By Nick Armstrong and Brandan Mantei
Introduction
A rogue wave is generally defined as a wave that has a
height that is double that of the significant wave
height (SWH).
The significant wave height is the average height of the
largest third of the waves recorded in a given period of
time.
Graphical Example
Background
Until recently it was believed that rogue waves were
extremely rare events that occurred only once every
10,000 years and only lasted for a few brief moments.
This belief was based on the idea that oceanic waves
followed the linear Schrödinger equation.
Numerous first person acounts suggested otherwise.
Draupner Wave
The Draupner wave was measured by a wave sensor on
one of the Draupner oil rig platforms in the North Sea
100 miles off of Norway.
This wave was the first rogue wave to be recorded by a
scientific instrument and therefore the first scientific
proof of the existence of rogue waves.
This wave and the later observation of several other
rouge waves led to further research.
A New Explanation
Because of the number of rouge waves observed since
the Draupner Wave, the linear Schrödinger equation
has been dismissed as appropriate for describing rogue
waves.
The Non-linear Schrodinger Equation (NLS) has since
become the most acceptable model.
How
The NLS has only analytical solutions but several have been found
that simulate rogue waves that occur in varying conditions.
Here is one that describes deep water waves:
i( Ψt + CgΨ x) − μΨxx − νΨ|Ψ|2 = 0.
Where:
Cg = ω0/2k0
μ = ω0/8k20
ν = ω0k20/2
And Ψ is a slowly varying envelope (amplitude) function of x and t.
How
According to the NLS, a rogue waves starts as a normal
sinusoidal wave, but at some point in time starts to rob
energy from neighboring waves.
The increase in energy leads to an increase in amplitude
and ultimately a rogue wave develops.
Modeling Rogue Waves
http://www.youtube.com/watch?v=VQsk5l2DV5w
6:45-8:25
Cite
 http://www.cems.uvm.edu/~mreardon/Pictures_files/
Math%20295C%20Presentation.pdf
Currently
As of today, data and models suggest that deep water
rouge waves are in fact real and occur on a fairly
consistent basis in deep open water. Even as often as
once or twice a week on earth as opposed to the
previously accepted 1 in 10,000 years.
There is no current means of forecasting rogue waves.