Rogue Waves: Examining Why Linear Models Failed

[Ivan Seeking]

Integral called my attention to a Sci Channel show about Rogue Waves called "Killer Waves". Rogue waves are now known to exist, but for about a century experts have argued that these thirty meter monsters can't exist because the linear model used by the shipping industry says that monster waves should only occur once every ten-thousand years. So it was assumed that centuries of mariners stories [eyewitness testimony] are all wrong.

I would bet that in the beginning we simply assumed that the linear model used applies to all ocean waves, maybe because it was the only model that was practical to use, and this was then used to argue what could and could not be possible.

 

[Bystander]

http://www.mxak.org/weather/waves.pdf#search='wind%20fetchwave%20height'

 

[TheStatutoryApe]

Makes you wonder just what all is going on yet unrecognized as being possible. I've been rather sad to find over the last few years that I have been investigating that so many thing I had thought were real have been thuroughly debunked. One of my exs would get angry with me when I would explain to her that so many of these "proofs" of the unexplained were in fact explained. I hope more things start to come out as real.

 

[Integral]

The show is on Discovery Science, I was nearly screaming at the TV. Alarm bells started chiming when early in the show they mentioned the "Linear Model" as the basis for rejecting the possibility of "killer" 30m waves. The problem, of course, is that the surface of the ocean is HIGHLY nonlinear. Therefore, anyone with a understanding of numerical modeling will know that the predictions made by a linear model will be limited. Specifically any interesting nonlinear behavior will not show up. It turns out that one scientist (possibly a physicist, but not I am not 100% on that detail) was applying the nonlinear wave equation and seeing huge waves in his results. But once again these predictions were rejected because they did not show up in the Linear model! This is an excellent example of misplaced faith in the abilities of math to model the real world.

Eyes were opened when an oil rig in the middle of the North Sea recorded a 30m wave. The wave shape was exactly that predicted by the nonlinear model.

 

[Ivan Seeking]

a related story in the news.

A British research team has observed some of the biggest sea swells ever measured. A whole series of giant waves hammered into their ship that were so big, according to computer models used to set safety standards for ships and oil rigs, they shouldn't even exist [continued]

http://service.spiegel.de/cache/international/spiegel/0,1518,408953,00.html

 

[Chronos]

Picture the energy required to lift a wave to 30M above the suface. It obviously depends on depth. It also depends on the contour of the ocean bottom. A wave colliding with a deep sea ridge [transverse wave] will break high, and expend most of its energy on the surface. A wave traveling parallel to a deep sea ridge that slopes toward the shore is much more dangerous.

 

[SGT]

Every natural phenomenon is nonlinear. Only when we limit the amplitude of the phenomenon can we approximate a curve, a surface or a hypersurface by its tangent line, plane or hyperplane. This is called linearization and is useful to analyse most phenomenons.
If we talk about giant waves, it is very likely that a linear model could not apply. I wonder why any scientist would dismiss a phenomenon because it can't be explained by a linear model.

 

[Ivan Seeking]

I think people simply forget about the limitations of models used when not of practical concern for the job they do.

 

[Integral]

Every natural phenomenon is nonlinear. Only when we limit the amplitude of the phenomenon can we approximate a curve, a surface or a hypersurface by its tangent line, plane or hyperplane. This is called linearization and is useful to analyse most phenomenons.
If we talk about giant waves, it is very likely that a linear model could not apply. I wonder why any scientist would dismiss a phenomenon because it can't be explained by a linear model.

That is exactly what had be screaming (well, nearly) at the TV the night I was watching that show. Supposedly these guys had PhDs How could they get the idea that the linear model (and that is what they called it!) predicted all possible wave phenomena. Using a variation on the Schrodinger wave equation, rogue waves are predicted, and are not all that rare.

 

[Bystander]

(snip)Supposedly these guys had PhDs How could they get the idea that the linear model (and that is what they called it!) predicted all possible wave phenomena.(snip)

TV science? What linear model? There is no "linear" model for wave height, length, frequency, velocity, or size distribution, therefore, no "failure of such linear model."

 

[Ivan Seeking]

Here is one example of linear modeling of ocean waves.

Based on linear shoaling theory, our surf zone model amplifies the wave heights of incoming waves as the bathymetry or depth of the ocean floor decreases. The wave amplification data is derived from the ocean engineering literature [1] which gives the relationship between a depth to wavelength ratio to a wave amplification factor.

http://www.d-a-s.com/ocean.html