



Video: Watch the fluid equivalent of tying a knot in a smoke ring

The vortex knot was made using bubbly water (Image: Dustin Kleckner and William T.M. Irvine) The strip forming 3D-printed knot used to create the vortex has the cross section of a hydrofoil (Image: Steve Koppes)


Tying a knot in a smoke ring sounds like a feat worthy of those enjoying a certain kind of cigarette. But treat smoke as an example of a fluid, and it becomes a physics problem.

Now for the first time a fluid knot has been created – from water rather than smoke. The achievement will allow us to probe what had been theoretical objects, and this might in turn lead to better models of airflow around aircraft wings, or of strange quantum substances like superfluids.

Unlike the knots in your shoelaces, the knots that physicists and mathematicians talk about are closed entanglements that cannot be untied as they have no ends. The simplest of these are the trefoil, a loop that crosses itself three times, and the Hopf link, two linked loops.

The idea of a knot made of fluid first cropped up in the 1860s when the mathematical physicist Lord Kelvin suggested that atoms might be knots in the ether – a mysterious fluid then thought to permeate the entire universe. That idea fell flat, but since then, knots have become central to many aspects of science, from mathematics to biology. And that has led to renewed interest in the idea of a fluid knot.

Never unravels

Mathematicians have shown that just as knots in string can’t be untied no matter how much you prod and pull them, fluid knots should also never unravel – even though the particles that make up the fluid will be circulating around. But this non-unravelling property only applies if the knot is made of a theoretical “ideal fluid”, one that has no viscosity – in other words, no resistance to flow. How a knot in a real fluid such as smoke or water would evolve is unknown, as is whether these structures exist in nature or in the plumes created by machines such as aircraft.

To investigate, Dustin Kleckner and William Irvine of the University of Chicago, Illinois 3D-printed strips of plastic shaped into a trefoil knot and a Hopf link. Crucially, the strips had a cross section shaped like a wing, or hydrofoil (see picture).

Next, the researchers dragged the knots through water filled with microscopic bubbles. Just as a wing passing through air creates a trailing vortex, the acceleration of the hydrofoils created a knot-shaped vortex that sucked in the bubbles. The result was a knot-shaped flow of moving bubbles – the first fluid knot created in a lab – which the team imaged with lasers.

Once formed, the knots move, rotate and eventually appear to dissipate, though whether the vortices completely unknot, unlike in ideal fluids, or somehow preserve the knottedness but in a more diffuse form remains an open question.

Knotted smoke

It should be possible to create knotted smoke rings using a similar technique, as a smoke ring is simply a vortex in air containing trapped particles of smoke. However, in water, the rings stick around for longer, making them easier to study.

Kleckner and Irvine are now investigating whether they can make more complicated knots. “We don’t think there is a fundamental limit: we’re trying to make all sorts of things,” says Irvine.

Studying water knots could improve understanding of other kinds of vortices, such as those that come off aircraft wings. “People can do simulations to model these problems, but there’s always the issue of knowing whether the simulation is right,” says Irvine.

Knotted vortices might also show up naturally, for example in mysterious superfluids. These frictionless quantum fluids have been created in the lab by cooling helium to near absolute zero and are thought to exist inside neutron stars. Creating knots in water provides an easier way to study their quantum cousins, as the lasers used to image the knots would heat up a superfluid, destroying its properties.

Being able to both create and image these knots is impressive, says Mark Dennis at the University of Bristol, UK. “Kelvin spent a long time trying to understand how vortex knots would flow in fluids, and since then experimentalists have tried to realise his idea.” Now theory and experiment have come full circle, which should help with further study of both knots and fluids, he says.

Journal reference: Nature Physics, DOI: 10.1038/NPHYS2560