Rogue Waves

by James Komisarjevsky, RJD Intern

Imagine being out on a ship and facing a 60 meter high wave. An extremely large wave like that is known as a rogue wave. Rogue waves can be anywhere from two or more times higher than the average wave crest. They can be anywhere from 20 meters to 60 meters high. As one can imagine they have also taken up the name of “killer waves” (Bludov et. Al, 2009). For centuries, seafarers have been telling tales about giant waves which were capable of sinking ships and then disappearing without a trace. It wasn’t until recently that these tales were started to be believed when the first rogue wave was documented in 1995 on an oil platform in Norway (Figure 1) (Solli et. Al, 2007). In the following years, a program developed called “MAXWAVE”, showed that rogue waves with heights of 25 meters were actually common occurrences (Bludov et. Al, 2009).

This graph shows the surface elevation for the rogue wave that was recorded on an oil platform in Norway 1995. The surface elevation for the rogue wave is near 20 meters and in this cause the surface elevation more than doubled. (Picture source: http://commons.wikimedia.org/wiki/File:Draupner_wave(800x496px).png).

Many might ask, why study these rogue waves or how can they even be studied if they are random? There is a practical application for understanding this random phenomenon but first the physics behind these “killer waves” must be understood. If we can understand the physics behind these random rogue waves and the conditions in which they are created, then we will be able to create them in the laboratory to be able to better study and predict them. There have been many documented cases in recent years of ships being severely damaged (figure 2) and even having crew members killed because of these “killer waves”, and because of this, rogue wave prediction would be of great importance (Bludov et. Al, 2009). Even though these waves occur randomly in the middle of the sea, they can have a grave impact on mariners.

Figure 2- This picture shows a ship after being damaged by a rogue wave. (Photo credit: H. Gunther and W. Rosenthal, source- http://en.es-static.us/upl/2011/04/wave_destruction.jpeg)

There are many proposed mechanisms for the formation of rogue waves. One of the major proposed mechanisms is by the creation of Akhmediev breathers (AB) which appear because of modulation instability. These Akhmediev breathers appear when energy is concentrated in a certain place. Rogue waves will become larger as the Akhmediev breathers collide with one another. The collisions of two or three Akhmediev breathers in the ocean will cause giant rogue waves with two to three times the amplitudes than the average wave crests of that area (Akhmediev et. Al, 2009). Observing collisions of AB’s is difficult and has only been done analytically. Further studies are needed in order to see these collisions and prove this as a mechanism of rogue wave formation.

To understand and predict rogue waves is no easy task because of the randomness fashion they occur in. Because they occur randomly in the ocean, Scientists are using different methods in order to recreate these waves and study the conditions which cause them. Recently, they have been observed using nonlinear optics. This is using optical fibers with continous-wave laser radiation to create pulses which can reach extremely high amplitudes. Although this is not the same as the ocean medium, its high wave peaks that occur are very similar to the random high wave peaks that occur in the ocean (Bludov, et. Al, 2009). Rogue waves have also been studied using optical systems. It was found that there are striking similarities between the rogue waves which occur in these optical systems and the rogue waves which occur out at sea. It was found that in this optical system, “if the random noise happens to contain energy with a frequency shift of about 8 THz within a 0.5-ps window centered about 1.4ps before the pulse peak, a rogue wave is born” (Solli et. Al, 2007). This system shows that rogue waves can be generated and condition/s which may cause them. With further study, the mechanism of power transfer seen in optical systems, may be the same mechanism causing rogue wave formation in the oceans.

Figure 3- This pictures shows a ship washed ashore after being hit by a freak or rogue wave in the Irish Sea. (Photo credit: Susan Noble, http://commons.wikimedia.org/wiki/File:Freak_wave_washed_boat_ashore_-_geograph.org.uk_-_674357.jpg

Physicists Bludov, Konotop, and Akhmediev have recently shown that rogue waves are also natural in the microworld and can possibly be observed in a Bose-Einstein condensates (BECs). A Bose-Einstein condensates is a system in which a dilute gas of Bosons, are cooled to near absolute zero temperature (0K). Using this system provides many advantages including it representing a fluid and being well controllable objects. These physicists have provided the initial conditions to be able to observe the rogue waves in a BECs. Through the application of mathematical equations with a BECs, they have shown that rogue waves can be created in a controlled manner and are able to be controlled by phase and amplitude engineering. Using a BECs, one is able to manipulate the conditions of the rogue wave formed. One can now observe rogue waves in a place where the other waves created and homogenous and stable. These are great advantages compared to other methods because this replicates the mechanisms occurring in the ocean medium (Bludov et. Al, 2009).

There is still much to be discovered of rogue waves. These new methods for observing rogue waves in different ways can lead to new discoveries in the field. In the future, by using the different methods for studying rogue waves, scientist may be able to understand the conditions which cause these random killer waves to form so that they are able to predict them.

REFERENCES:
Akhmediev, N., J. M. Soto-Crespo, and A. Ankiewicz. “How to Excite a Rogue Wave.” Physical Review A 80.4 (2009): n. pag. Print.

Bludov, Yu. V., V. V. Konotop, and N. Akhmediev. “Matter Rogue Waves.” Physical Review A 80.3 (2009): n. pag. Print.

Solli, D. R., C. Ropers, P. Koonath, and B. Jalali. “Optical Rogue Waves.” Nature 450.7172 (2007): 1054-057. Print.