TURBULENCE: THE DESTRUCTIVE FORCE THAT CAN NEVER GO WITH THE FLOW
▶ NYU Abu Dhabi’s Nader Masmoudi plans to discover the truth about the phenomenon, writes Robert Matthews
If you want to witness one of the greatest mysteries in science, forget space probes and particle accelerators. Simply light a candle, watch it burn for a while then blow it out. The sleek flame will vanish to be replaced by straggly tangles of smoke in the grip of turbulence.
It’s a phenomenon at work everywhere from the sky to the cores of distant stars. Turbulence can offer thrills to canoeists riding rapids and provoke fear in seasoned pilots.
Yet despite its ubiquity and importance, scientists have only the most basic understanding of how it works.
Now researchers in Abu Dhabi are taking on the challenge of turbulence. Led by Prof Nader Masmoudi at New York University Abu Dhabi, their aim is to find out how and why it happens, and what it can reveal about the world around us, from the flow of ocean currents to the movement of city traffic.
Prof Masmoudi and his team will use cutting-edge techniques in mathematics and computing to help them find answers. And they are going to need those techniques, because at the heart of turbulence lurks one of the most formidable formulas in science: the Navier-Stokes equations.
First written about 200 years ago and named after Claude Louis Navier and George Stokes, the French and Irish mathematicians who derived them, the Navier-Stokes equations certainly look baffling.
To experts, the alphabet soup of letters and symbols captures the behaviour of fluids under Newton’s laws of motion. Add the relevant quantities and out pops predictions about how the fluid will behave.
That’s the theory, but there are some nasty surprises buried among those symbols.
For a start, the Navier-Stokes equations are “non-linear”, meaning that small changes to whatever is added to them don’t necessarily have small consequences.
That sounds technical, but most people will be familiar with non-linearity. For example, if we leave our homes only a little later than usual, we can run into much worse traffic on the way to the office than we usually do and can then miss a deadline entirely. A delay of only a few has ballooned into something far bigger.
For scientists grappling with turbulence, such non-linearity is a major problem. It stymies their standard trick for solving complex equations – find the messy stuff and ignore it.
Do that with Navier-Stokes and things don’t go well. In the 1990s, two experts on turbulence used a stripped-down version of the equations to estimate the speed of the Nile on its journey to the sea.
Plugging in the various quantities, out popped the answer: 330,000 kilometres per hour. But ignoring the messy stuff eliminated the braking effect of turbulence, leading to a hopelessly incorrect result.
It’s one of the reasons weather forecasts go wrong. Even using the powerful computers we have today, solving the Navier-Stokes equations is a major challenge.
But the fact the Nile isn’t lethally fast also highlights an important fact about turbulence – it’s often regarded as a bad thing. You need only ask an airline passenger who’s been hurled up and down during a rough flight.
Formula One car designers also loathe turbulence, as the drag it creates can spell defeat on the race circuit.
But it can be beneficial. If you want to cool a bath, it will happen faster if you add cold water with plenty of turbulence.
Nature also exploits its powers. Only last month, researchers at several universities in Europe produced a study that showed the long-distance flight of dandelion seeds was the result of controlling the turbulence of air generated by their spoke-like structure.
The researchers made the discovery using computers and the Navier-Stokes equations to study how the form of a fluffy dandelion seed affects the flow of air through its filaments.
Remarkably, they found that about 100 filaments work best – the same number found on typical dandelions, which can drift for 100km or more.
Prof Masmoudi and his team plan to focus on what happens when fluids stop flowing smoothly and become turbulent.
Again, it’s something that most of us will have witnessed. For example, if we turn a tap on slowly, the water flows out in a smooth, clear stream. But turn the tap a little more, and suddenly the stream becomes messy and turbulent.
That’s because the energy of the water becomes concentrated in tiny eddies – swirls of water – which themselves then break apart into even smaller eddies, and so on.
In principle, the whole process can be explained by the Navier-Stokes equations. But amazingly, no one knows for certain.
It’s possible that one day researchers will plug in certain values to the equations and it will go crazy.
Prof Masmoudi is one of the world’s leading experts on this possibility, which is known as “blow up”.
Because of the importance of the Navier-Stokes equations, proving that it never misbehaves is regarded as one of the biggest challenges facing mathematicians today.
But for now at least, Prof Masmoudi and his colleagues have set their sights on discovering what these calculations can reveal about more everyday problems, such as how the ocean interacts with the coastline and how traffic flows in cities.
And who knows, perhaps the 200-year-old equations will solve the 21st century blight of all those rush-hour tailbacks.
An airline passenger on a rough flight will probably tell you that turbulence is a bad thing ... but it can be beneficial