Math Reveals The Secrets Of ‘Rogue Waves’

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These enormous waves, until thought to be a maritime myth, can pose major dangers to ships at sea. Scientists are now working on techniques to anticipate them before they happen as reported by National Geographic.

Maritime myths

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.

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 was largely written off as maritime myths.

Today a rogue wave is defined as one that is more than twice as tall as the waves around it.

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.

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. 

How waves can grow

As shipbuilding technologies advanced in the 20th century, the number of surviving witnesses to rogue waves grew.

The ship sustained significant damage and three people were drowned, but most who were on board made it safely back to shore.

The crew aboard the MS München, a German container ship, weren’t so lucky.

After reporting bad weather and sending out distress signals in the early morning hours of December 13, the ship and everyone on it disappeared.

Scientific doubts about these mysterious, giant waves were not completely dispelled until 1995 when a rogue wave hit the Draupner oil rig, a natural gas platform in the North Sea off the coast of Norway.

Data tracking 

Scientists have since figured out that unlike tsunamis, which are large waves produced by a sudden displacement of water from an event such as an earthquake or landslide, rogue waves form due to a chance combination of wave movements through the ocean.

One reason for the uncertainty is that rogue waves are rare.

Even now, there’s a dearth of quality tracking data.

A 2019 study led by Chabchoub evaluated several rogue wave observations and models, and the team concluded that the inciting rogue wave mechanism can change depending on the varying factors in the sea at a given time, known as the sea state.

To compensate for limited observations of rogue waves, scientists rely on wave tanks. 

“Recreations in a laboratory mimic almost one-to-one what happens on the ocean surface,” Chabchoub says.

WAVEWATCH III

When water is trapped in a narrow channel such as a wave tank, it’s much easier for large waves to form and to be observed.

The National Oceanic and Atmospheric Administration are developing a system that can forecast potentially hazardous areas of the ocean every hour using a program called WAVEWATCH III.

It’s a useful tool to help mariners steer clear of dangerous seas, but it may not be enough to protect them from a rogue wave that appears out of the blue.

Johannes Gemmrich, a research scientist at the University of Victoria in Canada who analyzed the 2020 rogue wave near Vancouver Island, says rogue waves are most often generated when waves travel at different speeds and occasionally overlap, supporting the linear addition model.

But he believes wave asymmetry—when waves have higher peaks and lower troughs—plays a crucial role as well.

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 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 actually observed ones,” says Tobias Grafke, a mathematician at the University of Warwick in the United Kingdom.

If you’re the captain of a ship, the most helpful forecasting information would be derived from real-time observations, not statistical probabilities.

Grafke says his team’s formula can account for the specifics of a given sea state, but the more variables you fold in, the harder it becomes to solve quickly.

“It is, therefore, a trade-off between accuracy and time to obtain useful results.”

Real-time forecasting

Scientists have been moving toward real-time wave prediction technology, but the newer approaches need to be tested in real-life settings—a challenge given the rarity of rogue waves.

In many cases, the computation process needs to be ramped up to match the speed of the waves.

Rogue waves can form in just “10 to 15 seconds in rough seas,” Fedele says. 

To predict a rogue wave, scientists would need a radar system to continuously measure waves near a boat, so they could run data through a mathematical model that paints a picture of the ocean’s surface at that moment.

A model that calculates a new surface every five minutes would offer a relatively accurate prediction of how waves would evolve in the next several minutes.

The question now is How [do] you make it fast?

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Source:  National Geographic