Enormous ‘rogue waves’ can appear out of nowhere. Math is revealing their secrets.

Once considered a maritime myth, these towering waves can pose serious risks to ships in the open sea. Now scientists are developing ways to predict them before they strike.

Katsushika Hokusai’s iconic woodblock print, Under the Wave off Kanagawa, depicts a large wave many often misidentify as a tsunami. The large off-shore wave depicted is more likely a rogue wave.

In 1826 Captain Jules Dumont d’Urville, a French scientist and naval officer, was caught in a turbulent storm while crossing the Indian Ocean. He watched as a wall of water rose some 100 feet above his ship, the Astrolabe. It was one of several waves more than 80 feet tall that he recorded during the wild storm. One of his crew was lost to the sea. Yet after Dumont d’Urville made it back to land, his story, backed by three witnesses, seemed so outlandish that it was dismissed as fantasy.

Scientists at the time believed waves could only reach about 30 feet tall, so the handful of 19th century reports of massive waves rising in the open ocean were largely written off as maritime myths. Only later would scientists realize that the accounts were rare because many mariners who experienced these so-called rogue waves didn’t survive to tell the tale.

Today a rogue wave is defined as one that is more than twice as tall as the waves around it. These giant swells can appear suddenly and seemingly out of nowhere. With steep sides and a deep trough below, they resemble a wall of water rising out of the sea. They can occur during storms with choppy seas but have also been reported in calm waters, which is one reason they’re so difficult to predict.

Scientists have recognized rogue waves as real phenomena since the mid-1990s—but keeping sea travelers safe from them is still a major challenge. Though they are relatively rare, rogue waves can cause severe damage and loss of life if they hit a ship in the open sea. In the vastness of the ocean, the interaction of the many forces leading to rogue waves can be difficult to untangle. More recently, mathematicians have been combining real-world data collected from monitoring buoys with statistical models to understand what causes these gargantuan waves to form. Their work offers hope that we may even be able to predict rogue waves before they strike.

A general formula for the sea 

One school of mathematicians says it doesn’t matter what causes a rogue wave, because one can still predict rogue waves quite accurately using a statistical framework for rare occurrences called large deviation theory.

The idea behind this method is to model the most efficient way a rogue wave can form, then use that model to chart a particular rogue wave’s path of development. The theory can factor in linear and nonlinear effects depending on the scenario, which is why its proponents consider it a unifying theory—one that could perhaps be used to predict rogue waves in various ocean conditions.

“If you just look at the absolute most efficient way of forming these waves, it very nicely agrees with the actual observed ones,” says Tobias Grafke, a mathematician at the University of Warwick in the United Kingdom.

Grafke and a team of researchers tested this theory in wave channels, measured results against real-time wave observations, and found the method could predict rogue waves in both settings surprisingly well.

Source: NatGeo