Calculating the phase velocities of shallow water and deep water waves from the dispersion relation sometimes seems a bit pointless to students (at least it sure did to me (Mirjam) when I had to do it during my studies years ago). So Elin and I played around with it a bit (thanks to a suggestion by Tor Gammelsrød, who always comes to visit us in the lab!), and now there is a new experiment included in GEOF213 to complement the theoretical exercises that were already in place.

Look at Elin exciting shallow water waves in the picture below. It’s quite easy to imagine how one could measure the waves’ phase speed in the lab, just by taking the time it takes for them to run over a known distance, right? (Btw, this is the shallow water experiment that is part of the 2nd-year instruction, so students should already be familiar with shallow water waves)

Things get a little more complicated if there is more water in the tank, as you see in the picture below. Not only do waves have a smaller amplitude (because we didn’t want to risk flooding the lab), but also there is the thing about phase velocity and group velocity in deep water, that makes both of them a lot harder to observe! We don’t want any spoilers here, but you know what I am talking about…

This is such a simple experiment to run, but having the 6m long tank really helps because it gives us at least some time to observe waves before the reflections from the far end come back to haunt us.

And it is quite difficult to excite waves with more or less constant wave lengths. “Allegro!” is what Elin gave me as instructions for what kind of waves she wanted. Playing with a tank with Elin is always the best!

In the image above, we see planetary Rossby waves. They are propagating along the slope with shallow water to the right. But why? This is the kind of thing one might learn in GEOF213: “Dynamics of Ocean and Atmosphere”. This is theoretical subject, with equations filling the blackboard in most of the classes. To make it more fun, to help understanding of mechanisms and to motivate why a little theory really can’t be avoided, Elin and I (Mirjam) set up a couple of experiments over the last couple of weeks. Some working better than others, but that was to be expected…

But one that worked super well are planetary Rossby waves. We use a square tank with a sloping bottom which is spun up to solid body rotation. Then, a colored ice cube is placed in the shallow eastern corner of the tank. As it starts melting, a column of melt water forms below it. Because the melt water column is being stretched as it is sinking, it starts spinning. Once it reaches the sloping bottom, it is stretched even further. In order to conserve potential vorticity, it moves back up the slope again, starting to form a Rossby wave which then propagates westward.

Below you see an experiment both from the top (upper left corner) and the side.

What I find super cool is that the ice cube, sitting on top of its rotating Taylor column, spins in the same direction as the tank, but even faster than the tank itself! Physics says it has to, of course, but this is the kind of counterintuitive stuff that is just really nice to directly observe.

Here is another experiment, shown in real time.