How to Tie a Knot in a Bubble Ring

Nobody has been able to make knotted vortex loops. Until now. A new fluid dynamics video explains how it’s done

You’re probably familiar with filamentary vortex loops, otherwise known as smoke rings and created by sending a puff of smoke into clean air through a narrow opening. Volcanoes, artillery and anyone with a bong can produce them with ease. Even dolphins, beluga and whales blow the underwater equivalent—bubble rings.

These vortices have a peculiar property: in a perfect fluid, they are indivisible—perfectly stable. Back in 1867, the physicist William Thomson, later Lord Kelvin, observed that this property ensures that if a smoke ring became knotted like a trefoil or if two rings became linked, they could never be unknotted. “It being impossible for the matter in any line of vortex motion to go through the line of any other matter in such motion or any other part of its own line,” he explained.

Since then, fluid dynamicists have spent a good deal of time and effort studying the properties of knotted vortex loops, at least as far as theory allows. Experiments to test their ideas have been impossible. The sad fact of the matter is that nobody has been able to make knotted vortex rings partly because the same property that prevents unknotting also prevents two rings combining.

(If you have any doubt, try spending a lazy afternoon blowing smoke rings and attempting to link them together.)

All that changed earlier this year when Dustin Kleckner and pals at the University of Chicago revealed that they had created knotted vortex loops made of bubbles in water. That was the first time anybody had made a knotted vortex loop in the lab.

Now they have produced a video that explains their work as an entry for this year’s Gallery of Fluid Motion at the annual meeting of the American Physical Society’s Division of Fluid Dynamics. You can download the video here (high-res mp4 122.8MB or low-res mp4 9.5 MB)

Their technique is inspired. They start with a 3D printed model of the vortex loop they want to create. So for a trefoil knot, they print out a trefoil.

The experiment starts with the trefoil immersed in water mounted on a stand that accelerates the model rapidly downwards. The sudden movement generates a vortex at the edge of the model. And since the edge follows a trefoil, the vortex is trefoil-shaped too.

What’s more, the sudden movement shakes loose tiny bobbles on the surface of the model and these become trapped at the centre of the vortex, allowing the researchers to study it. And by sweeping the action with a laser and recording the scattered light, they are able to create a 3D model of exactly how the vortex behaves. Their models are almost as impressive to watch as the vortices themselves.

What’s clear from these models is that the behaviour of knots in real fluids is significantly different from those in an ideal fluid. The vortices are all unstable and various kinds of reconnection events cause a single knotted vortex to divide into two loops, a phenomenon that would surely shock Lord Kelvin.

These results raise a number of interesting questions, say Kleckner and co. For instance, are all knotted vortex loops unstable? And since similar reconnection events occur in magnetic field lines and in superfluids, do the same physics apply in each?

Questions that Kleckner and co will no doubt be hoping to answer in future.

Ref: arxiv.org/abs/1310.3321: The Life of a Vortex Knot