# Topographic Rossby wave

Next attempt at the topographic Rossby wave! This time with following the geosci.uchicago.edu instructions more closely…

…and then the tank had hickups, so we did get waves, but a lot more diffusive than we had hoped, because the tank slowed down a lot more and in a more bumpy fashion than I had planned…

# Setup of the topographic Rossby wave experiment

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, from a cylinder in the middle to the outer wall. My solution: Take a 1.5 cm (outer) diameter hose, tape it to the bottom of a tank to achieve a ridge with smooth edges
• 7 cm water depth
• spin up the tank to approximately 26 rpm
• wait for it to reach solid body rotation (ca 10 min)
• introduce dye all around the cylinder in the middle
• 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
• watch it change from laminar flow to eddies downstream of the ridge. Hopefully ;-)

# Planetary Rossby waves

I ran my new favourite experiment again, the planetary Rossby waves. They work super well on the DIYnamics table we built in Kiel and they also worked really well the other day in Bergen.

I mainly ran it today because I wanted to get an idea of how robust the experiment is, i.e. what to prepare for when running it with students in terms of weird results that might have to be explained.

Here is a side view of the square tank with a sloping bottom. The blue ice cube is melting. The melt water is forming a Taylor column down to the bottom of the tank. Some of it then continues down the slope.

Here we are looking at the slope and see the same thing (plus the reflection at the surface). Note how the ice cube and its  meltwater column have already moved quite a bit from the corner where I released it!

When the blue ice cube had crossed half the width of the tank and the blue melt water had almost reached the other edge, I released a green ice cube. Sadly the dye wasn’t as intense as the blue one. But it’s quite nice that the wave length between the individual plumes going down the slope stays the same, for all the blue plumes as well as for the new green ones.

Here in the side view we see the columns of the blue and green ice cube, and we also see that each of the plumes going down the slope still has Taylor columns attached at its head.

Here is an accelerated movie of the experiment, 20x faster than real time. Not sure why there is still sloshing in the tank (this time I made sure it was level), but it’s very nice to see that the ice cubes are spinning cyclonically, faster than the tank! As they should, since they are sitting on Taylor columns…

I think next time I really want to make a side view movie of the Taylor columns and plumes. Not quite sure yet how I will manage the lights so they don’t get super annoying…

# Planetary Rossby waves filmed with co-rotating camera

And here is my new favourite experiment again: Planetary Rossby waves! This time filmed with a co-rotating camera.

We have a square tank with a sloping bottom at solid body rotation (except this annoying slogging because the rotating table wasn’t levelled out [meaning: I didn’t level it before starting the experiment…]). We then release a blue ice cube in the eastern corner of the shallow end of the tank and watch as the melt water column stretches down to the bottom, and is driven back up the slope to conserve vorticity. A planetary Rossby wave develops and propagates westward!

Above, we are looking at the tank east-to-west. Note the sloping bottom with the deep side on the left. And just look at all these beautiful eddies!

This is what it looks like in motion:

Watch the full experiment here if you are still curious after seeing the 1.5 minutes above :-)

# Topographic Rossby wave

Finally trying the topographic Rossby wave experiment I wrote about theoretically here!

And it is working — ok-ish. If you know what you are looking for, you can kind of see it. So check out the picture above so you know what you expect to see below ;-) We are rotating the tank fairly rapidly (and there are a lot of inertial oscillations in the water even after a long spinup, don’t know why) and then slow it down just a little bit to create a current relative to the topography.

So it turns out that following instructions better might actually have been a good idea. We will do that some other day on a different rotating table.

Here is what we did today:

# Setup of the topographic Rossby wave experiment

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. My solution: Take a 2.3 cm (outer) diameter hose, tape it to the bottom of a tank to achieve a ridge with smooth edges
• important difference to the geosci.uchicago.edu setup: We are just using our cylindrical tank without a solid cylinder in the middle. Therefore our ridge goes all the way across the tank. Main reason is that our rotating tank’s camera sits on six rods, so at fast rotations it is very difficult to insert dye and I thought this way might be easier. But that might not actually be true…
• 10 cm water depth
• spin up the tank to approximately 26 rpm (23 seconds for 10 rotations == 36.5 on the display of GFI’s large rotating table)
• wait for it to reach solid body rotation (ca 10 min)
• introduce dye upstream of the ridge,
• reduce rotation slightly, to approximately 23 rpm (26 seconds for 10 rotations == 33 on the display of GFI’s large rotating table) 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
• watch it change from laminar flow to eddies downstream of the ridge. Hopefully ;-)

# Taylor column in a rotating tank

For both of my tank experiment projects, in Bergen and in Kiel, we want to develop a Taylor column demonstration. So here are my notes on the setup we are considering, but before actually having tried it.

Since water under rotation becomes rigid, funny things can happen. For example if a current in a rotating system hits an obstacle, even if the obstacle isn’t high at all relative to the water depth, the current has to move around the obstacle as if it reached all the way from the bottom to the surface. This can be shown in a rotating tank, so of course that’s what we are planning to do!

We are following the Weather in a Tank instructions:

• rotating our tank at 5rpm 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 little (they suggest as little as -0.1 rpm) so water moves relative to tank and obstacle, i.e. we have created a current flowing in the rotating system.

As the current meets the obstacle, columns of water have to move around the obstacle as if it went all the way from the bottom to the surface. This is made visible by the paper bits floating on the surface that are also moving around the area where the obstacle is located, even though the obstacle is far down at the bottom of the tank and there is still plenty of water over it.

In the sketch below, the red dotted line indicates a concentric trajectory in the tank that would go right across the obstacle, the green arrows indicate how the flow is diverted around the Taylor column that forms over the obstacle throughout the whole water depth.

Or at least that’s what I hope will happen! I am always a little sceptical with tank experiments that require changing the rotation rate, since that’s what we do to show both turbulence and Ekman layers, neither of which we want to prominently happen in this case here. On the other hand, we are supposed to be changing the rotation rate only very slightly, and in the videos I have seen it did work out. But this is an experiment that is supposedly difficult to run, so we will see…

I also came across about a super cool extra that Robbie Nedbor-Gross and Louis Dumas implemented in this demo: a moving Taylor column! when the obstacle is moved, the Taylor column above it moves with it. Check out their video, it is really impressive! However I think implementing this feature isn’t currently very high on my list of priorities. But it would be fun!

# Spin down — lots of shear instabilities in our tank!

When you stop a rotating tank, lots of stuff happens and it is usually very impressive to watch. Sometimes we stop tanks on purpose to show for example the development of Ekman layers, but sometimes we are just done with an experiment and then get to see cool stuff to see just as part of cleaning up.

Like below: When the tank stops, the water inside continues to spin, but friction with the sides and the bottom of the tank starts slowing the water down, inducing shear. Shear in turn produces turbulence and the structures cause smaller and smaller eddies. Very cool to watch!

# Parabolic surface shape of a tank of water in solid body rotation

One of the first exercises Torge and I plan on doing with the students in our “dry theory to juicy reality” project is to bring a water-filled tank to solid body rotation and measure rotation, surface height at the center of the tank and the sides, as well as water depth before rotation, and then have them put those together according to theory.

Setup of the experiment as we did it using a glass vase my mom gave me as tank (diameter 24.5 cm). The non-rotating water depth was 9.2 cm. Once we rotated the tank with 10 rotations per 8.6 seconds, the maximum water level at the outside edge of the tank was approximately 10.8 cm, and the minimum 7.9 cm.

Seeing how difficult it is to “measure” the surface heights while the tank is rotating (we chose to draw circles on the outside of the tank at the heights where we thought the water levels were, in order to measure them later on a non-rotating tank), we were quite pleased with those results once we plugged them into the equations.

Calculating the resting water level as arithmetic mean between the rotating maximum value at the rim and the minimum value in the center, we are only off by 0.1 cm, so not too shabby!

And calculating the height difference between resting water level and rotating maximum level from the tangential velocity and radius of the tank, we are only off by 0.4 cm. So all in all, that’s working well!

Btw, below you see the resting water level and above the mark for the rotating maximum value. Quite impressive difference, isn’t it?

Anyway, looking at rotational surfaces and volumes and stuff this way is a lot more fun than doing it the dry theoretical way only! At least that’s what I think ;-)

# Rotating vs non-rotating turbulence — now with movie!

Lots of demonstrations being prepared for Torge’s and my “dry theory to juicy reality” project. Shown here today: rotating vs non-rotating turbulence. Because the only way to really appreciate how amazing rotating flows are is to compare them with non-rotating ones. And not everybody does have a clear idea what non-rotating flows would even look like.

So here we are dropping dye into a non-rotating tank. Top view shows it forming tons of small eddies and spreading to the sides.

Side view shows that most of the dye sank to the bottom of the tank and is spreading there, showing 3-dimensional turbulence.

Now, for comparison, the rotating case!

Top view shows one single, clean eddy.

And side view shows that the structure is coherent all the way from surface to bottom. Now doesn’t this look really fascinatingly different from the non-rotating case?

To show the difference even more clearly, check out the movie below. Speed of both movies is the same!

# Spinning dye curtain — when a tank full of water has not reached solid body rotation yet

With all the rotating tank experiments I’ve been showing lately, one thing that comes up over and over again is the issue of solid body rotation.

On our DIYnamics-inspired turntable for our “dry theory to juicy reality” project, Torge and I came up with a fun way to illustrate the importance of full body rotation in tank experiments, again inspired by the DIYnamics team, this time their youtube channel.

For the spinning dye curtain experiment, we start up the rotating table, and then pretty much immediately add in some dye. Below, you see what happens when you add in the dye too late (we waited for 2 minutes here before we added it): The water is so much in solid body rotation already, that we only form columns and 2D flow.

But if we add in the dye right away after starting up the tank, we form these spirals where the water further away from the center is spinning faster than the water right at the center, thus distorting the dye patches into long, thin filaments (Btw, I’ve shown something similar in my “eddies in a jar” experiment earlier, where instead of starting up a turntable I just stirred water in a cylindrical tank).

But as the tank continues to spin up, the eddies eventually stop spinning and the tank turns into solid body rotation. If new dye is added now, only columns form, but they stay intact as if they were, indeed, solid bodies.

But seeing the behaviour of a fluid change within half a minute or so is really impressive and something we definitely want to do in class, too!

# Baroclinic instabilities / Hadley cell circulation in a tank

The DIYnamics-inspired turntable that Torge and myself have been working on for our “dry theory to juicy reality” project is finally working well!

This is what the setup now looks like (how simple is that?!) and we had an exciting morning testing different experiments!

The one experiment that we have been using as test case in all our previous sessions is the Baroclinic Instability / Hadley cell circulation. There are sketches of the setup and the expected circulation in this blogpost, so just a quick reminder: We place a cold core in the center of our tank (here a glass with blue ice in it), spin the tank (at approximately 20rpm) into solid body rotation, and introduce dye (blue towards the center, red towards the outer edge of the tank).

And what happens then is just beautiful: We get 2D instabilities that transport cold (blue) water outwards and warmer (room-temperature, red) water towards the center of the tank.

We’ve run the experiment three times with different water levels (and once with Southern Hemisphere rotation just for fun) and it worked beautifully each time.

I find it always fascinating how there is hardly any mixing between the red and blue curtains (and there shouldn’t be any because rotating flows become 2D (as shown here)).

Just look at how the dye curtains form when we first add the blue dye…

And then a little later added some red dye…

And then let the field develop.

So I think we’ve got this experiment down and can run it with the students once the semester starts up again in October! :-)