Freak waves — a personal view (sans equations)


Freak waves are not tsunamis — freak waves are just wind generated waves which are much larger than those around them. Alternative names for them are “rogue waves” or “extreme waves”. Exact scientific definitions vary — usually they are defined as waves which are much larger than some multiple of the significant wave height. However, the random nature of ocean waves means that we expect some waves to occasionally exceed such a threshold — what engineers are really interested in is how often such extreme events occur and what increases (or decreases) our chance of encountering one.


A quick search on youtube will present you with numerous videos of “freak waves”. Sailors have always told stories of ships being hit by abnormal waves. Depending on the fine print of the insurance policy, shipping companies or insurers have been known to blame ship sinkings on freak wave events. So there are plenty of anecdotal accounts of strange waves. However, engineers are rather more interested in measurements and on 1 January 1995 a very unusual wave was recorded at Statoil’s Draupner platform in the North Sea1. This led to a renewed scientific interest in studying extreme waves.


Draupner New Year Wave; Freak wave; Rogue Wave

Several factors are known to cause abnormally high occurrences of very large waves. Mechanism for   generating abnormal ocean wave are where waves interact with currents or the sea-bed topography causes wave energy to be focussed in a small area. Whilst these mechanisms are known to cause freak waves we cannot at present make robust statistical distributions for waves so there is still much work to do.


However, none of these mechanisms can explain why some areas in the open ocean, where the water is deep and there are no strong currents, seem to have an abnormal number of large waves. Much work has gone into the analysis of a mechanism known as the Benjamin-Feir instability2. A rather nice laboratory demonstration of this can be seen here. Essentially this mechanism causes waves travelling in one direction to become unstable and bunch up together at some points. The susceptibility of random sea states to this phenomenon is given by the Benjamin-Feir index3.

Benjamin-Feir instability; wave focussing; NewWave group


However, whilst the Benjamin-Feir index produces abnormal waves in uni-directional seas the evidence is a lot more mixed about whether this actually occurs in the open ocean where waves can move in 2 dimensions. Whilst there still seems to be a contraction in the direction the waves are moving, rather than increasing in size the waves tend to spread out laterally — forming a long “wall of water”4,5. But exactly what actually happens out at sea we don’t yet know.


Another way we think freak waves might form is in crossing seas — where there are two systems of waves moving in different directions. There is some evidence that the Draupner wave occurred in such a sea6 — a movie of what this would have looked like can be found here. However, we still don’t really understand why a crossing sea might have an abnormal number of freak waves.


Links


An excellent talk by Prof. Paul Taylor on rogue waves http://www.gresham.ac.uk/lectures-and-events/giant-waves-on-the-open-sea-mariners’-tall-tales-or-alarming-fact

Not freak waves — but well worth watching to understand what offshore waves are like En un Mar Picado


References


  1. 1.Haver, S. A Possible Freak Wave Event Measured at the Draupner Jacket January 1 1995

  2. 2.Brooke Benjamin, T. and Feir, J.E. The disintegration of wave trains on deep water Part 1. Theory

  3. 3.Janssen, P.A.E.M. Nonlinear Four-Wave Interactions and Freak Waves

  4. 4.Gibbs, R.G. and Taylor, P.H. Formation of walls of water in ‘fully’ nonlinear simulations

  5. 5.Adcock, T.A.A., Gibbs, R.G. and Taylor, P.H. The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water

  6. 6.Adcock, T.A.A., Taylor, P.H., Yan, S., Ma, Q. and Janssen, P.A.E.M. Did the Draupner wave occur in a crossing sea?