# Vortex gets tied in knots

Physicists use 3-D printing and tiny bubbles to capture twisted-up water

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Swirling rings of fluid have for the first time been tied in a knot. Physicists accomplished the feat with the help of some unlikely lab tools: YouTube videos of dolphins and a 3-D printer.

“It’s a remarkable experiment,” says Carlo Barenghi, a mathematician and physicist at Newcastle University in England. The creation of these knotted vortices in the lab, reported online March 3 in Nature Physics, could help scientists understand the flow of plasma on the sun and the flow of air, blood, and other fluids here on Earth, Barenghi says.

A vortex is a swirling mass of fluid, such as a tornado or a whirlpool within a cup of coffee after stirring in milk. Vortices can also bend and warp into various configurations; the most familiar example is a smoke ring, a twisted cylinder of circulating smoke particles.

In 1867, Scottish physicist Lord Kelvin went a step further and suggested that vortex rings could tie in knots. His idea didn’t get much traction at first, but throughout the 20th century, mathematicians and physicists offered evidence that knotted vortex loops could emerge in various fluids and plasmas and affect their flow. More recently, in January astronomers spotted braided rings of plasma generated by the sun’s magnetic field in the solar corona.

But scientists had had no luck creating knotted vortices in the lab. The difficulty was twofold: They had to generate the knots, which would be very small and disappear quickly, and then capture proof of their existence. Last year, University of Chicago physicists Dustin Kleckner and William Irvine set out to do both.

Kleckner and Irvine came up with the idea of a wing that drags through water. When a wing accelerates suddenly through a fluid (as a plane’s wing does through air), two vortex rings form around it. The twist in the physicists’ plan was to make a wing that was itself tied into a knot, which they hoped would knot up rings in its wake.

The difficulty was getting it built. “It’s almost impossible to make an object like that in a machine shop,” Irvine says. Fortunately, a colleague down the hall had a 3-D printer in his lab. Within a day the printer spat out a knotted wing made of rigid plastic.

But now Kleckner and Irvine had to figure out how to detect any vortex knots their tied-up wing would generate. The scientists hit on an idea by watching a YouTube video of dolphins creating and manipulating vortex rings in a tank at an aquarium. (Click for an example.) The rings are clearly visible because the dolphins blow bubbles that get caught up in the core of the vortex. Kleckner and Irvine decided to mimic this feat by zapping the water with an electric current to produce scores of microbubbles.

The Chicago physicists finally put their wing to the test by coating it with bubbles and then rapidly dragging it through a tank of water. As a swarm of bubbles collected in the wing’s wake, a high-speed camera shooting at 76,000 frames per second captured the movement of the bubbles in three dimensions. When the researchers analyzed the shots, the results were unambiguous: The wing had generated knotted vortices. In the course of several tenths of a second, those entwined loops grew in size and then broke up into separate loops.

The next step, Kleckner says, is to study the structure and interaction of the knotted vortex loops and apply it to the flow of various fluids.

A knotted vortex forms in the wake of a plastic knot dragged through water.
Credit: D. Kleckner and W. Irvine