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ScienceWise - Sep/Oct 2009

Monsters of the Deep

Article Illustration
Dr Adrian Ankiewicz, Natasha Devine, Wonkeun Chang and Professor Nail Akhmediev of the ANU Optical Sciences Group
Article Illustration
Second-order rational solution of the nonlinear schrödinger equation simulating the behaviour of rogue waves observed by mariners

How Nonlinear Optics is Shedding Light on Rogue Waves

The history of seafaring is filled with romantic stories of far-away lands and fantastic things. Some of these can be dismissed as fanciful sea stories, but others may turn out to have a grounding in real physics. One recurrent report is of rogue waves - giant walls of water that seem to rise out of the ocean from nowhere and disappear just as quickly. Within the laws of linear wave physics this makes no sense. Whilst two waves can meet to create a larger one, the likelihood of such an event concentrating the energy into one monster wave is essentially zero. Yet over the years, reports from experienced mariners and physical evidence of damage to ships continues to mount.

Professor Nail Akhmediev of the ANU Optical Sciences Group is a world leader in the field of non-linear optics, spending most of his time modelling phenomena like solitons and laser pulses in waveguides. But although such work is driven by a desire to improve optical devices, it may also have important implications in explaining these rogue waves.
“Waves on the ocean and light beams may seem like totally different, things, but the underlying mathematics is almost exactly the same.” Professor Akhmediev explains. “There’s no reason why models based on mathematical concepts like the nonlinear Schrödinger equation can’t work as well for water as they do for light and quantum wavefunctions.”
This is a view shared by oceanographers like Dr Kristian Dysthe of University of Bergen, who began adapting some of Professor Akhmediev’s solutions of the nonlinear schrödinger equation to ocean waves and looking at the higher than usual waves they predicted.
“Dr Dysthe’s work really got me interested in the applications of the nonlinear schrödinger equation to oceanography so I began to explore more advanced solutions that might account for rogue waves exactly as they’ve been described by mariners.”

One particular class of solution presents a scenario where two waves amplified by nonlinear effects occur in the same place at the same time purely by coincidence. This leads to further nonlinear behaviour resulting first in a great hole appearing in the water followed by a massive peaked wave many times higher than the average wave height in the local conditions.

This is an almost perfect description of an incident experienced by the passenger liner Queen Elizabeth II back in 1995. The captain is quoted as saying “The ship’s bow dropped into a “hole” of a trough behind the first wave and was hit by a second wave of between 91 and 96 feet high that cleaned a mast right off the foredeck.” Fortunately none of the passengers or crew were injured and the ship survived, but not every vessel hit by a rogue wave has been so lucky. In 1978 the 37,000 ton MS München, a modern and well maintained ship, was lost with all hands. Although no one can be certain of the cause, the ship’s lifeboat was found with damage to its mountings suggesting that it was torn from the davits almost 20m above sea level by some huge force.

An accumulation of such incidents lead the European Union to set up a program called MaxWave to gather data on wave behaviour. 30,000 satellite snapshots of the ocean surface each 5 by 10km wide were analysed to investigate the frequency of rogue waves. Based on the MaxWave dataset, scientists have been able to calculate that at any given time there are something like ten rogue waves somewhere on the planet. Fortunately the oceans are very big and these waves are relatively localized so the chance of one hitting a ship is quite small. However given the hundreds of thousands of ships at sea every day, that small chance is definitely not zero.

It’s estimated that one ship every week disappears in unexplained circumstances and whilst many are small and poorly maintained craft that may have sunk due to lack of seaworthiness or human error, many others are not. 200 large modern ships have been severely damaged or even sunk by huge waves in the last 20 years. Such waves can reach incredible heights and when they crash into the side of a ship the force exceeds 100tons per square meter. Way higher than any steel structure is designed to come with.

Unfortunately, understanding the mechanisms behind rogue waves doesn’t mean that they can be easily predicted. There are some regions of the world where they occur with increased frequency such as the southern tip of Africa, where the Agulhas current flows along the coast. But they also occur in the deep ocean where there are no such currents.  “There are so many variables that the behaviour of ocean waves is a highly chaotic system,” Prof Akhmediev says, “So although there are conditions like bad weather and current flows that increase their probability, when and where they appear is largely just a matter of chance.”

“But this doesn’t mean it’s hopeless. You never know what will happen in the future. Maybe now we understand what’s going on one day it will be possible to predict or even disrupt such waves as they begin to form near ships.”
Professor Akhmediev and Dr Ankiewicz have recently found important new solutions for wave patterns, and these could be used to explain the formation of the rogue waves, or even find areas where they would not occur, thus benefitting shipping.

Coming full circle, these strange non-linear energy concentrating ocean waves may now lead to advances in optics, possibly explaining mysterious energy spike damage sometimes seen in fibre optic infrastructure.
“We have begun to study rogue waves in optics. If they can be so powerful, we began asking ourselves, why not see if we can deliberately generate them and harness that energy in a useful way?”

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