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…
Waiting for an appointment, I sat in the sun next to this adorable little waterfall and looked at so many nice examples of phenomena.
What I like best: The standing waves that you see in the reflection of the tree to the right. They do move a tiny little bit back and forth, but overall stay pretty much in place. In that exact spot, the current velocity is clearly as large as the waves’ phase speed, so they can’t get away in either direction.
A close second place is how smooth the turbulent current gets right before it plunges down the waterfall (see how the turbulence upstream looks like structures are more or less as long as they are wide, and then they become really long ellipses as they are accelerated towards the waterfall and the front is going faster than the back?), and the submerged hydraulic jump (and check out the video in this post for another really cool one!). And I love how the water is boiling with turbulence below the waterfall — at least in the part in the front; in the back there is a lot less flow and a lot less turbulence. Isn’t it amazing how much there is to see in such a little bit of a stream?
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?
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! :-)
Today I went on a wave-hunt expedition to take pictures for posts on the Froude and Reynolds number over at Elin & team’s blog (which you should totally check out if you haven’t done that yet! I am actually proof-reading my posts there and that is saying something ;-))
Anyway. Let’s look at the picture below. Do you see how there are two qualitatively different flow regimes in the Isère? Closer to the banks, you see waves that look like normal waves, happily propagating wherever they want to. And towards the middle of the river, you see that there is a lot of turbulence, but disturbances don’t propagate wherever they want, they are being flushed downstream.
For comparison below a picture of a part of the Isère where it is turbulent all the way to the sides:
And below a nice example of how phase velocity of waves depends on wave length. See all the small, choppy stuff being flushed downstream and then standing waves caused by some obstacle in the middle of the river? That’s because the longer the wavelength, the faster the wave propagates (assuming that we are in deep water, which I think is a safe assumption in this case). So the river is so fast that the slower waves get flushed away and only waves of the length of those created by the obstacle (or longer) can stay in one place (or even propagate against the current). I think that’s pretty cool.
Below is one of my favourite wave-watching sights: A half slit.
And what I really liked: see the spot below where there are all of a sudden standing waves appearing in the middle of the river? Clearly there is a sill below, but I like that you cannot see the obstacle, just deduce that it must be there from how the waves look :-)
It’s not a hardship to be here, I can tell you ;-)
It is quite a beautiful place! And, by the way, this is my 600th blog post on this blog. Can you believe this?
One thing I find endlessly fascinating are – you might have heard it before – standing waves. At the waterfront in Kiel I saw some the other day:
Watch the movie below and be fascinated, too! :-)
Isn’t it amazing how wave crests and troughs seem to appear out of nowhere and vanish again? When we are so used to seeing waves propagate, this is such an interesting variation of the theme! And it makes it somehow more easy to accept that waves transport energy, not mass, because if we can’t see which way they propagate, which way would they transport mass?
One of the reasons I have been wanting to do the vortex street experiment I wrote about on Monday is that it is pretty difficult to visualize flow fields (especially if you neither want to pollute running water somewhere in nature, nor want to waste a lot of water by setting up the flow yourself). As a first order approximation, pulling an object through a stagnant water body is the same as the water body moving past a stationary object.
At the Thinktank Birmingham, they do have a small channel with water constantly running through, and a couple of objects that you can place in the current. Unfortunately, what you see is the wave field that is caused by the obstacle, not the current field.
Wave field developing around a body inserted into a channel
It is still pretty cool to play with it, though!
But neither of the setups (the channel discussed above or the vortex streets on a plate thing from Monday) is really optimally suited to teaching students the way a flow field will react to an obstacle. How amazing would it be if we had a flow field that could be modified to suit our needs? Stay tuned – I might have a solution for you on Friday! :-)
The standing waves are caused by rocks sitting in a current. From the pictures below it is not really clear where those rocks are situated, whether they are upstream of all this wave action or in the focal point of the wave fronts.
More standing waves.
Having stood there with my mom for quite some time the other weekend, just watching the water, I can tell you that it’s the upstream obstacle. You can see for yourself here:
What you also see in that video is that not all of the waves are, in fact, standing waves. The lower-amplitude waves to the left on both the image above and below are not – they are radiating away from some obstacle.
More standing waves.
Just from looking at that image it is clear that the bathymetry is very irregular and that the current speed is quite inhomogeneous, too. So maybe it is not surprising that the condition for a standing wave – that the current speed and the wave speed are the same, but going in opposite directions – is not met everywhere. Particularly, in many cases it is hypercritical and the waves are just flushed away. Note the current speed in the video below.
And all of this action is happening on an exciting river called … wait for it … Pinnau. In Mölln. And this is what it looks like to most people: Tiny little rapids somewhere in a forest.
P.S.: I just realized that when I’ve talked about standing waves before on this blog, I’ve always talked about the see-sawing kind. When obviously this kind is so much cooler!
The experiment we run to discuss the velocity of shallow water waves.
In this post, I discussed how it took us several years to modify an experiment to make it both student and teacher-friendly. But what can you actually see in that experiment?
The movies below show the type of standing waves that are excited in the tank. This movie for 24 cm water depth (Ha – this is going to come back and haunt me! I’m not actually sure what the water depth in this experiment is. It looks like this is the case with the highest water level we have run. But if you want to know for sure go ahead, measure the period, calculate the phase velocity (the tank is 175 cm long) and then calculate the water depth. Good practice! ;-))
And then this movie shows the experiment with a lower water level (12 cm? 8? I don’t remember).
It’s interesting to see how much more difficult it is to excite a nice standing wave if you have less water in the tank. Intuitively that makes sense, but does anyone have a good, not-too-theoretical explanation?