Ship in Bottle, Meet Rogue Wave in Tub

Toy boats beware! For the first time, physicists have created a rogue wave in a laboratory tank. Although the 3-centimeter-tall wave would topple only a tiny model ocean liner, the observation lends credence to the idea that a simplified theory of water waves can explain freak waves, which have been blamed for sinking real ships.

"There's been quite a lot of criticism over the years for using this simple model to describe this complex phenomenon," say Mattias Marklund, a theoretical physicist at Umeå University in Sweden who was not involved in the work. "But now that you see the wave coming through, it gives you confidence that you can apply this model," he says.

For a deckhand on a fishing boat, a rogue wave is a behemoth that appears out of nowhere, potentially capsizing the ship. For a physicist or an engineer, such a wave has a more precise definition: A rogue or freak wave is one that rises more than 2.2 times as high, from trough to crest, as the average of the largest one-third of nearby waves. So in seas with 3-meter-high waves, a rogue wave would measure 7 meters or more. Scientists and engineers once debated whether tales of such waves were merely myths. However, in recent years, wave measurements and satellite observations have proved that not only do they exist, but they are too common to be produced by chance when smaller waves overlap and simply add their heights.

Instead, rogue waves must somehow amplify themselves through some sort of "nonlinear" feedback. Scientists disagree about exactly how to account for this. The full mathematical equations of "hydrodynamics" are extremely difficult to solve, so theorists generally resort to simpler approximations. In the 1970s, researchers explored describing anomalous water waves with a differential equation—called the non-linear Schroedinger equation—that accounts for only the height, slope, and curvature of the evolving waves.

That equation has several weird solutions, including one with the basic properties of a rogue wave. Discovered in 1983, the so-called Peregrine solution consists of a single peak that suddenly emerges out of a smoothly varying wave train (a so-called sine wave) by sucking energy out of it, zipping along for a while, and then disappearing back into the sine wave. In October 2010, experimenters produced an optical version of that wave with light.

Now, mathematician Amin Chabchoub and physicist Norbert Hoffmann at the Hamburg University of Technology in Germany and physicist Nail Akhmediev of Australian National University in Canberra have produced a Peregrine rogue wave in a water tank 15 meters long, 1.6 meters wide, and filled to a depth of 1 meter. Using a computer-controlled paddle, the researchers generated a sine wave with an amplitude of 1 centimeter, which they measured with an electric depth gauge, as described in a paper in press at Physical Review Letters.

The researchers then briefly increased, or modulated, the size of the paddle's motion. "In the open ocean you can imagine the wind gives you a [similar] small modulation," Chabchoub says. That slight modulation triggers the growth of a rogue wave that zips down the tank at half the speed of the underlying sine wave and grows to three times the sine wave's height, exactly as predicted by the Peregrine solution.

Given the theoretical prediction, it's not surprising that the Peregrine solution has been achieved in a tank, says Al Osborne, a physicist at the University of Turin in Italy. Still, it's a signal result, he says. "It's saying, 'Look, we have these solutions to the nonlinear Schroedinger equation and they're relevant to real water waves,' " he says. "If you can prove that the equation is applicable, then you've taken a big step."

Exactly how applicable the Peregrine solution is remains to be determined. One criticism is that the solution is too simple in that, strictly speaking, it applies only when waves with a narrow range of frequencies are present. But numerical simulations suggest that similar peaks can arise from a chaotic mix of waves, Akhmediev says. Chabchoub says a next step is to try to create rogue waves from those messier beginnings, too.

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