Huge monster waves could appear out of nowhere.  Mathematics explains their secret.  † National Geographic

Huge monster waves could appear out of nowhere. Mathematics explains their secret. † National Geographic

Scientists then discovered that monster waves are created by a serendipitous combination of wave motions in the sea. This makes it different from tsunamis, which are large waves caused by sudden movement of water as a result of phenomena such as earthquakes or landslides.

There are now two important mathematical explanations for the origin of savage waves: linear summation and nonlinear concentration. The linear addition hypothesis assumes that waves move at different speeds across the ocean and that when they overlap, they can transform into a monster wave. The idea behind nonlinear focus is that waves travel in groups and can energize each other, sometimes producing savage waves.

One of the reasons this is so uncertain is that monster waves are rare. Even today, high-quality data is scarce.

Wave samples at sea are usually measured by platforms or buoys. “They record the water level and the time at a particular location, but nothing is known about what happened before or what happened after,” says Amin Shabshoop, a wave physicist at the University of Sydney in Australia. A 2019 study led by Shabshop evaluated several observations and models for monster waves. The team concluded that there could be several causes for monster waves, depending on sea conditions.

In the absence of observations of real monster waves, scientists are turning to wave tanks. “It’s almost possible to simulate what’s happening at the surface of the ocean in the lab,” says Shepshop. In such experiments, currents and winds can also be taken into account. However, this controlled environment also has its limitations.

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Water in a narrow tube, such as a wave tank, for example, forms large waves much faster than they can be observed. Such experiments are an “unrealistic scenario” because waves cannot travel in all directions as they do in the sea, said engineer Francesco Fidel of the Georgia Institute of Technology.

The US government agency NOAA (National Oceanic and Atmospheric Administration) is developing a system that can identify potentially dangerous areas in the ocean every hour, using the WAVEWATCH III software. Its latest version, released in 2019, uses a probability equation developed by Fedele in 2012 to predict where and when severe sea conditions will occur. This is a useful tool for warning sailors of dangerous situations, but perhaps not enough to protect them from brutal waves emerging out of nowhere.

Researcher Johannes Gemrich of the University of Victoria in Canada studied the monster wave that occurred near the Canadian island of Vancouver in 2020. He says monster waves often arise when waves travel at different speeds and sometimes overlap. This is support for the linear addition model. But he believes that wave asymmetry (which occurs when waves have higher peaks and shallower troughs) also plays a crucial role.

“Assuming greater asymmetry, the probability of severe savage waves increases exponentially,” says Jimrich.

general formula for sea

According to one school of mathematicians, the cause of the monster wave does not matter, because it is always possible to predict it fairly accurately using a statistical theory of rare events called the grand deviation theorem.

The idea behind this method is to make a model of the most efficient way a monster wave can appear and then map the evolution of a particular monster wave based on that model. The theory can explain linear and nonlinear effects depending on the scenario, which is why proponents see this as a theory that combines several hypotheses – and one that can be used to predict monster waves in different marine conditions.

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“If you look at the absolutely most efficient way in which these waves can be formed, it matches very well with observations of actual monster waves,” says mathematician Tobias Grafke of the University of Warwick in the UK.

Grafk and a team of researchers tested this theory in wave tunnels and compared the results to observations of real waves. They found that this method was surprisingly capable of predicting the waves of monsters in both modes.

But one of the problems with this theory is that it is very difficult to take into account all the factors of the situation at sea at any time. If you’re a captain on a ship, actual observations are most useful for making predictions, while statistical probability won’t help you much. According to Grafke, specific data about sea conditions can be entered into the formula for he and his colleagues’ equation, but the more variables it includes, the more difficult it is to get a quick result.

“The more complex the formulas, the better the prediction, but the more effort and time it takes,” says Shepshop. “So you have to make a trade-off between accuracy and time to reach a useful result.”

Real time predictions

Scientists are working on the technology to predict waves in real time, but these new methods have not yet been practically tested. This is not easy, given the rarity of waves of monsters. In many cases, the computation process must be speeded up to compete with the speed of the waves.

“In a raging sea, brutal waves can form in about 10 to 15 seconds,” says Fidel. “It is still very difficult to make fast and accurate forecasts in such a short time frame.”

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To predict the monster’s waves, scientists will need a radar system that constantly monitors the waves near the ship, so they can enter this data into a mathematical model that paints a picture of sea level at that time. A model that recalculates sea level every five minutes will provide a relatively accurate prediction of wave development in the following minutes.

Such a system does not yet exist. “The technical possibilities are already there. But the question is: How do you make sure the process is going fast enough? Says Fedele.

As more monster waves are measured, mathematicians may finally find a way to predict these killer waves before they emerge from the ocean — an engineering feat that Captain Dumont d’Urville only dreamed of in 1826.

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