Planet Earth

Rogue Waves

The physics of pure hell at sea

By Bruce StutzJul 25, 2004 12:00 AM


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Courtesy of NOAA


Off the coast of North Carolina, a ship is nearly engulfed by storm-tossed seas. Physicists now know that unstable conditions often give rise to waves that are freakishly large yet surprisingly predictable.

Alfred Osborne’s style is not to do one thing at

a time. At the moment he is trying to get a major wave experiment going at a huge tank in Trondheim, Norway. But his PC refuses to communicate with his Mac. And while he’s working on that, he’s trying to revise some formulas that will drive the waves in the tank. His young colleagues from Turin, Italy—Miguel Onorato and Carlo Brandini, both unshaven, uncombed, and turned out in travel-worn attire—make suggestions in Italian, then pass Osborne a pen and a paper full of equations. He answers in English, redoes the equations, and passes back the pen and paper. They respond in English. He answers in Italian with a Texas twang. It’s a bit as if they were in the middle of a Sergio Leone spaghetti western—only this film is called A Fistful of Formulas. The intense man with silvery hair and blue eyes has the Clint Eastwood role, and he doesn’t need dubbing.

Osborne is a long way from home—or homes. There is the one in Texas, where he was born and once worked for NASA; the one in Virginia, where he worked at the U.S. Office of Naval Research; and the one in Turin, where he teaches at the University of Torino and his wife and children live. He is in Trondheim to make waves. Big waves. The kind made famous in The Perfect Storm that sink ships and drown sailors, many of them in the cold North Sea that stretches southwest of the Trondheim waterfront. Called rogues or freaks, such waves are the stuff of mariners’ nightmares—towering, steep-faced walls of water that weigh millions of tons. Waves so unexpected they leave no time for escape, so powerful they can take out even supertankers and oil rigs.

Two thousand years ago, rogue waves were considered the work of angry gods like Neptune or Aeolus. More recently, seamen and engineers alike have dismissed them as easily explainable: If you know the speed and direction of the wind, if you know the distance over which it has been blowing and the depth of the water, you can predict the height, length, speed, and even the frequency of any wave. Two 10-foot waves become a 20-foot wave; two 20-foot waves become a 40-foot wave; but the waves can only grow so high before their energy dissipates and gravity takes them down.

There is only one problem: The wave models that offshore engineers have used for decades almost never come up with a rogue wave. They can make big waves, but not ones that rise—as rogue waves do—three to five times as high as the waves around them and seem to come out of nowhere, out of sync with the rest of the sea, from a direction completely different from that of the wind and other waves. Waves that big are, in the understated lexicon of naval architects, “nonnegotiable.” Perhaps they are mythological. Perhaps the memories of the mariners who lived to describe them were unreliable. The math says those waves are nearly impossible. But then again, few people have concentrated on ocean waves, not in an age of quantum mechanics, superstrings, and other mysteries. As Osborne says, “Nobody was going to win a Nobel Prize for studying ocean waves.” Unless, perhaps, you could re-create them somewhere other than the ocean.

The Trondheim wave tank is a raw industrial space, with concrete walls 30 feet high, 30 feet wide, and as long as a football field. When Carl Stansberg, the slim Norwegian engineer who runs the facility, arrives to escort us to it, I ask him what he thinks of Osborne’s attempts to create rogue waves. He smiles coolly and says, “We will see.” Osborne’s swagger seems a bit subdued as we wind our way through the laboratories and testing pools, past scale models of tankers and oil platforms detailed down to the company logos painted on their sides (no photos allowed). Wave tanks are where engineering is put to the test and theory can take a beating.

Onorato and Brandini are already at work when we arrive. They are standing on a steel footbridge raised several feet above the water, with an impressive bank of controls and computer terminals. Below, the water in the dark wave tank is so clear and still that it reflects without distortion the array of fluorescent ceiling fixtures above. Staring into the tank from the bridge, I have to keep reminding myself that I’m looking at water.

For the next few days this will be Osborne’s private ocean. He’ll be both Aeolus and Neptune, but his ability to create walls of water will depend solely on the soundness of his physics. Rogues are more events than waves, he believes. They arise from the unstable energy present in otherwise normal waves, like a monstrous sound blaring suddenly from the predictable harmonics of an orchestra. Osborne believes that he can make such waves appear when and where he wants. And if he can do that, perhaps he can predict their occurrence in the real world. “We’re going to be making magic,” he says.

Photograph by Jennifer Tzar


In a wave tank at the Stevens Institute of Technology in Hoboken, New Jersey, a three-foot-long model ship is effortlessly capsized by a simulated rogue wave. In real seas, waves like these sink one supertanker or freighter every year.

Osborne has studied rogue waves for 20 years, but physicists have known about them for much longer than that. In 1832 the Scottish engineer John Scott Russell was riding along a canal in Edinburgh when he saw a bow wave form behind a horse-drawn canal boat. It moved “at great velocity,” he later reported at the 1844 meeting of the British Association for the Advancement of Science, “assuming the form of a large solitary elevation, a well-defined heap of water which continued its course along the channel.” Russell followed the wave on horseback for nearly two miles. It never changed shape or slowed down.

The sight would obsess Russell for the rest of his life. “He was going around talking about a column of water that propagates itself,” Osborne says. “Miraculous. But it nearly destroyed his career. It took 70 years before it was solved. And it was solved like a problem in quantum mechanics. This beast, this solitary wave, this soliton, as they called it, was behaving like a particle.”


In the 3-D computer simulation below, a rogue wave rises suddenly from turbulent waters during an ocean storm. The wave crest (in red) towers a full 90 feet above mean sea level. Physicist Alfred Osborne views such monster waves as “fuzzy beasts lying between sine waves and solitons.” But unlike solitons, which generally travel great distances without losing speed or changing shape,

rogue waves can remain hidden behind a background of random waves (blue and green), only to rise up with sudden violence.

Solitons defy Newtonian logic. They are coherent structures that somehow emerge from a random background—structures with properties far different from those of the waves around them. When a soliton is moving fast, it can overtake a smaller soliton and pass through it unchanged. Since Russell’s discovery, scientists have found solitons everywhere there is wave motion. Telephone signals ride solitons in fiber-optic cables, enabling them to move unchanged across vast distances. Solitons have been found in the electrical activity of cardiac tissue and in the electromagnetism that affects the ionized gases, or plasma, that make up most of the visible universe.

But rogue waves are not exactly solitons. Osborne says that they lie somewhere in the hierarchy between sine waves and solitons. His first glimpse of one came in 1999, when he saw a graph of the data on a wave that had struck a drilling rig in the North Sea on New Year’s Day in 1995. The wave was 85 feet high and half as broad as a football field. It arose out of a storm-tossed sea of 30-foot waves and swept across the deck of the rig at 45 miles per hour.

It was perhaps the largest ocean wave ever measured. By the high standards of the Norwegian oil industry, it was an event that occurs only once in 10,000 years. The U.S. Coast Guard considers rogue waves so rare that it doesn’t even keep records of their occurrence. Yet maritime records are filled with stories of fishermen and sailors who claim to have been struck by them. Some of these stories are probably exaggerated. As one marine insurer put it, “If a captain loses a ship or crew in rough waters, they blame it on a rogue wave rather than admit they were out when they shouldn’t have been out.” But many rogue stories are not exaggerated.

Reports from the Norwegian and British shipping industry suggest that rogue waves sink one supertanker or freighter every year. Rod Rainey, an engineer who investigates ship damage, told the BBC that a storm wave 12 meters high hits a ship with a force of 6 tons per square meter. A ship can take a hit of 15 tons per square meter without damage; 30 tons per square meter will dent it. A rogue wave can bring 100 tons per square meter down on a ship. “That,” says Rainey, “will hole it.”

One of Osborne’s favorite descriptions of a rogue wave is from Virgil’s Aeneid: “A squall came howling from the north-east, catching the sail full on, raising the waves to the stars, breaking the oars in a single blow, wrenching the boat around to offer its flank to the waves as a mountain of water rose above them, immense and immeasurable. Some of the ships rocked on the crests of the waves; the other ships watched in the troughs as the sea parted, exposing the sands on the bottom as they whirled in the furious winds.”


1883: An enormous wave sweeps over the 320-foot Glamorgan, sinking the ship.

1933: A 112-foot wave strikes the Navy tanker Ramapo in the North Pacific. The wave is so tall that it lines up with the ship’s crow’s nest.

1942: The ocean liner Queen Mary is hit by a 75-foot wave 700 miles west of Scotland while carrying 15,000 troops.

1973: A rogue wave off the coast of Durban, South Africa, strikes the 12,000-ton cargo ship Bencrauchan. The ship is towed into port, barely floating.

1976: The oil tanker Cretan Star radios for help: “Vessel was struck by a huge wave that went over the deck.” The ship is never heard from again.

2000: A 70-foot wave hits the cruise ship Oriana, smashing windows. That same month, a freak wave strikes a trawler off Ireland, killing eight men.

“These large spikes are the rogues jumping out of a deepwater wave field,” Osborne says. “Water, the stuff we drink, is nonlinear! So in the end the exotic case is the more natural. Isn’t that pretty?”

As he talks, the water undulates down the tank in a lustrous black ribbon, then washes up on the concrete beach at the end of the pool. Osborne clambers down from the bridge and continues his commentary, almost coaching the water now. “The first wave starts to live its own life. Then it eats from the other waves.” A wave lifts. “There. That’s got to be the leading-edge effect.” Then, two-thirds of the way down the tank, a wave rises higher than the ones before or the ones behind. It has a steep face and a narrow crest. “There!”

As he speaks, the wave jumps the pool wall.

“Bravo!” Osborne, Onorato, and Brandini all shout. But before they can enjoy the moment, Osborne sees yet another rogue rearing up.

“Here it comes!” It, too, rears up, creating a trough before and after, then clears the edge of the pool, spilling water over the side.

Bella! I bet Carl’s about to drop his drawers! They told us we couldn’t do it, and we did. If we had a really big tank, we could take out a 10-story building!”

“Now what?” Onorato asks, a huge grin on his face.

Osborne doesn’t take his eyes off the tank.

“Turn it up.”

Courtesy of NOAA


A hurricane-driven wave strikes a seawall in Miami Beach, Florida, in 1947. Despite recent advances in meteorology and remote sensing, freakish seas continue to catch us off guard.

Oil companies, shipbuilders, fishermen, and the U.S. Navy are beginning to take rogue waves seriously. Despite Osborne’s efforts, however, there is a serious lack of data. The main means of measuring seas and waves is around 50 years old: Buoys at sea record the heights to which they’re raised. Although many buoys are now supplied with electronic transmitters and high-tech electronics, the likelihood of one being in the path of a rogue wave is small. Even if it is, its anchor will most likely pull it down off the face of the wave before the wave’s true height has been measured. Satellites and aircraft can measure only large-scale effects, and they’re limited by cloud cover.

The secrecy that surrounds offshore drilling rigs is another limiting factor. None of the reports on the wave that struck on New Year’s Day in 1995 mentions the exact nature of the damage it did. Drilling platforms are built to withstand even waves that occur once in 100 years, and none has ever been reported toppled. But that doesn’t mean it hasn’t happened, Osborne says.

Ten years ago, several European science organizations began to pool everything known about rogue waves. Between the scientists who didn’t believe the waves existed and the principals of oil, shipping, and insurance companies, who preferred not to discuss them if they did, MaxWave, as the project was known, had a great deal to find out. The project’s final report, released only months ago, summarizes the main findings of dozens of studies. It concludes that rogue waves not only exist but are also more common than previously thought. They can be described with nonlinear physics and reproduced in a wave tank. But while wave tanks can approximate the instabilities that cause rogues, they can’t replicate the constantly shifting winds and currents that make rogue waves impossible to anticipate in real oceans.

Over the next few years, Osborne and others hope to offer ship captains reports on the likelihood of rogue waves appearing in certain regions. The British Meteorological Office created a crude version of such a report in 2001, but it requires much more data to be useful. Meanwhile, the U.S. Office of Naval Research has considered Osborne’s work in designing its mobile offshore base—a floating platform as large as 10 aircraft carriers.

Osborne’s restless energy has led him back to the blackboard. He believes there’s more to be found in the nonlinear equations that describe solitons and rogues. What if the equations can describe even larger waves? What if rogue waves appear in plasma as well as in the ocean? And what if these nonlinearities can be controlled in nuclear fusion reactions? Who knows? We may one day use such plasma jets to ride rogue waves to distant planets. “Understanding the physics is paramount,” he says. “It’s lovely. Every time we turn a leaf we find another marvelous world.”

Anatomy of Waves

Graphic by Don Foley

click to enlarge (80k)

In their most basic incarnation, ocean waves appear perfectly linear and monotonous. They move in a straight line, and their behavior can be predicted by well-defined periodic functions (sines and cosines). These involve three fundamental parameters: Amplitude (A) is the height of a wave from trough to crest. Velocity (v) is the speed and direction at which the wave travels, and wavelength (l) is the distance between two consecutive wave crests.

click to enlarge (90k)


When two waves overlap, they combine in mathematically predictable ways: Where their peaks line up—a phenomenon known as constructive interference—they combine to form larger waves. Where they don’t line up—destructive interference—they cancel each other out. Top right: In this graph, two waves with slightly different frequencies (X and Y) are combined to form a jagged wave (Z) with tall crests and deep troughs, as well as some relatively flat areas. Bottom right: Waves that overlap from two or three directions at once can turn a calmly rolling sea (A) into an increasingly choppy one (B and C). Variations in wave frequencies and amplitudes can give rise to an infinite number of shapes, the French mathematician J. B. Fourier noted in 1807. This is the basis of Fourier analysis, the mathematical technique at the heart of rogue-wave research, in which complicated wave patterns are broken down into their constituent parts.

click to enlarge (27k)


A wave is a disturbance that transports energy and momentum through a medium. The disturbance travels, but not the medium itself. As a wave passes through the ocean, the water spins in circular currents (white arrows) below the surface. Winds over the ocean (blue arrow) also create currents on the surface, pushing the water up one side of the wave and down the other.

Rogue waves don’t seem to respect the conventional rules of wave interaction. In the turbulent waters where they arise, winds and currents collide from many directions at once, and waves combine in nonlinear ways to form freak amplitudes of astonishing height and power. Left: Rogue waves often cross the water at an angle to the rest of the waves, taking supertankers and offshore rigs by surprise.

click to enlarge (42k)

click to enlarge (41k)


The largest rogue wave ever measured—in the North Sea in 1995—towered 85 feet from trough to crest (as high as a 10-story building). The disturbance measured 1,415 feet across and sped over the water at roughly 45 miles per hour. Such a wave could easily topple an offshore drilling rig, physicist Alfred Osborne says. He believes that rogue waves are far more common than was previously thought.

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