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What Are Rogue Waves?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

The Nature of the Wave

Rogue waves have been reported for years, but what causes them? It was assumed that wave addition must be at play, with probabilities of the right wave combination giving the rogue behavior seen. But some people figure that amplitude addition and the energy that a wave carries don’t make conducive conditions for rogue waves to exist. If a wave gets too tall, it should collapse onto itself way before reaching the properties we associate with rogue waves (Stutz 50, Wood).

And yet people over the ages have reported waves 3-5 times the size of its surroundings, and often in directions not matching the wind that helps drive the surrounding waves. Also, wave addition models fall short of the expected probability distribution, but some have added triangle waves and other curves to the traditional sine-wave models to help bridge this discrepancy. But yet it still exists (Ibid).

This led people to suspect that rogue waves are in fact solitons, where a wave “somehow emerges from a random background” and has a radically different structure when compared to its surroundings. Solitons are effectively constant in their movement, not changing nor spreading out like traditional waves. But they are huge spikes, something that a rogue wave isn’t. Also, soliton behavior is a closed-system creation, like in a tank. But in a more open system like an ocean, there is likely too much noise to effectively allow solitons to operate (Stutz 51, Boyd).

Quantum Evidence?

Surprisingly, soliton evidence for rogue waves has risen from a study on ultracold atoms. In the research run by Randy Hulet (Rice University) and team, lasers and magnetic traps were employed to cool off minute amounts of atomic gases down to just a few millionths of a degree above absolute zero. In 2002, Hulet was able to show that soliton trains (waves separated by defined spaces) of these atoms were possible, and by 2014 he was able that two of these wave trains would effectively cancel each other out if meeting head on while traveling over one another, then reappear as normal (Boyd).

This sounds nuts, trying to apply some of this behavior to something like macroscopic rogue waves. But both the ultracold atoms and rogue waves do follow soliton behavior, that being nonlinear interactions. Because “the inputs have a disproportionate effect on the output,” this behavior seen at the quantum scale can inform us about rogue waves (Ibid).

This was further clarified when Hulet, along with scientist Jason Nguyen and grad student De Leo did a follow-up to the 2002 and 2014 work. Using a Bose-Einstein Condensate, an ultracold state where atoms act as one unit, the team was able to entice the material to exhibit “’modulational instability,’” which is a non-linear effect causing small changes in the wave to be grown (Ibid).

By mapping out what interactions cause certain behavior, soliton trains were able to be generated. This is the first time that the initial conditions could be modulated, offer scientists a possible avenue to further study soliton behavior, and therefore possibly rogue waves too. One initial result is that some initial conditions didn’t change the soliton train behavior, meaning it was just created with these properties rather than develop into he trains seen by researchers (Ibid).

It’s All The Same

Instead, it’s more like a hybrid between a soliton and a sinusoidal wave. Rogues do seem to come from nowhere like a soliton and can pass through waves without impacting its properties but rogues have a sine shape to them. But maybe it’s even simpler than that. Eric Vanden-Eijinden (New York University’s Courant Institute of Mathematical Sciences) and his team developed a mathematical statistics model to help determine the overall probability of encountering a rogue wave of either type (Stutz 51, Wood).

The trick is to implement the large deviation theory, which essentially compares related rare events to determine what is possible versus highly unlikely. Rogue waves would certainly be a rare event, and so by implementing the theory you look at the conditions which caused the event and extrapolate outward from there, regardless if the vent was wave-addition based or soliton based (Ibid).

The team first used this model in 2018 on a digital sea, setting the parameters for their rogue waves and teased out the conditions needed for the waves to appear. Compared to physical evidence, the model matches expectations, meaning that both types of behaviors can generate rogue waves, but even more powerful it is leading scientists to develop models for what sea conditions are likely to generate rogue waves (Ibid).

And really, isn’t that the best part of science?

Works Cited

Boyd, Jake. “Ultracold atom waves may shed light on rogue ocean killers.” innovations report, 05 Feb. 2017. Web. 15 Apr. 2021.

Stutz, Bruce. “Rogue Waves/” Discover July 2004. Print. 50-1.

Wood, Charlie. “The Grand Unified Theory of Rogue Waves.” Quanta, 05 Feb. 2020. Web. 15 Apr. 2021.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2022 Leonard Kelley