Rough math: focusing on rogue waves at sea.

In late 1942, carrying 15,000 U.S. soldiers bound for England, the Queen Mary hit a storm about 700 miles off the coast of Scotland. Without warning amid the tumult, a single, mountainous wave struck the ocean liner, rolling it over and washing water across its upper decks. Luckily, the ship managed to right itself and continue on its voyage.

Gargantuan waves, which appear unexpectedly even under calm conditions in the open ocean, have damaged and sunk numerous ships over the years. Now, researchers have identified a plausible mechanism that may account for the occurrence of these rogue waves. Using a mathematical model, they demonstrate that ocean currents or large fields of random eddies and vortices can sporadically concentrate a steady ocean swell to create unusually large waves.

The current or eddy field acts like an optical lens to focus the wave action, says applied mathematician Bengt Fornberg of the University of Colorado at Boulder.

Fornberg and Benjamin S. White of Exxon Research and Engineering Co. in Annandale, N.J., describe their model in a report submitted to the Journal of Fluid Mechanics.

Rogue waves can arise in all oceans. However, their frequency and size are particularly notable off the southeastern coast of South Africa. Every year, a few supertankers and other major vessels suffer severe structural damage while traveling southward along a standard route from the Middle East to the United States or Europe.

The vessels boost their speed by taking advantage of the strong, south-flowing Agulhas Current, which skirts the South African continental shelf. Depending on the prevailing winds, this current often meets a steady incoming wave swell nearly head-on. The interaction of wave and current reduces the spacing between the waves and changes their direction.

Applied mathematician Marius Gerber of Stellenbosch University in South Africa recently showed that changes in wave direction forced by a narrow, fast current can raise wave heights considerably in certain areas of the current. His calculations also suggest that such waves would have a distinctive shape, displaying a steep forward face preceded by a deep trough. Mariners who have experienced rogue waves have described such troughs as "holes in the sea."

This focusing mechanism is very likely responsible for the freak, isolated waves encountered in the Agulhas Current, Gerber argues. Such focusing could also occur within or near the Gulf Stream in the North Atlantic.

Fornberg and White have now shown, in principle, that similar focusing can take place when an ocean swell of regularly spaced waves traverses an area of random current fluctuations. They can compute the probability of particularly intense wave action and the formation of rogue waves in different regions of the field. These probabilities depend on how far the waves of the ocean swell have traveled through the eddies rather than on the detailed structure of the eddies themselves.

Exploratory work on the formation of rogue waves at sea and in currents has been largely theoretical so far. The chief problem is the extreme shortage of reliable, complete oceanographic data on this phenomenon to test the mathematical models.

The waves arise rarely, although they're very notable when encountered, Fornberg notes.

The ultimate goal of the researchers is to develop models to predict the location of danger areas and to forecast the occurrence of rogue waves, which would allow ships to proceed safely yet take advantage of ocean currents.

The Agulhas Current is a prime target for such an effort. The latest incident in the area occurred earlier this month, when a cargo ship with 29 people aboard sank after being hit by a wave, presumably a freak giant.