Exploring Rogue Waves from Observationsin South Indian Ocean

by

Paul C. Liu(NOAA/GLERL, U.S.A.)

and

Keith R. MacHutchon(Liebenberg & Stander International, South Africa)

What is a rogue wave?

Hmax/Hs > 2

How high can this ratio be?

Western Cape Coast Line of South Africa showing FA Platform locationWestern Cape Coast Line of South Africa showing FA Platform location

Atlantic Ocean Indian Ocean

FA Platformat 38S 22E

Wave Measurement

from a Marex Wave Recorder

Significant wave height (Hs)

Maximum wave height (Hmax)

Average zero crossing wave period (Tz)

FA PlatformWind and wave data

Wave data

Wind data

Significantwave height

Maximumwaveheights

Zerocrossingperiods

Hm/HsRatios

Hm/Hs <2

Hm/Hs >2

2< Hm/Hs < 3

3< Hm/Hs < 4

Hm/Hs > 4

Hourly ave1/3 highest

Wind Direction

Hourly maximums

Hourly averages

Hourly averages

FA PLATFORM:Wind & Wave Data Structure

Temporary Record

Time serieswaveelevations

Hourlymaximums

Hourlyaverages

PRIMARY PROCESSEDDATA BY WAVERECORDER

SECONDARY PROCESSED DATA

Wind Speeds

But that’s not the whole story!

What happen when Hmax/Hs

is much larger than 2?

Conventional Rayleigh conditions

44septillionseptillionyearsyears(10(102424))

11quadrillionquadrillionyearsyears(10(101515))

1717millionmillionyearsyears

14.514.5yearsyears

EstimatedEstimatedtimetimeneeded forneeded foroccurrence:occurrence:

1.9x101.9x103131

(19 nonillion)(19 nonillion)5.2x105.2x102121

(5.2 sextillion)(5.2 sextillion)7.9x107.9x101313

(79 trillion)(79 trillion)6.5x106.5x1077(65 million)(65 million)

N = N =

6 6 5 5 4 4 3 3HHmaxmax/H/Hs s ==

Conventional Rayleigh conditions

Comparing the results with some

laboratory experiments by

Chin Wu of University of Wisconsin

Normalize the wave heights withtheir corresponding zero-crossing

wave period, H/gT2

Concluding remarks No. 1

Agulhas Retroflection

Short and mediumperiod waves,with lengths from<200m to 500m,refracted by theAgulhas Current

Agulhas CurrentMedium and long period waves,

with lengths from 200m to 1500m, refracted by the Agulhas Bank

Composite wave fronts arising from the deep sea over a long fetch

Short waves, with lengths <200m, passing over the Agulhas bank

Schematic Diagram showing a possible mechanism for the combination of wave spectra, leading to the presence of Freak Waves, on the Agulhas Bank

Concluding remarks No. 2

Proposing of a new classification:

Typical rogue waves 2.0 < Hmax/Hs < 4.0

Uncommon rogue waves 4.0 < Hmax/Hs

Concluding remarks No. 3

With respect to

typical rogue waves,

Rayleigh distribution needs revision.

With respect to

uncommon rogue waves,

Rayleigh distribution needs overhaul!

Concluding remarks No. 4

We need more, actual, continuous

wave time series measurements

in order to substantially verify or

refute the existence of these

uncommon rogue waves!

Progress in science is sometimes madeby great discoveries. But science alsoadvances when we learn thatsomething we believed to be true isn’t.When solving a jigsaw puzzle, thesolution can sometimes be stymied bythe fact that a wrong piece has beenwedged in a key place.

-- Richard Muller