A bridge to explaining troubled waters
Put a cutting board or something else flat in the bottom of your kitchen sink and turn on the faucet.
You should see a thin film of water in the rough circle that makes up the middle, a band of roiling, albeit miniature, rapids after that and finally a stretch where the puddle you've made flattens and flows with more or less even regularity.
You're also seeing a liquid flow in its transition to turbulence, often referred to as the last major unsolved problem in classical physics.
Gustavo Gioia started thinking about turbulence because of the meanders on rivers like the Sangamon, rather than his kitchen sink, and having coffee with colleagues who also liked to speculate about what makes flowing liquids turbulent.
Now, Gioia, University of Illinois Professor Nigel Goldenfeld and graduate student Pinaki Chakraborty have taken a step toward a solution for fluid turbulence.
Goldenfeld, a physics professor, emphasized that their findings don't solve turbulence, one of the few physics questions for which a bounty has been placed on the answer.
But the UI research might help explain some of the fundamentals behind the jittery, swirling behavior of liquids and gases when they flow, which plays a role in everything from what makes it rain to how rivers run and how fish swim in them.
"I do think that what we've done is the first new step in this direction for a long time," Goldenfeld said.
While most of the flows around us in everyday life are turbulent flows over rough walls and obstacles, they have remained one of the least understood phenomena of physics, said Gioia, a theoretical and applied mechanics professor.
And yet, they have to be accounted for in a variety of quite practical situations.
Build an oil pipeline, for instance, and you have to factor in the friction the flow will experience to know how big a pipe you need to move it.
Likewise with air flowing around an airplane wing, where a design that decreases friction even a little could be worth billions in saved fuel costs, Goldenfeld said.
Johann Nikuradse, a German engineer, fashioned one of the best tools scientists and engineers have for dealing with the question in experiments in the 1930s. He carefully measured the friction a fluid experiences as it is forced through a pipe at varying speeds, resulting in tables that can be used to figure out friction's impact in a particular project.
Nikuradse also found that the friction decreases as the speed increases – but then surprisingly increases at high speeds before attaining a constant value, knowledge of which is vital to designers of pipelines, airplane wings and the like.
But being able to account for that phenomenon using experimental data, which also has to be generated for new materials as they come along, isn't the same as understanding why it occurs, allowing it to be calculated, or modeled, mathematically.
That's where the work by Gioia and Chakraborty, a graduate student in theoretical and applied mechanics, comes into play.
Over time, talking about it at coffee or lunch and working on it between other things, they came up with a theory that the phenomenon Nikuradse observed arises from the way energy is distributed in the eddies populating a turbulent flow.
Married to work done previously by other researchers and applied in calculations, their theory yielded results that mirrored, and even improved upon in some ways, the results yielded by the tables.
"We were surprised," Gioia said. "It was unbelievable."
Chakraborty said engineers should now be able to calculate friction's impact, rather than relying on tables based on the Nikuradse data.
Meanwhile, Goldenfeld saw their results and thought about the phases materials go through when, for example, they become magnetic, something understood far better than turbulence.
He suggested nearly a decade ago that turbulent flows might go through a similar statistically traceable "phase transition." Work he's now done with Gioia and Chakraborty backs the notion, offering a new way for theorists trying to understand turbulence to approach the problem.
Gioia and Goldenfeld said the National Science Foundation-funded research, outlined this month in the journal Physical Review Letters, also suggests that the roughness of a surface over which a flow passes, previously viewed as dispensable, makes a difference.
"People thought it was an unnecessary complication," Goldenfeld said. "But it turns out to be fundamental."