NYU scientists solve 100-year-old mystery of vortex rings

A team of researchers discovered an extraordinary property of vortex rings—how dolphins propel themselves underwater—that science had overlooked for a century.

Scientists from New York University and NYU Shanghai observed and reported how vortex rings, swirling donut-shaped masses, move through water and reach air without losing their shape, which had never been done before.

In a new paper published in Physical Review Fluids, the study authors explain that researchers have sought to crack the complex code of these agents of locomotion for centuries.

“This breakthrough adds to our understanding of their behaviors by revealing some of the factors that affect these rings’ fates,” says Jun Zhang, a professor of mathematics and physics at New York University and NYU Shanghai and the senior author of the study.  

The discovery contributes knowledge to a niche in science that has been studying the mysterious and famous agents of propulsion for over a century, as the natural phenomenon propels all locomotion, even cigarette smoke.

The study aided in understanding the power and limits of vortex rings in underwater propulsion, as seen in some marine animals.

A vortex ring of water traveling in a tank reflected off a water-air interface. Credit: John Zhuang Su et al., NYU Shanghai

Seriously cool jets

Since the mid-1800s, scientists have sought to unravel the mysteries behind the fascinating properties of vortex rings.

“Hermann von Helmholtz first mathematically analyzed vortex rings,” explain study authors in a recent announcement.

When a jet of fluid is ejected from an opening such as a dolphin’s blowhole, it causes a shear layer, which acts like a boundary between the jet and the surrounding fluid, which then rolls up into a ring shape.

These toroidal (donut-shaped) swirling masses of fluid move as a unit, so they don’t function like regular waves. They actively transport spinning fluid, allowing the moving vortex ring to maintain its shape over impressive distances without much energy loss.

It sounds a little more like a feat of acrobatics, but it couldn’t be more common. When someone releases cigarette smoke into the air, they create vortex rings. Vortex rings play a fundamental role in propulsion. They appear in various forms as a natural phenomenon: jellyfish movement and the wakes of birds. Even jet engines emit vortex rings in smoke.

Vortex ring state / U.S. Dept. of Transportation, FAA, Flight Standards Service

How do they work?

Researchers, such as Christiana Mavroyiakoumou, a notable instructor at NYU’s Courant Institute of Mathematical Sciences, conducted a series of experiments to better understand how vortex rings work.

Using a small piston that scientists submerged in a water tank, they generated vortex rings of different strengths and directional paths by varying the speed and angle of the piston to observe how that might affect their trajectory.

Depending on angle and speed, scientists identified four different outcomes when the vortex rings reached the water-air interface. They either dissipate, rebounding and maintaining their shape, break apart, or cross the interface and transform into a jet of water.

The direction of their movement makes or breaks the process. When weak, they dissipated. When they were strong and vertically aligned, they broke through the interface and reached air.

The study shed light on a century-old mystery. The latest findings provide valuable data for creating more accurate models of vortex ring behavior, and they assist in comprehending volcanic eruptions and thermal plumes.

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