A Weight-y issue

Waves on the surface of of a coffee. But what do we know about gravity driven waves rather than surface tension driven ones?

Ever swung a bucket of coffee round in circles swooping down towards the floor and then over your head? Why would you, you may well ask? Well, the answer may surprise you. It’s all about turbulence.

We have probably all come across turbulence, perhaps by watching how milk is added to a black coffee or seeing the steam interact with the air as it evaporates off a hot mug of tea. But it turns out that there is a lot that we do not yet understand about turbulence and this is where the bucket of coffee comes in.

Waves on the surface of a coffee can be dominated by gravity or capillary effects. Capillary waves are short wavelength (higher frequency) waves that are forced into oscillation by the effects of the surface tension of the liquid pulling the surface of the coffee back into shape once its been distorted. Gravity waves are longer wavelength (lower frequency) waves where the disturbed surface of the coffee is pulled back into shape by gravitational effects rather than surface tension effects.

Benjamin Franklin famously stilled the (capillary) waves on one of Clapham Common’s ponds by adding just a teaspoon of oil to it.

The frequency at which there is a crossover from gravity dominated waves to capillary dominated waves is dependent on both the density and surface tension of the liquid as well as the strength of the gravitational acceleration experienced by the mug of coffee. (We’re getting to the bucket). On Earth, the gravitational acceleration is 9.8m/s, the ratio of a liquid’s density to surface tension is quite similar for many liquids and so the transition frequency between these two regimes is generally in the region of 10Hz.

What this means is that if you wanted to study the turbulence affecting one type of wave only you could measure at higher frequency (and so measure capillary waves) or measure the turbulence in a liquid in lower gravity eg. on the International Space Station (so that capillary waves dominate at lower frequencies too). But both of these types of measurement don’t give any insight into what’s happening to turbulent waves sustained by gravity, such as Rossby waves which travel the whole circumference of planets with atmospheres and affect the weather in different parts of the globe.

So how could you study turbulence in the gravity dominated surface waves of water? It goes back to the bucket mentioned earlier. By putting a freely moving bucket (the authors called it a ‘gondola’) at the end of the arm of a centrifuge of 8 m diameter, the authors of a recent paper created an effective gravitational force on a liquid of up to 20x the value of the Earth’s gravitational acceleration. It’s sort of like the bucket of coffee being whirled around in a circle apart from a lot bigger and capable of moving at up to 67 rpm! This meant that they could measure the effects of turbulence on gravity driven waves up to about 100Hz allowing them a large frequency range over which to compare their results to theoretical predictions.

Coffee, Van Gogh
Turbulence comes in many forms: What do you see in your coffee cup?

And when they did so, they proved one nagging problem for theoreticians studying turbulence: the size of the ‘container’ becomes important, something that models had previously neglected. For the 23cm wide bucket of distilled water used by the authors, this may be something that we can easily visualise but the research has consequences for how we understand the Rossby waves that circle our planet as well as the large wavelength waves in oceans. Slightly more connected with coffee (or at least doughnuts), the results are also important for understanding turbulence in plasma waves in tokamaks.

You may have better things to do over the holidays than swirl a bucket of coffee round and round while watching for the waves on top of it, but if you are stuck for something to do…

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