A stone hitting a pond can produce a tiny supersonic splash, a new study has found.
Researchers studying the shape of an air cavity made when an object hits a liquid noticed a similarity to the shape of the nozzles that are in supersonic jet engines. Sure enough, air escaping from the cavity can reach supersonic speeds, the team reports in a paper published online January 11 in Physical Review Letters.
After an object such as a stone hits a flat liquid surface, it carves a tube of air through the liquid in its wake, Stephan Gekle of the University of Twente in the Netherlands and his colleagues had found previously. The tube immediately starts to collapse under the hydrostatic pressure of the surrounding liquid, forming an hourglass of water with an ever-shrinking neck. At the instant the cylinder’s walls meet, water rushing into the neck shoots needlelike jets of water up and down into each half of the hourglass cavity.
In the new study, the team looked at how air escapes from the hourglass before the walls touch. Rather than dropping a stone into a pond, which would be difficult to do exactly the same way every time, the researchers pulled a thin circular disk through water at a constant speed. They filled the air above the water with smoke from a smoke machine, such as those “commonly used for light effects in theaters and discotheques.” Next, they illuminated the smoke with a laser and took pictures at 15,000 frames per second to capture the smoke’s movement through the cavity. Computer simulations refined the observations.
The results show that as the shrinking nozzle forces air out of the cavity, the air can reach speeds approaching the speed of sound in air, which is 343 meters per second. Such high speeds were possible even when the cavity neck was as large as 1 millimeter wide.
“People may have expected that you’d get supersonic speeds only at micrometer sizes,” Gekle says. “The exciting and surprising thing is that it actually happens at macroscopic neck diameters, which are important and observable in reality.”
So far, the researchers say, they’ve heard no evidence of a miniature supersonic boom.
As a stone plows into still water, it plows out a column of air. The column collapses in an hourglass shape, and the escaping air (in this video, the air is filled with smoke for visibility) shoots through the shrinking opening at supersonic speeds.
Credit: Stephan Gekle/Physical Review Letters 2010