Rogue Waves

For centuries sailors have shared stories of “rogue waves,” gigantic walls of water capable of destroying ships at sea. Many chalked it up to maritime tall tales. It was assumed eye witnesses were exaggerating, and in the time of wooden or single-hulled ships, anyone who actually experienced a rogue wave probably did not come home. In 1826, Captain Jules Dumont d’Urville along with three colleagues reported a massive wave as high as 33m (103ft) in the Indian Ocean, but their account was discredited, as at that time, it was believed waves could not get taller than 9m (30 ft).

The first rogue wave detected with scientific equipment, called the “Draupner wave,” occurred on New Year’s Day 1995 in the North Sea. Since then, with improvements in satellite imagery and other observation tools, we now know that rogue waves are very real. Over a three-week period in February - March 2001, radar-equipped satellites detected 10 rogue waves over 25m (82 ft) tall across the world’s oceans, demonstrating rogue waves are much more common than previously believed.

What could cause such massive waves? First, we need to start with the basics.

What are ocean waves?

Most waves are created by wind: as air moves across water, friction transfers energy from the air to the water. As the wind blows, crests form in the water and move in the same direction as the wind. Wave height is determined by wind speed, duration (length of time that the wind has been blowing across the generating area), and fetch (how far the wind blows across the generating area from a single direction while at a constant speed). If the wind is strong, but only blows for a short time, then high waves do not have time to form. Similarly, gentle winds blowing for a long time with lengthy fetch will not generate high waves. High waves only occur when strong winds are constant over a long time period and long fetch.

A wave is composed of the crest (the highest surface part of the wave), and the trough (the lowest part). The wave height is measured from trough to crest. Wavelength is the distance between two crests or two troughs. The wave period is the amount of time it takes for a complete wavelength (peak to peak or trough to trough) to pass.

Courtesy of the National Ocean Service/NOAA.

Due to variations in wind speed, direction, duration, and fetch, there is usually a wide range (or spectrum) of waves moving past a point at a given time in the open ocean. The total sea state is a combination of many wave heights and periods. When forecasting how rough the seas are along a vessel’s path, it is important to understand that waves are more complex than a single height measurement - there is an entire spectrum of possibilities.

Below is an illustration of a statistical wave distribution. Most waves will be close to the modal wave height, but through natural variations, there exists the possibility for much taller waves. The lighter blue section is the tallest one-third of waves in a sea state. The significant wave height is the average height of the upper third of waves. AMI provides significant wave height in forecasts, as it is easy for an observer on board a ship to estimate, and it gives a better understanding of the tallest possible waves, which are more likely to lead to navigational problems or damage. About one out of every seven waves passing a point will be greater than the significant wave height. Assuming 1 out of 1000 waves is double the significant wave height with a period of about 10 seconds, waves of twice the significant wave height will pass a point about 8-9 times in a 24-hour period.

Courtesy of MetEd/COMET

As waves spread out from their point of origin, they travel at a speed depending on their period and length. Shorter wavelengths carry less energy and dissipate relatively quickly, while longer wavelengths become swells as they propagate out of their generating area and disperse across oceans.

Waves coming from different directions, or having different periods, can interact with each other to produce both higher wave heights (constructive interaction) and lower wave heights (destructive interaction). One example of this is “cross sea” or “square waves” where waves approach each other almost perpendicularly, with the crests combining to form a grid of squares on the water surface. Square waves can present navigational challenges for large commercial ships as well as smaller coastal vessels.

Based on the distribution of wave heights discussed above, we already know that waves much higher than the average wave are possible at any given moment. What makes a rogue wave so unusual?

Rogue Waves

Rogue waves are defined as waves whose heights are more than twice the significant wave height. They are distinct from tsunamis - rogue waves are not caused by sea bottom movements, and they can occur in both coastal areas and in the open ocean. These waves are present generally only for a short period of time, and are giants compared to surrounding seas. They can appear suddenly and travel in a different direction than the primary swell. The inverse of rogue waves - rogue holes - are also possible, with a trough much deeper than those in the nearby seas.

From NOAA: “A rogue wave estimated at 18.3 meters (60 feet) in the Gulf Stream off of Charleston, South Carolina. At the time, surface winds were light at 15 knots. The wave was moving away from the ship after crashing into it moments before this photo was captured.”

Rogue Wave Formation

Since the first detected rogue wave in 1995, the exact mechanism for rogue wave formation has not been definitively determined and research is ongoing. Two prominent theories are constructive interference and focusing of wave energy.

Constructive interference is a consequence of waves interacting with each other. In the open ocean, wind waves and swells travel at different speeds and directions. When a wave catches up to another wave, they temporarily overlap and add together, making the crests taller and the troughs deeper, resulting in a higher wave. Sometimes constructive interference can produce waves that are substantially higher than the surrounding seas. They are usually short-lived, but may last for several minutes if the interfering waves are propagating in the same direction. If waves interact such that the crests and troughs overlap, they cancel each other out, leading to destructive interference, as indicated below.

Constructive interference (left) vs. destructive interference (right). Courtesy of the University of Connecticut.

Focusing of wave energy is a result of waves interacting with ocean currents. Waves slow down if they are moving in the opposite direction to a local current, especially a strong current. The back of the wave starts to catch up to the front, causing a shortening of wavelength, while the wave steepens. This process can compress waves together, leading to a higher, steeper wave. Under this process, rogue waves tend to have a longer life span. With the requirement of strong currents, some parts of the oceans are more prone to this rogue wave generation mechanism than others, such as areas near the Agulhas current, Gulf Stream, and Kuroshio current.

Research of rogue waves offshore South Africa in the Agulhas Current has shown that wave energy can reflect off the Agulhas Current and focus in areas away from the actual current, producing unexpectedly high waves which have been shown to damage large ships.

Various experiments have been performed to try to recreate conditions necessary for rogue wave formation. Several groups have used wave tanks and pools to demonstrate that the above mechanisms can generate rogue waves. An interesting study done by Cambridge University suggests that crossing seas can contribute to rogue wave formation. When a wave reaches a critical amplitude/steepness - usually when the wave height is 1/7 the wavelength - the top of the wave overturns, or breaks (think waves near the shore). However, when ocean waves and/or swells are crossing, especially at angles between 60° and 120°, waves break differently. Instead of breaking downward, the waves can break upward, stretching even higher in a jet of water. Under the right conditions, crossing seas can produce unusually steep breaking waves, and sometimes rogue waves.

The Draupner Wave

The most famous rogue wave ever recorded is the aforementioned Draupner Wave in the North Sea. In the early morning hours of New Year’s Day 1995, a polar low off the coast of Norway started to move quickly southward, bringing with it intense northerly winds and heavy seas. As the low continued southward, the Draupner oil platform (located near 58°11’N 2°28E, about 160km / 99 miles off the southwest coast of Norway) experienced significant wave heights of around 12m (almost 40 ft). A little after 1500 UTC, a downward-pointing laser measuring the sea height below Draupner recorded a single wave pass with a maximum height of 25.6m (84 ft), or 18.5m (nearly 61 ft) above the still water level.

Wave height measurements from the Draupner platform on 1 January, 1995, in the 10-minute period when the rogue wave occurred. From the American Physical Society and University of Oslo.

In the time serires above, the rogue wave is evident compared to the already heavy sea state in the vicinity of the Draupner platform. Buoys and other observation equipment were less common in the 90’s, so it is impossible to know the direction of the background waves vs. the rogue wave, and whether there were crossing seas. However, based on the movement of the low-pressure area and the wind field, it seems likely that crossing seas were present. Overall, the Draupner wave proved the existence of rogue waves and continues to spur scientific study and theory of their formation.