Fragile knots untangle deep physics questions

Idea for innovative research began with musing about smoke rings

A Vortex Tied in Knots

UChicago physicists have succeeded in creating a vortex knot—a feat akin to tying a smoke ring into a knot. Linked and knotted vortex loops have existed in theory for more than a century, but creating them in the laboratory had previously eluded scientists.


By Steve Koppes
Photo by Robert Kozloff

There’s actually around 50 years of theory on this subject with no clean experiments.”
—William Irvine
Assistant Professor in Physics

William Irvine became interested in knot physics several years ago while watching a smoke-ring demonstration in New York City’s Washington Square Park.

“I was thinking, ‘Oh, I wonder if you could tangle these things up?” recalls Irvine, an assistant professor in physics at the University of Chicago. So Irvine, then a postdoctoral scientist at New York University, borrowed two smoke-ring cannons and tried shooting them at each other.

Irvine soon learned that tying up smoke rings—what physicists call knotted vortices—is actually quite difficult. After unsuccessfully trying to make them himself, he learned that many others had tried before and failed.

“At some point the enthusiasm wanes and you worry about whether there’s a very good reason why nobody has ever done this,” Irvine said. “But sometimes going into a new field with a little naïveté can be helpful.”

He tried again soon upon arrival at Chicago, with assistance from Dustin Kleckner, a postdoctoral scientist in the James Franck institute. The duo overcame their experimental difficulties by designing and fabricating various hydrofoils (wings used in water) on a 3-D printer. They tried around 30 different shapes before they created the desired vortices in the laboratory for the first time.

Knots bring insights into bigger puzzles

Their work, published in Nature Physics, relates to deep questions in a variety of physics subfields, including turbulence, plasma physics, ordinary fluids and the more exotic superfluids. Knotted structures are thought to occur in all of these phenomena but are difficult or impossible to observe.

“We look at plasma physics and turbulence every day in the sun,” Irvine says, yet such phenomena pose longstanding, unsolved scientific puzzles. Knots created in the lab may help untangle the complicated behavior of the electrically charged gas in plasma flows, for example, and for understanding the energy transport of complex flows in regular fluids and superfluids.

In addition to the work’s scientific importance, the short-lived loops are beautiful and a little hypnotic to watch. The UChicago videos of the lab’s work have attracted more than 90,000 views on YouTube.

The roots of their work date back to the days of Lord Kelvin, more than a century ago. Kelvin had seen a demonstration of a vortex ring by Peter Tait, and was fascinated by their elegance and stability.

Vortex rings should, in principle, be persistent, stable phenomena. “The unexpected thing is that they’re not,” Kleckner says. “They seem to break up in a particular way. They stretch themselves, which is a weird behavior.”

This behavior culminates in what the UChicago researchers call “reconnection events.” In these events, the loops elongate, begin to circulate in opposite directions, move toward each other and collide (the reconnection). Parts of the vortices then annihilate other parts, changing their configuration from linked or knotted into one that is unlinked or unknotted.

Uniting theory and experiment

Conservation of quantities like energy and momentum are among the most important principles in physics. In many systems, the degrees of “knottedness” can be represented as a precise physical quantity that also is conjectured to be conserved. “If confirmed, this would deepen our understanding of the dynamics and connections between many disparate physical fields,” Irvine says. “We don’t know if it’s true or not, but I think we can finally test this in experiment. There’s actually around 50 years of theory on this subject with no clean experiments.”

Irvine and Kleckner overcame the experimental difficulties in generating vortex knots by designing and fabricating various hydrofoils (rings used in water) on a 3-D printer. They tried approximately 30 different shapes before they successfully created the desired vortices. When accelerated in a tank at more than 100 g, hydrofoils leave behind bubble-traced vortex loops, whose dynamics the researchers recorded with a high-speed camera.

“The bubbles are a great trick because they allow you to see the core of the vortex very clearly,” Irvine says.

The collaborative, intellectual spirit and shared resources of the James Franck Institute also proved critical. “We wouldn’t have succeeded without this sort of atmosphere,” he says.

In future research, Irvine and Kleckner hope to perform some of their experiments at larger scale to investigate whether size would lend greater stability to vortex rings. They also are investigating the fine-scale features of the vortices and whether “knottedness” is, or can be, conserved in fine-scale twisting of the vortex loops. “This is not something we presently know,” Kleckner says.