Looking at a creek on a Sunday stroll, and seeing lots and lots of concepts from hydrodynamics class.
For example below, you see waves radiating from each of the ducks. And you see interference of waves from all those ducks.
What happens if the ducks bring their waves closer?
At some point, all those waves from the ducks are going to hit the weir in the picture below.
And there, they are going to somehow react to the flow field caused by the changes in topography.
And you can spot so many different phenomena: Standing waves, hydraulic jumps, and lots more!
Watch the movie below to see the whole thing even better!
Btw, you might remember this spot, I have talked about standing waves from right there before. Interestingly, the wave pattern in the other post looks really different, probably due to different water levels or changes in topography (maybe someone threw in rocks or they did some construction work on the weir?). But it is still just as fascinating as last time :-)
And for those of you who like to see a “making of”:
A common problem in hydrodynamics is to distinguish between all the different kinds of lines that characterize a flow field: Stream lines, streak lines, path lines, time lines, and probably more that I can’t think of right now.
A common way to think of streak lines is that they are similar to hairs caught in the flow of a blow dryer. So when I saw these long grassy things caught in a flow recently, I thought they would be a nice visualization of streak lines.
But when you look at them moving, you realize that they are not actually showing streak lines. Streak lines would be visualized if, at the root of each of those blades of grass (or whatever they are, I’m not a biologist), dye was dispersed. The dye streak would be exactly showing the streak line. But looking at the grass move, you see that it is sometimes being jerked one way or another, when the direction of the flow changed and the blade is pulled in the new direction of the flow, even though the downstream end might still be caught up in some old flow.
So yes, there are points in time when a streak line is visualized by hairs in the air or grass in the river, but there are also times when they are not. Right?
I’ve promised a long time ago to write a post on vorticity (Hallo Geli! :-)). So here it comes!
Vorticity is one of the concepts in oceanography that is often taught via its mathematical formulation, and which is therefore pretty difficult to grasp for those of us with less mathematical training. But it’s also a concept that you can have an intuitive grasp of, and I’ll try to show you how.
The easiest way to imagine what “vorticity” is, is to think of a little float in a flow. In a vorticity-free flow, that little float will always keep its orientation (see below). However if there is a shear in the flow, i.e. the flow field carries vorticity, it will start to turn.
This even holds true for vortices: There are vorticity-free vortices as well as those that carry vorticity (as the name “vortex” would suggest).
If you think back to the discussion on a tank spinning up to reach solid body rotation, you might recognize that only the vortex with vorticity moves like a solid body. To me, a solid body is basically a fluid with so much friction in it, that molecules cannot change their position relative to each other. And that serves as my memory hook for one condition for the formation of vorticity – the flows must have viscous forces and friction in it.
This sounds very theoretical, but there are a lot of instances where you can spot vorticity in real life, for example twigs caught up twirling in eddies at the edge of streams are clearly moving in a vorticity-filled environment. Below, for example, the stream is clearly not vorticity-free.
Eddies. Dips in the surface and shadows on the ground.
I always get really fascinated by watching how eddies are generated by obstacles in a fluid. But it is especially exciting when you don’t only see the eddies because you see how they deform the surface, but when the water is clear enough so you can see the “shadows” on the ground!
Of course, the dark spots you see aren’t shadows, strictly speaking. As light enters the water from the air, it is being refracted. And since the eddies’ surface imprints are dips in the surface, light is being refracted away from the perpendicular, leading to a less-well lit area – the dark spots.
But isn’t it fascinating to watch how eddies form when the water passes the stick and stones in the water when there is absolutely nothing going on upstream?
When you throw a stick in the water and the waves don’t form circles.
Throwing something in the water usually results in waves traveling out in circles from the point of impact. But if you throw your stick into a current, the waves get distorted. Watch the movie below!
Slightly confusing that the stick drifts away, too, so that it doesn’t mark the center of the circle. But still it is clear that waves travel a lot faster downstream than upstream – at least relative to the whole system, not the water ;-)
More pictures from the same spot at the banks of the Pinnau.
Looking more closely, you can see the water strider:
And now a real close-up from the pond in my parents’ garden (because those pesky little bugs are too fast to take pictures off when you are ashore and they are on the water, and the water is wider than a meter in each direction).
See how you can see the impression its feet make on the water surface?
Talking about how a deformation in the surface leads to light being focussed in different ways here and here, another example came to my mind. Remember how my mom and I were watching the standing waves at the Pinnau a while back? That was the same place where we also observed the “shadows” of the eddies, so as we were playing with water and light anyway, this happened:
See how the stick is deforming the water surface? This again leads to a focussing of light at the ground which you can observe if you follow the stick until you reach the ground and then follow its shadow.
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!