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 :-)
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…
I love the little meandering river in the picture above!
We are now approaching the west coast of Norway and all prejudices when it comes to weather over there are being confirmed. It’s grey and overcast. Still, there is a lot of cool water watching to be done on this train ride!
I think it was around this point of my 7 hour train ride, from which I sent a minutt for minutt live broadcast to my friend Kristin, that she pointed out that she had just noticed the common thread in the pictures I was sending: Water!
What a surprise… ;-)
Anyway, it’s getting darker outside, so the quality of the pictures is rapidly decreasing, but I will still show you some rapids in the rivers.
Because they just look super awesome!
And again, waves breaking upstream because the river is flowing so fast, it’s ripping their bases away from underneath them.
And some impressive gorges!
…and very low-hanging clouds.
But the landscape is a lot lusher and greener again!
For both of my tank experiment projects, in Bergen and in Kiel, we want to develop a Rossby wave demonstration. So here are my notes on three setups we are considering, but before actually having tried any of the experiments.
Here are different setups for Rossby wave demonstrations I am currently considering.
Topographic Rossby wave
For a demonstration of topographic Rossby waves, we want the Coriolis parameter f to stay constant but have the depth H change. We use the instructions by geosci.uchicago.edu as inspiration for our experiment and
build a shallow ridge into the tank. They use an annulus and introduce the ridge at a random longitude, we could also build one across the center of the tank all the way to both sides to avoid weird things happening in the middle (or introduce a cylinder in the middle to mimic their annulus)
spin up the tank to approximately 26 rpm (that seems very fast! But that’s probably needed in order to create a parabolic surface with large height differences)
reduce rotation slightly, to approximately 23 rpm so the water inside the tank moves relative to the tank itself, and thus has to cross the ridge which is fixed to the tank
introduce dye upstream of the ridge, watch it change from laminar flow to eddies downstream of the ridge (they introduced dye at the inner wall of their annulus when the water was in solid body rotation, before slowing down the tank).
What are we expecting to see?
In case A, we assume that the rotation of the tank is slow enough that the surface is more or less flat. This will certainly not be the case if we rotate at 26rpm, but let’s discuss this case first, anyway. If we inject dye upstream of the obstacle, the dye will show that the current is being deflected as it crosses the ridge, to one direction as the water columns are getting shorter as they move up the ridge, then to the other direction when the columns are stretched going down the obstacle again. Afterwards, since the water depth stays constant, they would just resume a circular path.
In case B, however, we assume a parabolic surface of the tank, which we will have for any kind of fast-ish rotation. Initially, the current will move similarly to case A. But once it leaves the ridge, if it has any momentum in radial direction at all, it will overshoot its circular path, moving into water with a different depth. This will then again expand or compress the columns, inducing relative vorticity, leading to a meandering current and eddies downstream of the obstacle (probably a lot more chaotic than drawn in my sketch).
So in both cases we initially force the Rossby wave by topography at the bottom of the tank, but then in case B we sustain it by the changes in water depth due to the sloping surface.
My assessment before actually having run the experiment: The ridge seems fairly easy to construct and the experiment easy enough to run. However what I am worried about is the change in rotation rate and the turbulence and Ekman layers that it will introduce. After all, slowing down the tank is what we do create both turbulence and Ekman layers in demonstrations, and then we don’t even have an obstacle stuck in the tank. The instructions suggest a very slight reduction in rotation, so we’ll see how that goes…
Planetary Rossby waves on beta-plane
If we want to have more dramatic changes in water depth H than relying on the parabolic shape of the surface, another option is to use a rectangular tank and insert a sloping bottom as suggested by the Weather in a Tank group here. We are now operating on a Beta plane with the Coriolis parameter f being the sum of the tank’s rotation and the slope of the bottom.
place a dyed ice cube (diameter approximately 5 cm) in the north-eastern corner of the tank
What do we expect to see?
Ice cube and its trajectory (in red) on a sloping bottom in a rotating tank. Note: This sketch does not include the melt water water column!
Above is a simplified sketch of what will (hopefully!) happen. As the ice cube starts melting, melt water is going to sink down towards the sloping bottom, stretching the water column. This induces positive relative vorticity, making the water column spin cyclonically. As the meltwater reaches the sloping bottom, it will flow downhill, further stretching the water column. This induces more positive relative vorticity still, so the water column, and with it the ice cube, will start moving back up the slope until they reach the “latitude” at which the ice cube initially started. Having moved up the slope into shallower water, the additional positive vorticity induced by the stretching as the water was flowing down the slope has now been lost again, so rather than spinning cyclonically in one spot, the trajectory is an extended cycloid.
My assessment here (before having run it): I find this experiment a little more unintuitive because there are the different components of stretching contributing to the changes in relative vorticity. And from the videos I’ve seen, we don’t really get a clear column moving, but there are cyclonic eddies in the boundary layer that are shed. So I think this might be more difficult to observe and interpret. But I am excited to try!
Planetary Rossby wave on a cone (cyclical beta-plane?)
Following the Weather in a Tank instructions, we plan to also do the experiment as above but with cyclical boundary conditions, by using a cone in a cylindrical tank instead of a sloping bottom in a rectangular one.
The experiment is run in the same way as the one above (except they suggest a slightly slower rotation of 10 rpm). Physics are the same as before, except that now the transfer to reality should be a little easier, since we now have Rossby waves that can really run all the way around the pole. Also the experiment can be run for a longer time, since we don’t run into a boundary in the west if we are moving around and around the pole.
Ice cube and its trajectory (in red) on a cone in a rotating tank. Note: This sketch does not include the melt water column!
My assessment before actually having run the experiment: This shouldn’t be any more difficult to run, observe or interpret than the one above (at least once we’ve gotten our hands on a cone). Definitely want to try this!
In earlier posts on drop photography, you might have noticed that the reservoirs for the water that drops out and creates the beautiful liquid art has a weird cork on top, sealing it off, and a glass pipe sticking through. I’ve been wanting to explain what that’s all about for a while, but had to finally draw the picture for our liquid art workshop yesterday. So here we go!
Above, you see Wlodek adjusting something about it, and below is my sketch: A Mariotte’s bottle!
Very useful little thing to control pressure in a reservoir, and with pressure the “reservoir height” that is felt at the outflow, even though the reservoir height is actually changing. Basically, it’s a way to trick the system to feel a constant hydrostatic pressure.
Below on the left, you see the bottle when it has just been filled. A cork is sealing the top of the bottle, except that the inside and outside are connected by a pipe on top and the outflow at the bottom. Initially, the water level inside the top pipe and the bottle are the same and the pressure on both water surfaces is the atmospheric pressure.
As water flows out of the bottle, the water level in the bottle starts sinking. The head space (the air inside the bottle above the water) is sealed off from the outside, so as the water level sinks, its volume increases and its pressure (and thus the pressure on the water surface inside the bottle) sinks. In the middle plot below you see what happens then: The water level inside the pipe starts sinking to compensate for the missing volume inside the bottle.
Eventually, air starts bubbling out of the pipe into the headspace, and the water level inside the pipe is at the very bottom end of the pipe (right plot above). The pressure at this level (marked as A) is now atmospheric pressure, not only at the bottom of the pipe, but throughout the whole bottle. And the pressure at this level will continue to stay at atmospheric pressure levels for as long as the water level is still higher than the bottom end of this pipe. Occasionally, air will bubble out of there to compensate for further outflow.
So at the outflow, we always have the hydrostatic pressure relating to the height from B to A, no matter how much or little water there is in the reservoir. That means that all drop pictures in a series will have similar conditions, even as the reservoir is slowly getting empty. How cool is that? I love those kind of things. So simple, yet so efficient! :-)