Physicists Finally See 'Kelvin-Wave Turbulence' Lord Kelvin Predicted in 1880, in a Tank of Water
A Paris team shook the top of a draining whirlpool and filmed its core with a high-speed camera. Energy cascaded from large ripples to ones 100 times smaller, exchanged six waves at a time, exactly as theory said.
Anyone who has watched a bathtub drain has seen a whirlpool form above the plughole, its narrow core wobbling and twisting. For nearly 150 years, physicists have predicted that those wobbles can turn turbulent, handing energy from big ripples down to ever smaller ones. Now a team in Paris has seen it happen for the first time.
The researchers, led by Eric Falcon of Université Paris Cité, report in Physical Review Letters that they observed what is known as Kelvin-wave turbulence along the core of a controlled whirlpool in a tank of water.
Kelvin waves are corkscrew-shaped ripples that travel along the core of a vortex. The Scottish physicist Lord Kelvin described them mathematically in 1880. Today they are thought to be central to the behavior of superfluids, exotic ultracold liquids that flow with no friction at all. When a superfluid is stirred, its motion collapses into tangles of extremely thin vortices that launch Kelvin waves as they cross and reconnect. Theory says those waves pass their energy to shorter and shorter ripples until it can finally escape as sound. Because superfluids have no friction to slow them, this cascade is believed to be how their turbulence dies away.
Testing that idea directly has been close to impossible. In some superfluids the vortices are only fractions of a nanometer wide, far too small to film. Falcon's team took a different route, reasoning that Kelvin waves ride along any vortex, including a large one in ordinary water. They continuously pumped water into a cylindrical tank about 21 centimeters across and let it drain through a small hole in the bottom, creating a long, steady air-cored vortex. A ring at the top of the vortex shook its upper end in a random pattern, while a high-speed camera filmed the core along much of its length so the team could track exactly how it moved in space and time.
The footage showed energy from the shaking ring spreading from large, slow ripples into smaller, faster ones across a range of sizes spanning roughly a factor of 100. The way the energy was distributed across those sizes closely matched the predictions of Kelvin-wave turbulence theory. The team also pinned down the mechanism: the ripples swapped energy in groups of six waves at a time, just as the theory predicted.
The result gives long-awaited experimental support to ideas physicists have been developing for decades, and it turns a humble water tank into a laboratory for effects normally locked inside ultracold liquids. The researchers say the setup can now be used to study more complex situations, including many vortices interacting with one another.
That could help physicists understand turbulence in systems ranging from laboratory superfluids to the interiors of neutron stars, where matter is thought to flow as a superfluid threaded with enormous numbers of quantized vortices. The paper, by Jason Barckicke and colleagues, is titled "Experimental Evidence of Kelvin-Wave Turbulence along a Vortex Core."
