麻豆传媒

WHEN the cruise ship Louis Majesty left Barcelona in eastern Spain for Genoa in northern Italy, it was for the leisurely final leg of a hopscotching tour around the Mediterranean. But the Mediterranean had other ideas.

Storm clouds were gathering as the boat ventured eastwards out of the port at around 1 pm on 3 March 2010. The sea swell steadily increased during the first hours of the voyage, enough to test those with less-experienced sea legs, but still nothing out of the ordinary.

At 4.20 pm, the ship ran without warning into a wall of water 8 metres or more in height. As far as events can be reconstructed, the boat鈥檚 pitch as it descended the wave鈥檚 lee tilted it into a second, and possibly a third, monster wave immediately behind. , almost 17 metres above the ship鈥檚 water line. Two passengers were killed instantly and 14 more injured. Then, as suddenly as the waves had appeared, they were gone. The boat turned and limped back to Barcelona.

鈥淒escending the first monster wave, the boat was pitched into a second and possibly a third behind鈥�

A few decades ago, rogue waves of the sort that hit the Louis Majesty were the stuff of salty sea dogs鈥� legend. No more. Real-world observations, backed up by improved theory and lab experiments, leave no doubt any more that monster waves happen 鈥� and not infrequently. The question has become: can we predict when and where they will occur?

Science has been slow to catch up with rogue waves. There is not even any universally accepted definition. One with wide currency is that a rogue is at least double the significant wave height, itself defined as the average height of the tallest third of waves in any given region. What this amounts to is a little dependent on context: on a calm sea with significant waves 10 centimetres tall, a wave of 20 centimetres might be deemed a rogue.

If that seems a little lackadaisical, for a long time the models oceanographers used to predict wave heights suggested anomalously tall waves barely existed. These models rested on the principle of linear superposition: that when two trains of waves meet, the heights of the peaks and troughs at each point simply sum. It was only in the late 1960s that Thomas Brooke Benjamin and J. E. Feir of the University of Cambridge spotted an instability in the underlying mathematics. When longer-wavelength waves catch up with shorter-wavelength ones, all the energy of a wave train can become abruptly concentrated in a few monster waves 鈥� or just one.

Longer waves travel faster in the deep ocean, so this is a perfectly plausible real-world scenario. The pair went on to test the theory in a , complete with wave-maker, at a UK National Physical Laboratory facility on the outskirts of London. Near the wave-maker, which perturbed the water at varying speeds, the waves were uniform and civil. But about 60 metres on they became distorted, forming into short-lived, larger waves that we would now call rogues (though to avoid unwarranted splashing, the initial waves were just a few centimetres tall).

It took a while for this new intelligence to trickle through. 鈥淲aves become unstable and can concentrate energy on their own,鈥� says , an oceanographer at the University of Tokyo in Japan. 鈥淏ut for a long time, people thought this was a theoretical thing that does not exist in the real oceans.鈥�

Theory and observation finally crashed together in 1995 in the North Sea, about 150 kilometres off the coast of Norway. New Year鈥檚 Day that year was tumultuous around the Draupner sea platform, with a significant wave height of 12 metres. At around 3.20 pm, however, accelerometers and strain sensors mounted on the platform registered a . According to the prevailing wisdom, this was a once-in-10,000-year occurrence.

The Draupner wave ushered in a new era of rogue-wave science, says physicist at Tallinn University of Technology in Estonia. In 2000, the European Union initiated the three-year . During a three-week stretch early in 2003, it used boat-based radar and satellite data to scan the world鈥檚 oceans for giant waves, turning up 10 that were 25 metres or more tall.

We now know that rogue waves can arise in every ocean. The North Atlantic, the Drake Passage between Antarctica and the southern tip of South America, and the waters off the southern coast of South Africa are particularly prone (see map, below). Rogues possibly also occur in some large freshwater bodies such as the Great Lakes of North America. That casts historical accounts in a new light (see 鈥�Seven giants鈥�), and rogue waves are thought to have had a part in the unexplained losses of some . Most recently, what is thought to have been a freak wave struck the cruise ship Marco Polo in the English Channel this February, smashing windows in a restaurant on deck 6 and killing a passenger.

Rogue elements

So rogue waves exist, but what makes one in the real world?

at the University of Torino, Italy, has spent more than a decade trying to answer that question. His tool is the non-linear Schr枚dinger equation, which has long been used to second-guess unpredictable situations in both classical and quantum physics. Onorato uses it to build computer simulations and guide wave-tank experiments in an attempt to coax rogues from ripples.

Gradually, Onorato and others are building up a catalogue of real-world rogue-generating situations. One is when a storm swell runs into a powerful current going the other way. This is often the case along the North Atlantic鈥檚 Gulf Stream, or where sea swells run counter to the Agulhas current off South Africa. Another is a 鈥渃rossing sea鈥�, in which two wave systems 鈥� often one generated by local winds and a sea swell from further afield 鈥� converge from different directions and create instabilities.

Crossing seas have long been a suspect. A 2005 analysis used data from the maritime information service Lloyd鈥檚 List Intelligence to show that, depending on the precise definition, up to occur in crossing seas.

In 2011, , and Onorato thinks it might also have been the Louis Majesty鈥檚 downfall. When he and his team fed wind and wave data into his model to 鈥渉indcast鈥� the state of the sea in the area at the time, it indicated that , one from a north-easterly direction and one more from the south-east, separated by an angle of between 40 and 60 degrees.

鈥淗indcasting the state of the sea revealed two wave trains converging on the ship, separated by 40 to 60 degrees鈥�

Simpler situations might generate rogues, too. Last year, Waseda revisited an incident in December 1980 when a cargo carrier loaded with coal lost its entire bow to a monster wave with an estimated height of 20 metres in the 鈥淒ragon鈥檚 Triangle鈥�, a region of the Pacific south of Japan notorious for accidents. A Japanese government investigation had blamed a crossing sea, but when Waseda used a more sophisticated wave model to hindcast the conditions, he found it likely that a strong gale had poured energy into a single wave system far larger than conventional models allowed.

He thinks such single-system rogues could account for other accidents, too 鈥� and that the models need further updating. 鈥淲e used to think ocean waves could be described simply, but it turns out they鈥檙e changing at the same pace and same time scale as the wind, which changes rapidly,鈥� he says. In 2012, Onorato and others showed that the models towering as much as 11 times the height of the surrounding seas, .

Early warning

With climate change potentially whipping up more intense storms, such theoretical possibilities are becoming a serious practical concern. From 2009 to 2013, the EU funded a project called , which brought shipbuilders together with academic researchers including Onorato, with the aim of producing boats with hulls designed to better withstand rogue waves.

That is a high-cost, long-term solution, however. The best defence remains simply knowing when a rogue wave is likely to strike. 鈥淲e can at least warn that sea states are rapidly changing, possibly in a dangerous direction,鈥� says Waseda.

Various indices have been developed that aim to convert raw satellite and sea-state data into this sort of warning. One of the most widely used is the Benjamin-Feir index, named after the two pioneers of rogue-wave research. Formulated in 2003 by Peter Janssen of the in Reading, UK, it is calculated for sea squares 20 kilometres by 20 kilometres, . 鈥淪hip routing officers use it as an indicator to see whether they should go through a particular area,鈥� says Janssen.

The ultimate aim would be to allow ships to do that themselves. Most large ocean-going ships now carry wide-sweeping sensors that determine the heights of waves by analysing radar echoes. Computer software can turn those radar measurements into a three-dimensional map of the sea state, showing the size and motions of the surrounding swell. It would be a relatively small step to include software algorithms that can flag up indicators of a sea about to go rogue, such as quickly changing winds or crossing seas. Such a system might let crew and passengers avoid at-risk areas of a ship.

The main bar to that happening is computing power: existing models can鈥檛 quite crunch through all the fast-moving fluctuations of the ocean rapidly enough to generate fine-grained warnings in real time. For Waseda, the answer is to develop a central early warning system, such as those that operate for tsunamis and tropical storms, to inform ships about to leave port. Thanks to our advances in understanding a phenomenon whose existence was doubted only decades ago, there is no reason now why we can鈥檛 do that for rogue waves, says Waseda. 鈥淎t this point it鈥檚 not a shortage of theory, but a shortage of communication.鈥�

This article appeared in print under the headline 鈥淗igh rollers鈥�