# Mathematicians construct monster waves

## Researchers succeed in producing lifelike production of a giant wave based on a model

Scientists are on the track of the puzzle of the formation of giant waves: they have created a monster wave in the wave channel, which was based purely on a mathematical formula. With this model, they succeeded for the first time to accurately copy the properties of real giant waves. It remains to be tested how applicable this model is, the researchers say. However, future predictions of such giant waves could help prevent major accidents or even catastrophes.

They are enigmatic and dreaded, and no one can predict where and when they appear: monster waves are at least twice, often three times the highest waves in the current sea. So they can become about 15 meters high in a swell of 5 meters. Such giant waves can damage ships on the high seas, and many ships that have disappeared to this day are likely to be on their account. The experts have long been searching for a model to depict the emergence of monster waves. For the first time, this is the first time that a German-Australian research team from the TU Hamburg and the National University in Canberra has succeeded.

The physicist Norbert Hoffmann and the mathematician Amin Chabchoub of the TU Hamburg as well as the physicist Nail Akhmediev of the National University in Canberra carried out their experiment in the wave channel of the TU Hamburg. A paddle creates the waves there, creating modulations similar to those created by wind in the open sea. These eventually cause the growth of a wave that is three times as high as the waves before and after.

The model experiment follows the nonlinear Schrödinger equation, a simplified model equation for water waves. "In this equation, there is the so-called Peregrine solution, which describes how a wave arises out of nothing and disappears into nothingness. So you have a normal wave field that suddenly turns into a huge wave, "says Chabchoub. The Peregrine solution represents a single wave event and involves both space and time.

### Calm before the wave crucial

Significant in the emergence of a monster wave is apparently the moment of calm shortly before. The waves suddenly become shallower before the giant wave piles up, which often happens in a triple formation. "Just as the Peregrine solution shows. It's absolutely amazing that we were able to produce the wave exactly like that, "Hoffmann says happily. display

The successful laboratory test has shown one thing in each case: The emergence of monster waves can be represented by a mathematical model and its solutions. How applicable the observed Peregrine solution is in reality remains to be seen. In any case, the researchers will continue to devote the topic. In the future, besides Hoffmann, Chabchoub and Akhmediev, other scientists, such as an oceanographer from the Russian Academy of Sciences, will be working to unravel the ropes of waves.

### Improved models could warn ships and wind turbines

Although the attention of the marine technicians is based on the theory and they are primarily interested in the mathematical-physical understanding of the solutions, they leave the

Do not forget practical benefits, which could be enormous, especially for shipping. For if one could predict waves and wave periods based on measurements and calculations, this would help to prevent serious accidents or even disasters. It would be conceivable

On board a ship, a sensor registers the wave motion and attaches it before the occurrence of a monster wave sei and only 10 to 20 seconds before. Then passengers and crew could be warned and the course of a ship can be corrected, so that the impact causes less damage.

"Even for the producers and operators of wave energy power plants such calculations would be very helpful, because the monster waves can destroy the plants, " says Hoffmann. Although these solutions were derived mathematically for the first time in the 1970s, there has been no proof of this ever since. The current results of the researchers have appeared in the journal "Physical Review Letters".

(Technical University Hamburg-Harburg, 17.08.2011 - NPO)