Footballers move around pitch like chaotic particles in a fluid
If you’ve watched any England football games recently, this news might not surprise you. Footballers seem to move across the pitch in much the same manner as particles move in a chaotic flow of fluid.
In fluid dynamics, a turbulent flow is a swirling fluid with faster or slower areas and higher or lower pressure. When a stream of milk curls and twists as you pour it into your tea, that chaotic behaviour is turbulence.
Wouter Bos at the École Centrale de Lyon in France and his colleagues have now tracked a turbulent fluid’s motion by picking one point and following it as the fluid tosses it about. “You follow it in time on its spiralling turbulent trajectory and evaluate on which timescale, on average, its direction changes,” says Bos.
The team calculated how the particles twisted and turned in two dimensions over time. Over very short periods of time, regardless of the particles’ surroundings, they all appear to travel smoothly in a straight line. They haven’t moved far enough for a change in direction to be detectable.
Give them a little longer and the average change in direction becomes 90 degrees – as one might expect, since it’s the middle of all possible direction changes from 0 to 180 degrees – and it is dictated by the lack of uniformity in the fluid.
But when a line is drawn and the edges of the area are defined, the geometry of the system takes over. Confine the fluid in a rectangular space like a football pitch for a long period of time and on average the particles change direction by an angle of 120 degrees.
To confirm that those effects are due to the rectangular confines rather than the flow itself, the researchers compared their theoretical fluid particles with data taken from sensors on players during a football match at Nuremberg Stadium in Germany.
A football match is also constrained to a two-dimensional box, but the initial placements and movements of the players are (the coach would hope) not random, so any similarities were purely geometric. Nonetheless, the similarity was striking.
On short timescales, the data from the footballers isn’t reliable: anytime they’re jostling around more than running, such as during a free kick or a penalty, it’s nearly impossible to identify their trajectories.
On long timescales, though, the trajectories matched. The average angle by which the players changed direction, like for particles in a turbulent fluid, was 120 degrees.
“We expected some resemblance, but the fit was far better than expected,” says Bos. You might think players would move in every direction equally, giving an average of 90 degrees, but they seem to open up that angle as they travel up and down the longer side of the pitch. In other words, being confined to a rectangle was more important than the different natures of the system or even the fact that one contains random particles and the other strategically placed humans with minds of their own.
“Turbulence is a major issue in all industrial applications,” says Bos. “Almost everywhere where something moves in air or in water you have energy that is wasted from turbulence.”
Bos hope such analogies will help give us insight into the many aspects of turbulent systems that are still not understood.
He might have better luck in more complicated systems that aren’t dominated by their boundaries, says Filippo De Lillo at the University of Turin in Italy.
“Most non-trivial dynamical features of turbulence, for which we still lack a satisfying theory, are actually contained in those intermediate scales which are not reflected in what we witness during a Sunday at the stadium,” he says.
Journal reference: Physical Review Fluids, DOI: 10.1103/PhysRevFluids.2.064604
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June 19, 2017 at 11:54AM