From The University of Chicago
3.20.24
Louise Lerner
A new study finds regular patterns can emerge from turbulent motion, usually thought to be completely chaotic. Above, wisps of steam are a traditional example of turbulence. Image by George Dolgikhv / Shutterstock.com.
Physicists show how patterns can emerge from chaos in turbulent fluids.
The turbulent motion of a tumbling river or the outflow from a jet engine is chaotic: that is, it contains no obvious pattern.
But according to a new study, regular patterns can emerge from the turbulent motion of fluids. What you need is an intriguing property called “odd viscosity” that arises under certain conditions, such as when the particles in the fluid all spin in the same direction. Though it’s a specialized circumstance, there are many contexts in nature where a version of this effect may exist, such as in the corona of the sun and the solar wind.
“This surprising effect may add to the growing toolbox to control and shape turbulence,” said Michel Fruchart, formerly a postdoctoral researcher at UChicago, now faculty at the French Centre National de la Recherche Scientifique (CNRS) and co-first author of the paper describing the findings.
The study, a collaboration between the University of Chicago, Eindhoven University of Technology in the Netherlands, and CNRS, is published March 20 in Nature.
Fig. 1: Cascade-induced pattern formation.
a, Direct energy cascade: in a turbulent 3D fluid, energy injected at large scales (red arrow) is transferred to smaller and smaller length scales (black arrows) to microscopic length scales in which dissipation occurs (blue arrow), as captured by the so-called energy spectrum E(k), which describes how much kinetic energy is contained in modes with wavenumber k. The energy transfer across scales can be traced to vortices breaking up into smaller and smaller vortices up to dissipative scales. This mechanism is intrinsically nonlinear: it relies on triadic couplings between the modes of the system. b, Inverse energy cascade: in a turbulent 2D fluid, or in a rotating 3D fluid, there is instead a transfer of energy from the scale in which energy is injected (red arrow) to larger and larger scales, and the energy is either dissipated or piles up at the largest scale available (blue arrow), the size of the system. Correspondingly, vortices merge together until only a single positive vortex and a single negative vortex remain, both of which have approximately half the size L of the system. Inverse cascades can also arise in 3D from mirror symmetry breaking [4*],[55*],[56*] or by imposing large-scale shear [57*]. c, In a hypothetical situation in which a direct cascade and an inverse cascade can be put together in the right order (black arrows in the figure), energy will be transferred to an intermediate length scale , leading to the appearance of structures with a characteristic size independent of the size L of the system. This nonlinear wavelength selection mechanism relying on combined turbulent cascades can be seen as an instance of pattern formation. d, Standard pattern formation from a linear instability: the wavelength corresponding to the most unstable linear mode (that is, the one with the largest growth rate σ(k)) is selected. As an example, we have shown the coat pattern of a cat.
*Science paper reference.
See the science paper for further instructive material with images.
A chaotic nature
Despite how much we’ve learned about classical physics in the past centuries, there’s one problem that still resists full explanation: the phenomenon known as turbulence. Though turbulence appears every day around us—from the clouds churning in the atmosphere overhead to the very blood flowing through our vessels—it is still not as well understood as other common physical phenomena.
“Turbulence might be commonplace in nature, but it is still only partially understood,” said Xander de Wit, co-first author of the publication and a Ph.D student with Eindhoven University of Technology.
This is despite the fact that if we could understand and control turbulence, we might be able to achieve many breakthroughs; perhaps we could design more efficient airplane wings, engines, and wind turbines, for example.
However, there are things scientists do know about turbulence. If you shake a bottle of water, you’ll see eddies forming. They start out at roughly the size of the length of the bottle; then the eddies split into smaller eddies, and then again into smaller eddies, and so on until the eddies dissipate. This is known as a cascade. But if you do the same thing but confine the water to a thin layer, the eddies will instead merge to form one big vortex—the Great Red Spot on Jupiter’s surface is an example of this phenomenon, said Fruchart.
The group of scientists wondered if it was possible to make, and hold, medium-size eddies—neither one big eddy, nor smaller and smaller ones.
The answer is yes—if your fluid has is displaying a property known by the term “odd viscosity.”
Viscosity usually means a measurement of how hard it is to stir—for example, it’s harder to stir a jar of honey versus a jar of water. In normal viscosity, the movement dissipates the energy you’ve injected to it by stirring with your spoon. But “odd viscosity” changes the way objects move but doesn’t dissipate energy. It’s been seen in certain rare conditions in the laboratory.
The researchers built a simulation where the particles displayed ‘odd viscosity,’—in this case, by making all of the particles of the fluid spin like tops. Then, by tweaking the parameters, such as how fast the particles spin, the researchers found a surprise. At a particular point, they began to see patterns instead of random eddies.
Left image: Normal turbulence is a random mix of eddies. Right image: Patterns with a particular characteristic size form when each of the particles spin like tops. Image courtesy de Wit and Fruchart et al.
“The trick, we found, is to create a mixed cascade, where large eddies tend to split and small eddies tend to merge,” said Fruchart. “If you get the balance just right, you see patterns form.”
“When we first saw these effects, we didn’t fully understand what we were looking at, but you could tell there was something different even to the unaided eye,” said study co-author and UChicago Ph.D student Tali Khain. “We had to develop a theory to explain it, and that was really exciting.”
Though not all particles in fluids spin like tops, there are examples in nature. For example, electrons or polyatomic gases in a magnetic field do behave this way.
“In addition to the sun and solar wind, there are diverse contexts where a version of this effect may exist, including atmospheric flows, plasmas and active matter,” said UChicago Prof. Vincenzo Vitelli, one of the senior authors on the paper.
As the scientists work to develop a fuller understanding of their findings, they hope it will lead to a better understanding of the interplay between eddies and waves in turbulent flows.
“We are only at the beginning,” Vitelli said, “but I am fascinated by the idea that you can take a turbulent state that is the epitome of chaos, and use it to make patterns—that is a profound change made by just a twist on the smallest scale.”
The computing was performed at the Netherlands Organisation for Scientific Research SURFsara facility.
SURF, the national HPC centre, supports research and education in the Netherlands.
“These are complex simulations that used more than 3 million CPU hours on a supercomputer; that is the equivalent of running 1000 modern laptops for more than 15 days non-stop,” said Prof. Federico Toschi, the other senior author of the paper.
See the full article here .
Comments are invited and will be appreciated, especially if the reader finds any errors which I can correct.
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