Rogue waves are quasi-randomly occurring oceanic local waves which spontaneously form (and then disappear) as a result of interactions between the wavelengths of the 'normal' sea wave state.
They are defined as waves which have a height that is more than twice the size of the surrounding seawater.
They occur without warning and are extremely dangerous to shipping - both large and small craft - and have even downed small low-flying aircraft.
More than 20 international research centres are currently trying to develop accurate modelling techniques in an effort to understand the conditions which lead to rogue waves.
But, although it's quite straightforward to generate rogue waves in research tanks and in computer models :
“We don’t have that random messy theory for nonlinear waves. At all. […] People have been working actively on this for the past 50 years at least. We don’t even have the start of a theory.”
Quote from Peter Challenor, from the UK's National Oceanography Centre. in The Wave (Susan Casey, 2010)
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