How do water rings “bounce”? New discovery answers decades-old question

Air rings blown by dolphins swimming underwater and rings of smoke emitted by jet engines are just two examples of vortex rings. These doughnut-shaped structures and their  mesmerizing movement have been studied for decades given their role in propulsion and—in the case of jellyfish and other invertebrates—biological locomotion. 

A team of researchers at New York University and NYU Shanghai has uncovered a remarkable property of vortex rings that had been overlooked for more than a century—one that illuminates how these rings respond when they move through water and reach air (i.e., at the water-air interface). 

When a vortex ring traveling sideways and up through water reaches the surface and meets air, it can rebound while largely maintaining its shape—much like a tennis ball bouncing off a wall. After the reflection, the ring loses only a small fraction of its energy. However, if the vortex ring moves more directly upward, it breaks apart instead of bouncing. 

The discovery aids in the understanding of the power and limits of vortex rings in underwater propulsion, including in the locomotion of some marine animals, and in more fully comprehending oceanographic phenomena, such as underwater volcanic eruptions and thermal plumes.

“Since Hermann von Helmholtz first mathematically analyzed vortex rings in the mid-1800s, scientists have sought to unravel the mysteries of their properties,” says Jun Zhang, a professor of mathematics and physics at New York University and NYU Shanghai and the senior author of the study, which appears in the journal Physical Review Fluids. “This breakthrough adds to our understanding of their behaviors by revealing some of the factors that affect these rings’ fates.”

To explore vortex rings’ behavior at a water-air interface, the researchers—who also included Zhuang Su, a postdoctoral researcher at NYU Shanghai, and Christiana Mavroyiakoumou, an instructor at NYU’s Courant Institute of Mathematical Sciences—conducted a series of experiments and numerical simulations.

They generated vortex rings through a small piston submerged in a water tank. The scientists varied the release speed and angle of the piston to create rings of different strengths and directional paths. The rings’ movement was traced by fluorescent dye and recorded by a high-speed camera. 

Overall, the rings had four different types of outcomes when reaching the water-air interface: dissipating, rebounding and largely maintaining their shape, breaking apart, and crossing the interface and transforming into a jet of water. 

This video of one of the experiments shows how a vortex ring of water is reflected, or bounces back, once it comes close to the water-air interface.

While the rings rebounded or broke apart depending on their direction of movement, they dissipated when they were weak and crossed the interface when they were strong and aimed more vertically upward.

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