Rogue Waves

A killer wave, known to mariners as a “rogue wave,” was approaching a desolate area of Baja California below Ensenada. It had been born off the east coast of Australia during a violent storm; it had traveled almost 7,000 miles at a speed of 20.83 miles an hour. Driven by an unusual pattern of easterly winds, it was a little over 800 feet in length and measure about 48 feet from the bottom of it trough to its crest. On its passage of the Pacific, it had already killed thirteen people, mostly fishermen in small boats, but also an entire French family of five aboard a 48-foot schooner…

– Theodore Taylor, Rogue Wave: And Other Red-Blooded Sea Stories (1996)

For that matter, the Tamaroa herself, at 205 feet, is not necessarily immune to disaster. One freak wave could roll her over and put eighty men in the water.

– Sebastian Junger, The Perfect Storm : A True Story of
Men Against the Sea (1997)

In February 1933, the U.S. Navy steamship Ramapo was traveling to Manila from San Diego when it experienced a severe storm. Gale-force winds raged for several days, 50-foot swells brewed in the North Pacific. It was in these circumstances that the ship encountered one truly enormous upsurge of water. The officer on watch triangulated the monster wave and calculated its height at 112 feet — equivalent to a ten-story building. It is still the biggest wave ever reliably measured. It is called a rogue wave.

Rogue waves are monstrous waves of drastically larger dimension than the surrounding swell. They are defined as large amplitude waves whose heights exceed two times the significant wave height of the background sea. (Significant wave height or SWH is defined as the mean of the largest third of waves in a wave record.) According to naval hydrography terminology, waves 15 to 25 feet high are called sneaker waves, and waves100 feet high or over are classified as freak waves or rogue waves. They are likely to occur where a swell encounters a current that is moving in a curved path, or an eddy at it is called (Environmental Literacy Council, 2006, para 2).
Rogue waves are also caused by the accidental meeting of two or more relatively smaller waves. Open-ocean swells travel in wave trains and even in the same wave train, individual swell heights can differ. But when wave trains from different storms meet in the open ocean or in areas where there are strong currents, individual waves can combine their energy to form a surprisingly massive wall of water, which is known as a rogue wave. Thus a rogue wave is seen to be originating in a rare confluence of crests (Garrison, 2005, p.239). However, it is not clear how a simple superposition of waves, resulting in constructive interference, can result in waves of such gargantuan size, which moreover seem to occur not too infrequently.

Rogue waves represent a transient ocean phenomenon that usually occurs in the deep interior of the ocean, and plays out on relatively small surface areas in the vast ocean expanse. Though usually associated with storms, sometimes these rogue waves can arise out of nowhere in only mildly agitated ocean waters and disappear just as quickly, usually creating havoc if some ships happen to be traversing in their path. Even huge and robust vessels are known to be no match to the fury of ocean as manifest in rogue waves. Though mariners have always been aware of the ‘freak’ wave phenomenon, owing to lack of any reliable empirical data, these waves could not be predicted or quantified, and so could not be taken into account during the design process of a ship (Rawson & Tupper, 2001, p. 174) New ships are designed on the basis of previously successful models which have withstood very abnormal conditions, but most vessels that are built even today are simply not designed to weather the assault of a colossal rogue wave.

Rogue waves have for long remained the dreaded stuff of legends. Until well into the twentieth century, there was only sparse anecdotal evidence for these towering infernos of the sea, and scientists tended to classify the tales surrounding the monstrous waves as sea mythology that dealt with sea monsters, mermaids and so on. It was generally known that in any wave system, after a long enough time, an exceptionally high wave would occur. Nevertheless statistical models of sea states which have been used to predict the occurrence of extreme waves either concluded that waves over a hundred feet to be either a physical impossibility or as something which could occur only once in a thousand years (Schober, 2004, p.194). However, several instances of hard evidence, improved mathematical theory, and satellite survey data in the more recent times have all now converged to prove the existence of the monstrous waves beyond a tinge of doubt. Nowadays they are acknowledged to be a natural phenomenon of the ocean, just as tsunamis and mega-tsunamis are, though their causes and characteristics are different. The freak waves are no longer regarded as freaks really. Even so, the rogue waves are considered very rare, and rather elusive; improbable but still possible..

Rogue waves are definitely anomalous events in the sense that they fall outside the distribution of wave heights predicted by orthodox wave theory. Yet they are no longer thought of as unexplained quirks of nature, though scientists still very much a lack an adequate understanding of them, especially of their underlying causes. Scientific and mathematical advances in the recent years and decades, however, have led oceanographers to calculate their probability of occurrence, with the help by extensive wave data from buoys, ships and satellites. It is still not possible to predict their exact time of occurrence, though. Mathematical models are now able to predict where they are likely to form in general, although the exact location cannot be pinpointed.

The problem with understanding the rogue wave phenomenon is the highly complex non-linear mathematics that underpins it. The occurrence of rogue waves takes place in what is mathematically called a chaotic regime. According to the newly emerging science of chaos, some small perturbation in local conditions could crescendo into a disproportionately huge effect. But rogue waves are gradually becoming more understood. The Benjamin-Feir instability and nonlinear focusing have been proposed as a mechanism for the generation of rouge waves in deep water. Also, certain homoclinic solutions of the nonlinear Schrodinger (NLS) equation have been observed to exhibit many of the properties of rogue waves in deep water (Schober, 2003, p.735).

A deeper understanding of the mechanism by which rogue waves are formed is likely to help us narrow down our predictions about them, and thus save many lives. More extensive studies and investigations into rogue waves are not only essential for a better theoretical understanding of the dynamics of ocean but also to avoid a good deal of the huge losses to life and property that routinely occur in the seas.
On average, it is estimated that approximately two large ships sink at sea every week and rogue waves have been the purported cause behind a fair number of these sinkings. Though there may certainly be other causes behind the many mysterious ship losses, scientific analysis of the wrecks of ships sunk in recent decades indicates that a significant proportion of them have a damage pattern that seemed to suggest the hand of monster waves which can swell over a hundred feet. The sinking of many a supertanker in the latter part of the twentieth century has also been associated with rogue waves. In addition, there is some evidence that average wave heights are slowly rising and that freak waves of eighty or ninety feet are becoming more common. This trend is attributed to the intensification of the greenhouse effect which has made storms more frequent and severe. As a consequence, stresses on ships have been increasing along with the need to understand, predict and prepare for these monsters of the sea.

References:

• Environmental Literacy Council. (2006). Rogue Waves. Retrieved 22 October 2006
• Garrison, T. S. (2005). Oceanography: An Invitation to Marine Science. Belmont, CA : Thomson Brooks/Cole
• Junger, S. (1997). The Perfect Storm : A True Story of Men Against the Sea. p. 194. New York : HarperCollins Publishers
• Rawson, K. J. Tupper, E. C. (2001) Basic Ship Theory. Oxford : Butterworth-Heinemann
• Schober, C.M. (2003). Nonlinear Focusing and Rogue Waves in Deep Water. In, Mathematical and Numerical Aspects of Wave Propagation Waves, ed. P. Neittaanmaki, G. C. Cohen. New York : Springer-Verlag
• Schober, C.M. (2004). Rogue Waves and the Benjamin-Feir Instability. In, Dynamics And Bifurcation Of Patterns In Dissipative Systems, ed. G. Dangelmayr, I. Oprea. Danvers, MA : World Scientific Publishing Co.
• Taylor, T. (1996). Rogue Wave: And Other Red-Blooded Sea Stories. p.3. Orlando, FL : Harcourt Brace & Company