Waves

I find Tom Vanderbilt’s article When Good Waves Go Rogue illuminating:

The rogue waves are, at base, mathematical objects has meant that sailors, then scientists, have been slow to grasp their nature. Late into the 19th century, the line between sailors’ lore and science could be as blurred as fog-bound horizon, with reputable journals routinely reporting on the sightings of “monsters of the sea.” By the mid 20th century, though most of these monsters had been dispelled or explained — but not rogue waves. which continue to be misidentified and incompletely understood today. Even one of civilization’s most famous waves, Hokusai’s The Great Wave off Kanagawa, is often misinterpreted as a tsunami — the woodcut has even been used as a symbol of a UNESCO tsunami warning sign — when it is actually most likely to be a rogue wave, as several authors have argued.

So, straight off the bat, this article is on to something, as it explains a phenomenon that often falls off statistical coherence and conformity, a bad signal on the scatter diagram — convenient or easy to ignore. (I cannot help but draw a simile to Weierstrass’s monster.)

Under the right conditions, even rogue waves can appear, a fact first reported by UCLA physicist Daniel Solli and colleagues in a 2007 paper in Nature, in which they noted the appearance of “a noise-sensitive, non-linear process in which extremely broadband radiation is generated from narrowband input.”

Neil Broderick in his Viewpoint: Optical rogue waves on demand then extended Solli’s assertions further:

More speculatively, it is worth exploring what this work can tell us about wave dynamics in other systems. An attractive feature of the non-linear Schrödinger equation is that it describes waves in many different material systems, from Bose-Einstein condensates to ocean waves. While the existence of oceanic rogue waves is well established, questions remain as to their formation and growth dynamics, hence an understanding of extreme events in the optical domain could translate into an understanding of oceanic waves, although, of course, there are a number of important differences (there is no direct optical equivalence between the forcing wind terms for water waves, nor an oceanic equivalent of the Raman terms that drive much of the optical rogue wave dynamics). While most sailors would want to inhibit the growth of rogue waves, perhaps it is not too far fetched to think of using “seed pulses” along with the current trend of artificial reefs to create the “perfect wave” for surfers. In this way the work of Solli et al. might find applications far removed from optical labs.

Prof. Nail Akhmediev and his colleagues did exactly that when they reproduced this phenomenon in a wave tank in Hamburg.

In the video, a small Lego pirate ship sits gently bobbing atop silky undulations of the tank’s mirror surface water, as unseen, a wave generator beats out a steady pulse of fluid dynamics. And then there it is, a dark band in the distance, which engulfs and capsizes the hapless boat. It’s a “super” rogue wave, not twice the significant waves height (Hs), but five times.

When science is based on observations (records, and statistics), which is further followed by selective exclusion of non-conforming data, as engineers would like to idealize the problem to the most probable, the exposure to offshore facilities remains unquantified. In the words of Louis Pasteur, “In the field of observation, chance favours the prepared mind.”

As practising offshore engineers dealing with powerful forces of nature, it is both terrifying and challenging to deal with streak phenomena like rogue waves. We do not have a recipe for dealing with them, as they remain undefined action forms. The only consolation so far is that we deal with 100-year extreme waves, and lately the 10,000-year abnormal waves to perhaps implicitly cover for some of such occurrences. However, as we consider today, we use two environmental conditions predominantly to check for adequacy of structures:

  1. Extreme storm that corresponds to a 100 year return period, and
  2. Operating environment, typically 1-month to 1-year return period.

In the case of check for extreme storm, the understanding is that storm takes a while to develop, and lasts for a while (OK, say three hours). This would allow for monitoring, forecasting and early warning systems to alert the crew aboard vessels, facilities to go into a brace position for the on-coming storm, scale-down operations as required following procedures. The problem with a rogue wave is that it is not a storm condition, just a freak wave but with potential to inflict damage to the facility in operation as great as the extreme storm condition (or worse) without warning. A wave rider buoy can at best pick up some signal, which is more likely to be regarded like a blip than a warning.