The water-filled bowls, when rubbed with a leather-wrapped mallet, exhibit a lively dance of water droplets as they emit a haunting sound.
Now slow-motion video has unveiled just what occurs in the bowls; droplets can actually bounce on the water's surface.
A report in the journal Nonlinearity mathematically analyses the effect and could shed light on other fluid processes, such as fuel injection.
At the heart of the phenomenon are what are known as Faraday waves, which arise when a fluid such as water vibrates, constrained by a closed boundary such as the edge of a singing bowl.
As the frequency of the rubbing reaches that at which the bowl naturally vibrates, the bowl's edge begins rhythmically to change shape, from one slightly oval shape into another.
The energy of this shape-shifting partly transfers to the water, in which a range of interesting patterns can arise as the intensity of the rubbing increases.
Prince Charles heard Tibetan singing bowls as part of the Longplayer composition But at a certain point the water becomes unstable - and a fizzing display of droplets and chaotic waves results.
Slow-motion video of that transition now demonstrates how the irregular patterns of waves build up, the way that they crash into one another, and how that frees droplets that fly into the air.
What is more, under certain conditions, droplets can actually bounce repeatedly and skip on the surface of the water.
This "Faraday instability" behaviour and the bouncing drops are familiar from scientific contexts; in 2009, John Bush from the Massachusetts Institute of Technology used a range of fluids to demonstrate the effect in videos on a Discovery Channel programme called Time Warp.
"A woman named Rosie Warburton saw these and sent me an email saying that she had seen the same behaviour in her Tibetan singing bowls," Professor Bush told BBC News. "It was this email that inspired the study."
However, the bowls exhibited Faraday wave behaviour that Professor Bush called "odd by any standards, even to specialists in fluid dynamics such as ourselves".
Professor Bush and his co-author Denis Terwagne from the University of Liege in Belgium have now developed a mathematical model for how the water behaves in the bowls.
Studies of this sort are potentially of broader interest for applications in which the development of tiny fluid droplets is a concern, such as fuel injectors or perfume atomisers - or they may simply be a matter of irresistible intrigue.
"Deducing robust criteria for droplet break-up is important in a number of engineering applications," Professor Bush said. "This study was, however, purely curiosity-driven."
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