!
I got there about an hour before Pierre did. Not because he was late, but because I was so excited to finally see that tidal current I had heard so much about! And also because I had looked at the tidal forecast and wanted to make sure I would see the strongest current and not miss it by an hour.
Turns out that when I arrived, the current was indeed quite strong. But look at the water level relative to the structures. Pretty much half time between high water and low water, even though the current is strong, there is still a lot of water left in the reservoir!
I love watching the waves radiating from the edge in that wall, and the wedge of eddies that is separating the fast flow from the boundary.
Also look at how the waves are being deformed by both the eddy and the current in the picture below! Especially in the top left corner, where the “wake” of the edge follows the meanders.
As had been forecasted, it started to rain while I was wave watching. With the surface a little rougher now, I noticed these two long streaks. Not sure what was going on there?
It didn’t look like oil or any surface film, but I can’t really think of anything else right now. I was briefly considering Langmuir circulation, but I don’t think the wind was steady enough and also I don’t know if that would combine well with a strong current. Any ideas, anyone?
In any case, the stripes weren’t visible any more when the rain stopped. But look at all these amazing waves!
And, now looking downstream, some more eddies and whirlpools!
Looking upstream towards the bridge, we see the glossy V that is formed upstream of where the wakes meet that are formed by the walls on either sides of the outlet.
And downstream again — how awesome and cute are those little eddies? And how amazing is it that they can persist over long distances while maintaining a dip in the surface that is probably as long as my thumb?
And not two seconds look the same!
Below is a closer look of the two wakes of the sides of the outlet coming together and overlapping.
And here is another picture of the wedge of eddies that forms, separating the strong current from the more stagnant, turbulent boundary layer. Look at how irregular the wedge is, formed of eddies of different sizes that are being advected downstream! And also look at the waves that are being pulled with the current, leading to stripes along the current!
Here is another look at the wedge and the stripes of the waves that are being deformed by the current.
And another one, because the scenery is actually really pretty, too! Which I hardly noticed until I had taken about 500 pictures of the water ;-)
More eddies in the wedge.
Interesting how one side of the outlet forms a wedge while the other “just” forms a wake, isn’t it? I think it’s because the the left one, the one with the wedge, restricts the current a lot more.
And here is a new perspective: Looking at the wedge of a second, parallel outlet. You see really well how the boundary layers from both sides come together!
Looking upstream, the standing waves in the foreground give you an idea of how strong the current is!
And another beautiful wedge!
And more turbulence looking downstream. Funny how parts of the surface look so glossy and smooth, isn’t it? I think those are the areas outside of the current that aren’t turbulent.
Now a final excursion to the other side of the bridge, to look at the wakes of the structures. Notice how much less water there is now!
And here is the upstream part of the V.
And the beginning of the wedge.
Walking a little around the corner, we see that the wake begins already upstream of the corner!
And a final look at the wake.
This is how happy wave watching makes me, even when it’s cooold and raining! At least occasionally, not the whole 1.5 hours I was there… The rain, I mean. Happy I was all the time :-)
Two days later, I actually took the bus across the bridge (after another adventure with Pierre, more on that soon!) and the current went the other way! As it should, but it’s always nice to confirm theory.
Anyone taking this bus regularly? You should start taking pictures for a time series! :-)
When I wrote the blog post on “wave watching in a bucket” a couple of days ago, it strongly reminded me of a movie I had filmed already back in March 2018. I was sitting on a train, still inside the train station, and noticed the pattern in my mug (also I just had gotten my awesome lighthouse thermos, hence the awkward angle of the camera).
The train is vibrating, and that vibration makes standing, concentric waves appear and disappear.
I noticed the same pattern on the lady-next-to-me’s coke zero on the bus yesterday, but felt weird leaning over and filming it. So I had to post the old movie instead. And also now I am wondering again what exactly determines the pattern in the standing waves that we get when vibrating buckets or cups with fluids in them…
This experiment just doesn’t want to be filmed by me. Even though I spent more time on preparation of this experiment than on almost any other experiment I have ever done! I have written up the theory behind this experiment, run it with a blob of dye to visualize the wave, then with a ring of dye. But for some reason, something goes wrong every time. Like people opening the door to the lab to come and visit me just the very second I am about to put dye into the tank, resulting in me jumping and a lot of dye ending up in the wrong spots… Or the tank itself getting the hickups. Or the cameras not playing nicely if for once the experiment itself goes well.
Anyway, it is still a very cool experiment! So here are some pictures.
In all those pictures, the tank is rotating a lot more slowly than recommended in the instructions. I thought that might make it all easier to run (5rpm; dial at approximately 7 for GFI big tank, similar to Taylor column). And it looks just fine, except that the restoring force back to the middle isn’t really there (as was to be expected, since the surface is almost flat and the parabolic shape is needed for a difference in water depth).
Below, you see the “ridge”, a piece of hose that connects a solid cylinder in the middle of the tank to the tank’s outer wall. The tank is turning counter-clockwise.
The flow looks substantially different upstream and downstream of the ridge: Upstream, it is laminar and close to the middle cylinder. Downstream, it’s meandering (the Rossby waves!) and diffusive.
Fifth attempt (same as above)
In this experiment, the difference between the flow up- and downstream of the ridge are even more obvious. Look at those eddies!
It’s quite amazing to see how a small disturbance can make the entire system unstable.
Here is a side-view camera plus the top view, both cameras rotating with the tank. The movie is sped up 20x so in about 22 seconds, you will have a good idea of what happens:
And here is the same movie in real time. Here you can really beautifully watch the plumes of dense water sinking to the bottom while the whole column is rotating.
One thing to avoid when running this experiment: Don’t put the ice cube too close to the side of the tank, otherwise it will get stuck there. I don’t know if it was surface tension keeping it so close to the wall or if, since it couldn’t rotate, it decided not to move at all, but in any case: If the ice cube is too close to the wall, it will get stuck. In our case, the dense water then sank down in the small gap between the sloped bottom and the wall of the tank (as you see in the picture below, which is looking under the sloping bottom towards the deep end of the tank).
You still see columns forming underneath the sloping bottom, but that wasn’t quite what we were aiming to do…