Causing a stir

coronal hole, Sun

Where it all begins. The dark object is a Coronal hole on the Sun. Image credit and copyright NASA/AIA

What’s the difference between your cup of coffee and the solar wind (the fast stream of charged particles emanating from the Sun)? Perhaps this seems a strange question, we ought first to ask what connects your coffee with the solar wind. But, when we look at what connects them, you may be surprised to find the reason that they are different.

The solar wind is a flow of charged particles that streams past the Earth at roughly 400 km/s. To put this figure into some perspective, 400 km/s is 24, 000 km/min which means that the wind travels from the Earth to the Moon in 16 minutes. In comparison it took  Apollo 11 over 3 days between leaving Earth’s orbit and entering the Moon’s (over 4 days between launch and landing). The particles in the solar wind originate in the Sun’s Corona where temperatures get so hot that the gases have enough energy to escape the gravitational pull of the Sun itself. As these particles reach the Earth, they encounter the Earth’s magnetic field and, being rapidly slowed down by the Earth being in the way, a shock wave forms which is known as the Earth’s Bow Shock.

We must all have dragged a spoon through coffee and watched as the vortices form behind the spoon. It is a low-speed example of turbulent behaviour in the coffee. So it is perhaps not surprising that when the very hot and very fast solar wind hits the magnetic field region of the Earth, we find turbulence there too.

vortices in coffee

Vortices behind a spoon being dragged through coffee are an example of turbulence.

Now when we stir our coffee, we will see that there is one big rotation of fluid in the direction of the spoon but we may also notice smaller eddies in the drink. Some of these form from the fact that the coffee is rotating but the mug’s walls are staying motionless, friction forces the fast moving coffee to slow down at the walls. You can actually see this effect if, rather than stirring your coffee, you put it on a record player (or other rotating platform) as has been featured on Bean Thinking previously. Similarly, when you have a large vortex in the form of a smoke ring, it can decay into many smaller vortex “smoke rings” in what is known as a vortex cascade. This too is an effect that you can see in coffee (but rather than smoke rings you can make milk rings with a straw). Very often these milk rings will decay into many smaller rings in the same sort of vortex cascade as you get with the smoke, you can see a video of the effect here or at the bottom of this post. Big vortices decay into smaller vortices until they (to our eyes) disappear entirely.

vortices, turbulence, coffee cup physics, coffee cup science

Vortices created at the walls of a mug when the whole cup of coffee is placed on a rotating object (such as a record player). This is an image of water in a rotating mug with a drop of ink placed next to the mug’s wall.

The important thing is that this type of vortex cascade has also been observed in the solar wind. Rather than a giant spoon though, the solar wind stirs itself as the fast wind encounters the (relatively) slow Earth. We are used to stirring our coffee as a way of cooling it down, perhaps we blow on it gently to speed up the cooling process. But this is the difference between your coffee and the solar wind. When the solar wind is stirred up, it gets hotter. To examine how this occurs, scientists have been examining data from the Cluster set of satellites. Launched by the European Space Agency to study the magnetosphere of the Earth, Cluster has provided clues as to how the solar wind differs from a cup of coffee. Back in 2009, scientists analysed the data from Cluster looking at precisely how the turbulence produced as the solar wind meets the magnetosphere cascades into different sorts of eddies, different levels of turbulence. Comparing the data to theoretical models, they showed how the turbulence started off on large length scales (of the order 100 000 km), and decayed into smaller and smaller length scales until it reached 3km. At this point, all that energy, all that motion was dissipated as heat. Stirring the solar wind heated it up.

Why does stirring the solar wind heat it up whereas stirring your coffee cool it down? It’s to do with the environment of the coffee and the wind. On the Earth, the coffee will be surrounded by a cooler atmosphere. Stirring the coffee brings the hot liquid into contact with the cooler air and so the heat from the coffee can escape more efficiently into the atmosphere. They say in space, no one can hear you scream, which is another way of saying that there is no atmosphere through which sound waves can travel¹. No atmosphere means that there is no way of the heat generated by all that turbulence getting dissipated into a cooler air around it. So, as heat is energy, all that energy involved in stirring up the solar wind gets dissipated as heat in the wind which then has a higher temperature to that which we would naively expect.

So, next time you are waiting for your coffee to cool and stir it to hasten the process, take a moment to think about what is happening approximately 90 000 km above your head where the solar wind is being effectively stirred, and heated, by our planet’s magnetic field.

Seeing a vortex cascade in coffee:

 

¹The origin of the phrase however suggests that this was not quite the meaning that was intended, it was a promotional phrase used for the film Alien.

 

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