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.
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.
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.
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?