Scientists May Have Solved the Mystery of “Rogue Waves”

For centuries, sailors have returned to land with tales of being swept up in 100-ft swells, enormous waves appearing from an apparently calm ocean to terrorize even the most stalwart crew members, before sinking into nothingness just as suddenly as they appeared. The mariners who claim to have seen such “rogue waves” were few and far between—but it’s also not the sort of event that vessels can withstand, and there have always been ships lost at sea but never accounted for.

This famous woodblock print, entitled “Great Wave off Kanagawa”, depicts a wild wave swamping several boats.
Image Credit: Hokusai. Public Domain.

It wasn’t until 1995, however, that any true scientific credence was lent to what had in many regards become a legend of the sea. That’s when instruments on an oil platform in the North Sea registered a single wave at 84 feet—and the scientific community started paying a lot more attention to wave dynamics. Since then, a number of these rare but potentially dangerous events have been confirmed, leading researchers to look for an explanation.

Under normal conditions, the ocean surface can be described, like many other things, using Gaussian statistics; if you measure the height of each wave for a reasonably long period of time and then plot how frequently waves occur by their height, the graph will form a gentle hump with a tail trailing off to each end—a familiar bell curve. Although definitions of rogue waves vary, they are so much taller (at least twice) than their surrounding seascape that they fall far, far along the tail where their probability of occurring is miniscule. Nevertheless, they do occur—and at rates far above those predicted by Gaussian statistics.

Inspired by the seabed topography off the Gulf of Mexico, Nick Moore and his colleagues at Florida State University, Tyler Bolles and Kevin Speer, sought an explanation for this discrepancy. While a number of studies have outlined some of the dynamics that could contribute to the appearance of a rogue wave, they were curious about a less-explored but powerful mechanism: underwater cliffs.

The Gulf of Mexico is not a deep body of water. In fact, many locations in the gulf are considered to be within the “shallow-to-moderate regime”, which means that the depth is roughly the same as the average wavelength, or even a little less. It is also home to a fascinating underwater landscape replete with channels, plateaus, and cliffs. That last feature was of the most interest to the FSU team, especially since several recent studies had suggested that a vertical step in the ocean floor could be linked to rogue waves.

The group decided to investigate this lead further by bringing the ocean into the lab. They built a 6-meter long wave tank and outfitted it with a wave paddle programed to create waves according to the Gaussian distribution. They also added a dampener to the far end to keep waves from bouncing off the wall back towards the paddle, along with LED illumination at the bottom of the tank which allowed them to precisely record the wave motion on the surface of the “ocean” for later analysis. The finishing touch: a 9.5 cm step partway down the tank, mimicking an underwater cliff.

This diagram shows the experimental setup from the side of the wave tank.
Image Credit: Bolles et al.

Sure enough, when they trained the camera on the region just before and after the step, they found that what had hitherto been a standard Gaussian wave distribution became distorted, and displayed highly anomalous behavior immediately following the step. In fact, the tails of the Gaussian—which had made the existence of rogue waves a near-impossibility—fattened considerably, skewing the overall distribution towards taller waves.

Taken from the team’s recent publication, these graphs show the change in wave height distributions before and after the step. On the left, the distribution is a Gaussian and corresponds to the measured distribution before the step. (It looks slightly different from the Gaussian shown above because it’s a log-log scale.) To the right, the wave height distribution immediately following the step is greatly skewed towards taller waves, making the existence of rogue waves roughly 50 times more likely.
Image Credit: Bolles et al.

Of course, in order for these findings to be really useful they need to be scalable to the size of an actual ocean. Moore says that since secondary dynamics—like viscous and meniscus effects—are relatively small compared to the forces driving the waves, there’s no reason to doubt that this work can scale up easily. “Of course these experiments are idealized compared to what happens in the ocean,” he says. Without the complicating effects of wind, temperature/salinity variations, and wave cresting, “We are no longer dealing with the real ocean but a somewhat sterilized version of it.”

Nevertheless, it’s important to remember that every experiment performed in the laboratory is subject to simplification; after all, it’s by controlling variables that researchers can glean insight into a system at all. In this case, that insight is a glimpse at how a sudden variation in the ocean floor depth can cause rogue waves to become much more likely, assuming the water depth falls into the shallow-to-moderate regime (outside of this regime, different dynamics, like the Benjamin-Feir instability, have been shown to contribute to rogue waves).

Although they’ve collected plenty of data to create a detailed histogram of the anomalous wave distribution following the step*, Moore is anxious to describe the phenomenon on a theoretical level. He dreams of a “minimalist theory” that correctly accounts for the non-Gaussian behavior without introducing too many complicating factors. “It may sound easy, but it is not,” he says. “There are so many things that can go wrong.” Fortunately, with the lab’s beautifully detailed measurements he and other researchers will be able to rule out theories if their predictions don’t match the earlier experimental results.

In the meantime, sailors be warned: underwater cliffs could be bad news.

—Eleanor Hook

*For the mathematically inclined, it can be approximately fitted with a mean-zero gamma distribution.

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