Exploring Rogue Waves from Observations in 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 Platform at 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

Significant wave height

Maximum wave heights

Zero crossing periods

Hm/Hs Ratios

Hm/Hs <2

Hm/Hs >2

2< Hm/Hs < 3

3< Hm/Hs < 4

Hm/Hs > 4

Hourly ave 1/3 highest

Wind Direction

Hourly maximums

Hourly averages

Hourly averages

FA PLATFORM:

Wind & Wave Data Structure

Temporary Record

Time series wave elevations

Hourly maximums

Hourly averages

PRIMARY PROCESSED DATA BY WAVE RECORDER

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

HHmaxmax/H/Hs s == 33 44 55 66

N =N = 6.5x106.5x107 (65 7 (65

million)million)

7.9x107.9x1013 13

(79 trillion)(79 trillion)

5.2x105.2x1021 21

(5.2 sextillion)(5.2 sextillion)

1.9x101.9x103131

(19 nonillion)(19 nonillion)

Estimated Estimated time time needed needed for for occurrencoccurrence:e:

14.5 14.5 yearsyears

17 17 million million yearsyears

1 1 quadrillioquadrillion years n years (10(101515))

4 4 septillioseptillion years n years (10(102424))

Conventional Rayleigh conditions

Comparing the results with some

laboratory experiments by

Chin Wu of University of Wisconsin

Normalize the wave heights with their corresponding zero-crossing

wave period, H/gT2

Concluding remarks No. 1

Agulhas Retroflection

Short and medium period waves,with lengths from <200m to 500m, refracted by the Agulhas 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 made by great discoveries. But science also advances when we learn that something we believed to be true isn’t. When solving a jigsaw puzzle, the solution can sometimes be stymied by the fact that a wrong piece has been wedged in a key place.

-- Richard Muller