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.
For the first time, physicists have created a rogue wave in a laboratory tank (see above graph). Although the 3-centimetre-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.
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.
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, so a next step is to try to create rogue waves from those messier beginnings, too. Check the Norwegian site under the graphic below for more.