New Mathematical Model Helps Explain Rogue Waves

A tanker ship encounters a giant wave. John Lund/Getty Images

The high seas can be an unpredictable place, even for the saltiest old sea dog. Even when you don't have to contend with pirates or a great white whale, there's always the possibility your craft could be broadsided by a rogue wave.

Capable of sinking a ship or inundating an oil rig, these rare but powerful waves can reach up to 80 feet (25 meters) high, and pop up seemingly out of nowhere in the open ocean. Although scientists sometimes call them "extreme storm waves," they're not created by weather, but by underwater seismic activity similar to what causes a tsunami wave. The difference between a tsunami and a rogue wave is that while a tsunami travels vast distances through the open ocean at the height of only about a meter, growing into a shore-smashing monster as it reaches land, a rogue wave pops up out of the ocean without warning — a steep-sided, deep-troughed wall of water that lasts as few as 20 seconds before sinking back into the sea.


They can be extremely destructive, and until now, scientists have not been able to come up with a great formula to predict where or when they'll strike. But now, after a decade of intensive study, one research team has suggested a relatively simple mathematical equation to help us understand how rogue waves work. Their work appears in the current edition of the journal Scientific Reports.

Although scientists have been able to create a version of a rogue wave in a lab that's about twice the height of a normal ocean wave by applying a phenomenon called "modulational instability" to water in a tank, it's impossible to simulate the exact interfering wave patterns that travel and interact over immense distances in the ocean to create a true rogue wave dynamic.

"You have to account for the nonlinearity of the ocean, which is manifested in the lack of symmetry between the crests and the troughs," said Francesco Fedele, a professor in the Georgia Tech School of Civil and Environmental Engineering, in a press release. "These nonlinear effects can produce an enhancement of 15 to 20 percent in wave height."

Based on the data collected from three rogue waves measured at oil platforms in the North Sea over the course of a decade, the research team modeled interfering wave patterns in the ocean that could have combined to produce these three rogue waves. After much mathematical futzing, the team created models that exactly predicted the measurements of the waves.

Using this information, they were able to describe the complex convergence of different wave patterns coming together from different directions in the ocean that are ultimately responsible for creating a rogue wave. What's interesting is that the mechanics of rogue waves seem to follow patterns demonstrated by light waves rather than water waves.

"These are fascinating results," says researcher John Dudley from the Institut FEMTO-ST CNRS-Université de Franche-Comté, in the press release. "Many of us have spent years studying the effects of nonlinearity in wave amplification, but it is essential as a scientist to keep an open mind. It is not for us to tell Nature how to work — we must follow where it leads us, even if it means changing our ideas."

The models created by the study could produce data that would help shipping and oil rig companies find safe shipping routes or pumping sites, perhaps giving them an hour's notice to the effects that produce rogue waves, allowing them to avoid problem areas. But nature is rarely 100 percent predictable, and the rare combination of factors that go into creating a rogue wave is pretty random.

"It's just a bad day at the ocean," says Fedele.

Check out this video of a LEGO pirate having one such bad day in a rogue wave simulation: