With the right physics, it’s possible to blast a box of clear circuits across the Solar System with pinpoint accuracy to come within a whisker of distant worlds.
But stir a splash of milk in your tea and the best physicists can do is dangerous a guess at the kinds of patterns you’ll see swirling in the beverage.
Fluids are truly chaotic elements as far as science goes, but a new way to calculate their motion could soon make their flow a lot more predictable.
Not only could scientists use this to improve our understanding of hydrodynamics, but it could make everything from weather forecasts to vehicle design vastly more accurate.
Physicists from the Georgia Institute of Technology have shown it’s possible to identify moments when turbulence reflects measurable patterns, effectively finding flickers of mathematically ordained order within the pandemonium.
“For nearly a century, turbulence has been described statistically as a random process,” says Georgia Tech physicist Roman Grigoriev.
“Our results provide the first experimental illustration that, on suitably short time scales, the dynamics of turbulence is deterministic – and connects it to the underlying deterministic governing equations.”
Turbulence is tricky to predict largely because of the way small whirlpools, or eddies, form in a fluid. When material flows in a straight line in a smooth current, it’s easy to predict its speed and trajectory. Should any path in the current become sluggish, perhaps by being dragged along a less mobile surface, the fluid will curl back on itself.
With each new curling current, a new surface forms that can produce new eddies.
Just to make it even more complicated, each vortex behaves at the whim of a number of factors – from pressure to viscosity – quickly adding up to a tempest in a teacup that no computer could hope to keep track of.
Up close, it all seems so random. Take a step back, and statistics make it clear the overall process remains firmly embedded in the same old rules that govern every other moving object in the universe.
“Turbulence can be thought of as a car following a sequence of roads,” says Grigoriev.
“Perhaps an even better analogy is a train, which not only follows a railway on a prescribed timetable but also has the same shape as the railway it is following.”
Just as with our analogical railway, it’s possible to describe turbulence as either a numerical simulation or by way of physical models. And just as a train timetable is useful for getting you to work on time, sticking to a mathematical approach for turbulence is the only way to go if you want reliable predictions.
Unfortunately, all of those numbers can quickly add up, making computations costly.
To see if there was a way to simplify predictions, the team set up a tank with transparent walls and a fluid containing tiny fluorescent particles. Channeling the fluid between a pair of independently rotating cylinders and keeping track of the glowing contents was like watching trains roll through the station in real time.
However, the researchers actually needed to come up with timetables first and see which ones resembled what they were seeing.
Doing so involved computing solutions to a set of equations devised nearly 200 years ago. By aligning the experiment with the mathematical results, the team could identify when particular patterns of turbulence called coherent structures appeared.
While they regularly arise in moving fluids, the timing of coherent structures is unpredictable. In this particular setup, the coherent structures adhered to a quasiperiodic pattern comprising of two frequencies – one pitched around the axis of symmetry of the flow, the other based on another set of shifts in the surrounding current.
Though it’s not exactly a simple set of equations that can describe turbulence in all its forms, it does demonstrate the role coherent structures could play in making them more predictable.
By expanding on this work, future research could make their ‘timetables’ of turbulence more dynamic, describing them in greater detail than statistical averages could provide.
“It can give us the ability to improve the accuracy of weather forecasts and, most notably, enable prediction of extreme events such as hurricanes and tornadoes,” says Grigoriev.
“Dynamical framework is also essential for our ability to engineer flows with desired properties, for instance, reduced drag around vehicles to improve fuel efficiency, or enhanced mass transport to help remove more carbon dioxide from the atmosphere in the emerging direct air capture industry.”
It might even finally tell you what to expect to see in your next cup of tea.
This research was published in PNAS.