If you’re able to explain how smoke curls up from a cigarette, you can get rich. First, the smoke rises in a straight column – scientists already know the mathematical explanation for that bit. But then, the smoke begins to spiral before it goes off into all directions. The latter is turbulence. This turbulence is one of the biggest unsolved problems in physics. In fact, getting a mathematical grasp on it is so difficult that the American Clay Mathematics Institute of Cambridge has put up a one million dollar reward for the answer. Why not give it a try if you happen to be an advanced mathematics expert?

The stakes are high, which has everything to do with the fact that turbulence is all around us. We mostly know turbulence from our experiences with flying. When a current of air above the wing of an aeroplane collides with one coming from underneath the wing, you get wildly whirling currents of air. But we also know the phenomenon from tap water gushing out in a forceful stream, petroleum swirling through pipelines or the blood in our veins. Most liquids and gases can flow in a turbulent way.

Neon lamps and lightning

And then we haven’t even mentioned plasma yet. Not the plasma in our blood, but the ionised and extremely hot gas in neon lights, plasma lamps, and lightning. On our planet, we don’t come across a lot of substances in plasma state. But this makes Earth an exception to the rule, says Professor Tom Van Doorsselaere from the Plasma-Astrophysics Unit at KU Leuven. “The estimation is that – apart from dark matter – 99 percent of the mass in the universe consists of plasma. The stars, including our Sun, are made of plasma.” Van Doorsselaere’s research focuses on the corona of the Sun, the outer atmosphere that looks like a halo during a solar eclipse. This corona, too, consists of plasma.

The estimation is that – apart from dark matter – 99 percent of the mass in the universe consists of plasma.

In short: our universe is mostly made of plasma and turbulence is a frequent phenomenon. You may have guessed by now: the observations indicate that most plasma is in a state of turbulence. And yet, that is surprising in the case of the corona, Van Doorsselaere explains: “The corona is made of plasma dominated by a magnetic field. Think of it as billions of magnetic loops running through the plasma. You’d expect these magnetic loops to keep all the plasma neatly structured. But that’s not the case: our measurements show that there’s turbulence, and the question is how that develops. One theory dates back to the sixties and starts from the premise of colliding waves, comparable with the collision of the currents of air surrounding a plane. But this theory is not valid in all circumstances.”

These simulations show the waves that start on the surface of the Sun and, at first, pass through the corona of the Sun as straight cylinders. In the first image – a cross section – this results in dots of light. In the next stages, the cylinders bend and uniturbulence develops. In this type of turbulence, the waves don’t collide. © Norbert Magyar, Plasma-Astrophysics Unit at KU Leuven

Fluke

That researchers at KU Leuven have now found a new explanation for the development of turbulence is a bit of a fluke, says doctoral student Norbert Magyar. “I study the magnetic fields in the corona of the Sun with calculations that follow a complex mathematical model of the magnetic loops. I wasn’t looking for turbulence.”

In uniturbulence, the waves are buddies, not enemies.

After one month of calculations on one of the supercomputers at KU Leuven, Magyar was in for a surprise. “According to the simulation, turbulence develops because waves move in the same direction, not because they collide. The waves are buddies here, not enemies. As these are one-way waves, we’ve called this phenomenon ‘uniturbulence’.”



Vibrating loops

“The biggest difference with the current theory is that our mathematical model assumes that the plasma is not the same everywhere: it doesn’t have the same density everywhere, for instance, or the same magnetic strength. The magnetic loops in the corona vibrate, sending waves through the plasma. The differences in the structure of the plasma ensure that you always have buddy waves that are calm at first. But the interaction between the waves leads to the development of vortices, and eventually turbulence,” Magyar explains.

Uniturbulence © Norbert Magyar, Afdeling Plasma-Astrofysica, KU Leuven

“If we can to confirm these results with further research, that will be a big step forward in thinking about turbulence in physics. It would mean that turbulence can develop much more easily than we have thus far been assuming,” Van Doorsselaere adds.

Hot swirls

“Turbulence may also offer an explanation for the temperature of the corona – millions of degrees, 100 times warmer than the Sun itself. This doesn’t seem logical because you’d expect the temperature to decrease as you move further away from the Sun. With turbulence, you can explain why the temperature is nevertheless higher in the corona: the waves fall apart into a cascade of smaller and smaller swirls up to the point where you get collisions of atoms and thus heat.”

Exciting times in physics, in other words, although mere mortals probably won’t notice it. Or will they? In the corona of the Sun, solar winds and solar storms develop that determine the weather in space. As a result, the corona has a major impact on our satellites. So if your mobile phone or GPS stops working, turbulent plasma might have something to do with it.