Some say they are the responsible for the loss of many ships at sea, and survivors describe them as “a wall of water” over 30 m tall. Rogue or “monster” waves have long been an enigma to scientists with no convincing theory for their formation. But now physicists in UK and Russia think they may have stumbled upon a worthy mechanism through studies of another system — superfluid helium.

“The wave equations for the two systems are very closely analogous,” team leader Peter McClintock of Lancaster University told

McClintock, who is working with others at Lancaster and the Institute of Solid State Physics in Chernogololvka, came across the mechanism for generating rogue waves while performing unrelated experiments on a special type of heat transfer in superfluid helium called second sound. Unlike normal heat transfer in liquids, which involves diffusion, second sound is a faster, quantum-mechanical process that transfers heat as a wave.

In the researchers’ system, the superfluid helium is contained within a small cylindrical cryostat. At one end of the cryostat is a heater, powered by a sinusoidally varying voltage, which McClintock and colleagues use to instigate the second-sound waves. As the waves pass through the helium at speeds of up to 20 ms–1, the researchers can detect them at the far end using a thermometer.

Inverse cascade

Like most physical systems — including the ocean — superfluid helium is non-linear, which means that it does not respond in proportion to its stimulation. According to the Russian mathematician Andrei Kolmogorov, who presented a theory of non-linear wave interactions in the early 1940s, waves should decay in a process whereby energy “cascades” towards shorter and shorter wavelengths. Eventually, said Kolmogorov, viscosity would be able to dissipate the short-wavelength waves as heat.

Most of the time, McClintock’s team saw this Kolmogorov process for their second-sound waves. However, when they increased the size of the voltage above a certain threshold, and when they adjusted the oscillation of voltage to be in resonance with cryostat, the researchers were surprised to find that the cascade sometimes operated in the other direction — towards longer and longer wavelengths.

This “inverse cascade” could produce single rogue waves more than 50% bigger than their neighbours, similar to the ratio seen in oceanic rogue waves (Phys. Rev. Lett. in publication). Although German Kolmakov, a theorist at Chernogololvka, is analysing the results, the team cannot yet explain how the inverse cascade works. “We are still trying to understand it,” says McClintock.

If McClintock’s team is successful in understanding the mechanism behind monster ocean waves it might enable scientists to predict when they occur, which would be an obvious boon to seafarers. But it might also enable the huge waves to be created — an ability that could have military applications.