Dynamical similarity

Science involves designing experiments to test theories. I do not want to get distracted here by how a theory is defined or the precise ways in which a theory is tested by experiment. The point of this week’s Daily Grind is to look at the role of experiments in physics, where they can be used, where it is more difficult to use experiments to test hypotheses and, how this can be connected with coffee. Some physics can be relatively easily tested by observation or experiment: we can for example take photographs of distant no-longer-planets to test theories about the evolution of the solar system or measure the viscosity of a liquid as we add something to it. Yet there are some areas of physics where it is not immediately obvious how you would test any theory that you develop. One such area is atmospheric physics where the limitations of living on one planet with one atmosphere where many different things all happen at once, could potentially be a bit of a problem for doing experiments on the theories of atmospheric physics.

Fortunately, there is a way in which atmospheric physicists can test their theories with experiment and, perhaps unsurprisingly for the Daily Grind, that way involves a cup of coffee (or tea). The route out is called “dynamical similarity” and it is a consequence of the fact that the same mathematics describes much of that which happens in a cup of tea as it does the atmosphere. It is true that a tea cup is a lot smaller than the atmosphere but a vortex in a tea cup is the same as a vortex in the atmosphere even if one is only a centimetre across while the other has a core size of many kilometres. The mathematics will be the same. This allows people to test hypotheses formed about the atmosphere in an environment that they can control and repeat.

A vortex in the atmosphere

… is a vortex.
(Typhoon Nangka, Image Credit: NASA image courtesy Jeff Schmaltz, LANCE/EOSDIS MODIS Rapid Response Team at NASA GSFC. Caption by Kathryn Hansen)

A couple of months ago, I wrote an article in Physics World about the connections between coffee and physics. Shortly after it came out, I got an email from Paul Williams alerting me to an article that he had written in the journal Weather called “Storm in a tea cup“. It turns out that the subject of his research had been to study the impact on the weather of the interaction of two types of atmospheric waves: Rossby Waves and Inertia-gravity waves. The method that he had used to test this was, if not quite a tea cup, a bucket which he could rotate. Rossby waves and inertia-gravity waves are both present in the atmosphere and can be induced, albeit on a smaller scale, in a bucket. He was using the concept of dynamical similarity to explore what happens in our atmosphere. And the experiment was important. Before his experiments, it had been thought that the effect of the interaction of these two sorts of waves was minimal. His experiments revealed that this may not be the case, the inertia-gravity waves can significantly affect the Rossby waves. Given that Rossby waves are responsible for cold/warm fronts and weather phenomena in mid-latitude regions of the world (such as the UK) his results, and his cup of tea, were potentially very important.

I’m always very happy to hear about what others are doing with science in a tea cup or a coffee mug. Please share any thoughts in the comments section below.

Paul Williams “Storm in a tea cup” can be found in Weather, 59, (4), p.96 (2004) 

With apologies to Gertrude Stein.

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