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Direction de la Technologie Marine et des Syst


What is a Rogue Wave ? The Design Wave Philosophy Calculation of the design wave Wave forces on semi-submersible platforms Wave forces and bending moments in ... – PowerPoint PPT presentation

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Title: Direction de la Technologie Marine et des Syst

What is a Rogue Wave ?
The Design Wave Philosophy Calculation of the
design wave Wave forces on semi-submersible
platforms Wave forces and bending moments in
FPSO-ships Platform movements in large
waves Examples of heavy weather damage What
is a Rogue Wave ? Why, where and when
? Shall we design against Rogue and Freak Waves
? What can a platform master do against Rogue and
Freak Waves ? Remote-sensing of sea
conditions Search And Rescue and emergency
operations Decision making in an emergency
What is a rogue wave ?
What is a rogue wave ?
  • The various definitions
  • What are the problems for design ?
  • What are the problems for operations ?
  • What are researchers working on ?

What is a rogue wave ?
Lets start with What is a Wave ?
What is a rogue wave ?
In practice, you know it was a rogue wave once
you saw it.
What is a rogue wave ?
A good excuse when crew failed to install port
hole storm covers ?
What is a rogue wave ?
A 15 roll of the camera angle ?
What is a rogue wave ?
Just something that happens ?
What is a rogue wave ?
In physics and/or statistics, there are several
What is a rogue wave ?
Some say a wave that is more than twice the
significant wave height, but that may not be a
reliable definition.
What is a rogue wave ?
  • If significant wave height was constant and equal
    to 10 meters, one would encounter a wave of
  • 18.5 m every 3 hours
  • 21.5 m every day
  • 25.0 m every month
  • 27.5 m every year
  • 30.0 m every 20 years
  • 31.5 m every 100 years
  • 33.1 m every 1000 years
  • 34.8 m every 10000 years
  • The maximum in one day is also the maximum in the
    20 minutes or 3 hours surrounding it, so twice
    the significant wave height is by no means
    abnormal it happens every day !

What is a rogue wave ?
One of those waves in a large set of a given
height that make the set more numerous than it
should be from conventional theory.
What is a rogue wave ?
From the figures above, theory states that there
should be 500 waves above 2Hs in a year. If one
measures 1000 of them, they are rogue waves
about 500 freak and 500 normal extremes and of
course we cant distinguish easily which are
What is a rogue wave ?
A wave of unexpected severity given the
prevailing sea conditions at the time it occurs
What is a rogue wave ?
A wave of unexpected severity given the
prevailing sea conditions at the time it
occurs. Unexpected A good deal of damage can be
avoided if those exposed are fully aware there
and then. Severity Steepness, Front steepness
and other characteristics may be more damaging
than mere height.
What is a rogue wave ?
The famous Draupner wave
Reconstructed water surface elevations over a
1000 m span, from T-30s (blue) to T (red) for the
New Year Wave.
Where does it come from ?
Georg tells us (Lindgren, 1970) that if it comes
from the normal gaussian process, it is a wave
that looks in retrospect like the autocorrelation
function of the water surface elevation
signal. Sverre (Haver, 2000) states that it is a
freak wave if it represents an outlier when seen
in view of the population of events generated by
a piecewise stationary and homogeneous second
order model of the sea surface process, otherwise
only rogue. Miguel and Al (Onorato Osborne,
2005) tell us that according to the Schrödinger
equation, it sucks energy from its neighbors and
thus it is a freak invader from an outer
statistical population.
It is nice to be able to recognize a Freak or
Rogue Wave in the statistics after it occurred...
...For various reasons, a much nicer ability
would be that of being successful when
speculating that approaching waves are not rogue
waves, or even that they are.
  When a woman at a party asks me what I do, I
invariably say I m just a speculator. The
encounter s over. The only worse conversation
stopper is I m just a statistician.   Victor
Niederhoffer, The Education of a Speculator,
Wiley, 1997
Where does research stand with regards to rogue
waves recent studies.
  • A wave is coming.
  • In order to predict its rogueness, should we use
    quasi-deterministically the non-linear
    Schrödinger equation or merely rely on the
    statistics derived from, for instance, Slepian
    processes ?

Discriminating questions
  • 1. Do we have more high waves than our
    conventional long-term statistical models predict
  • 2. When we do have high waves, do other
    characteristics of the whole storm, of the sea
    state, or of the few previous waves look
    different from those of other storms, sea states,
    or sets of a few consecutive waves ?
  • 3. Especially, do characteristics related to
    theoretical deterministic constructions of rogue
    waves exhibit statistical evidence of predictive
    power ?

  • 20 years of data available from Frigg QP platform
    in the North Sea

  • 1979-1989 mostly 3-hourly measurements, many
    time-series available.
  • 1991-1999 mostly 20-minute statistics, only
    reduced parameters

  • Hmax and H1/3 retrieved preferably from the
    time-series when available (7), from the
    statistics elsewhen.
  • For storms, missing zero-crossing period
    information was derived from T1/3 (9.4) and
    drawn from the empirical H1/3-Tz distribution
    when no information at all was available (1.7).
  • The final database consists of 265147 statistical
    records, it is thus equivalent to nearly 9 years
    of continuous measurements.

EKOFISK, operated by ConocoPhillips Laser
measurements at the time of the Varg incident
North Sea
Storm freakiness
  • We (Olagnon Prevosto, 2005, Olagnon
    Magnusson, 2004) tried to investigate the widest
    time-scale the whole storm.
  • Especially, the maximum wave expected in a storm
    is a more useful forecast to seafarers than the
    maximum wave in some particular 1- or 3-hour
    duration sea state of that storm.
  • It may thus appear natural to relate the maximum
    wave in a storm to the maximum predicted H1/3 in
    that whole storm rather than to the prevailing
    H1/3 at the precise instant of Hmax.

Storm freakiness
Storms are defined as durations gt 12 hours with
H1/3 gt 5m
Storm freakiness
For each of the 187 identified storms, 1000
random simulations were made using the database
statistical parameters and a Jonswap wave
spectrum with gamma3. Second order correction
was then applied to all computed Hmax
values. Freakiness of a storm is defined as the
quantile rank of that storms observed Hmax/
H1/3max in the corresponding distribution over
the 187 actual storms (empirical) and over the
187000 simulated storms (2nd order theory).
Storm freakiness
QQ-plot of Hmax/ H1/3max blue dots. H1/3
green dots Hmax red dots Apart from a very
few ones, storms are less freaky than 2nd order
theory would predict.
Storm freakiness
QQ-plot of Hmax/ H1/3max blue dots. Mean storm
BFI red dots Benjamin-Feir instability at the
time-scale of a storm can only be very weakly
related to its freakiness.
Storm freakiness
Expectations based on experience rather than
theory would be definitely too low An
explanation for so many freak waves reported ?
Medium term the sea state time scaleFreaky sea
states ?
  • Nerzic Prevosto (98) proposed a Weibull-Stokes
    model for the distribution of maximum waves Hmax
    in a sea state, conditional to H1/3 and Tz of the
    sea state.
  • They used a 7 subset of the Frigg database,
    without any special emphasis on extremes, to
    derive their model.
  • We use the full database to study how the model
    performs with long-term extremes.

Distribution of maximum wave heights
No underestimation by model ! Again, an
appropriate transformation, limited to taking
into account standard non-linearities up to
second order, is sufficient to explain the
observed extremes
  • Comparison of empirical distribution of Hmax with
    Nerzic Prevosto model for H1/3gt5 m.

Kurtosis and Benjamin-Feir instability
  • When a similarity connection is achieved between
    two objects to 20 decimal places, the greater
    will move to the lesser
  • A.E. Van Vogt, The World of Null-A, 1945
  • Even though conventional Hmax models seem
    acceptable for long-term distributions, it might
    be possible to predict when the extremes in the
    distribution are most likely to occur at those
    times, the similarity between the actual world
    and the theoretical deterministic world of
    non-linear Schrödinger equation may be such that
    we can apply the rules of the latter for some
    limited time-space window. In that latter world,
    extremes are governed by Benjamin-Feir

Kurtosis and Benjamin-Feir instability
  • Benjamin-Feir instability, i.e. the ratio of
    steepness to bandwidth, and signal kurtosis are
    strongly related (Mori Janssen 2005)...
  • but are kurtosis (BFI) excursions away from
    regular values the cause of freak waves, or a
    mere consequence of their observation ?
  • In other words, is kurtosis (BFI) a predictor or
    only a detector ?

Kurtosis and Hmax
Hmax/ H1/3 exhibits a clear relationship to
Kurtosis and Hmax
but if kurtosis is computed with removal of
the largest waves time-duration, the
relationship can no longer be seen.
What value in MetOffices warnings ?
  • Mostly based on Benjamin-Feir instability, and we
    just saw not conclusive.

Difficult to assess how good the chosen omens
are. Difficult to find volunteers to go into the
worst areas of storms and validate the
What is there to be seen a few waves ahead ?
Instantaneous Benjamin-Feir instability index
H H1/3 BFI Index
What is there to be seen a few waves ahead ?
Irregularity factor ( of crests / up zero
crossings ) nothing.
H H1/3 Irr. Fact.
What is there to be seen a few waves ahead ?
Steepness lets have a closer look.
H H1/3 Steepness
What is there to be seen a few waves ahead ?
Crest H1/3 Steepness
H H1/3 Steepness
Conclusions so far
  • Extreme waves are not found more frequently than
    conventional long-term distribution models
  • When extremes are observed, no abnormal
    characteristic can be found in non-directional
    parameters at the time scale of the whole storm,
    of the sea state or of a set of a few consecutive
    waves. There is nothing more in rogue waves than
    what we can see in the statistics.

Associated risks
  • A small ship usually climbs up the wave...

Risks for small ships
  • but may get rolled over or caught from the back.

Risks for small ships
  • Flooding of the bridge or control room

Risks for larger ships
  • Get green water in addition to white on the

Risk for larger ships
  • and water weighs a lot !
  • for a while until they got it squared away, we
    launched them sailing backwards

Risks for larger ships
  • Breaking of the structure due to sagging or
    hogging, in the trough or on the crest.

Risky areas where not to sail ?
Risky areas ?
  • Only areas where there are more ships at risk...

The wrong place at the wrong time
  • Except if you are named Hosukai, of course...

Offshore platforms
  • Cannot avoid bad weather areas.
  • The deck has to
  • be high enough
  • to let the waves
  • pass by in the
  • transparent
  • part.

How the offshore industry deals with the risk.
  • Reliability targets of 10-4 yearly.
  • On one hand, 10000 years from
  • now, the North Sea may well be a
  • desert, on the other hand, risks
  • associated with waves are at
  • least one order of magnitude lower
  • than those of blast, fire, human
  • errors, etc.
  • The idea is to keep the metocean
  • risk at that relative level.

How the offshore industry deals with the risk.
  • Design methods were questioned
  • for a while, because of the possibility
  • of some phenomenon different from
  • the ones that had been used to derive
  • the theories that led to design values.
  • Experience and studies have shown
  • that there was no problem with those
  • theories onto the 10-4 limit.
  • To some extent, the shipping industry
  • uses a similar approach, but less openly.
  • To the shipowner, the risk of a rogue
  • wave is an acceptable one, as we would
  • say for the risk of a car accident when
  • driving to work.

The tsunami analogy
  • When you go to Hawaii, there is no sign,
  • to be seen on the real estate near the
  • beaches, that they could be washed
  • away by a tsunami at any moment.
  • Yet, if a tsunami occurs in Hawaii,
  • there will be loss of property, but
  • likely no loss of lives those subject
  • to the risk are properly trained, know
  • the ominous tokens and what to do
  • then.
  • Rogue waves can be considered in
  • the same fashion they may happen,
  • one should just train not to be caught
  • unprepared in that case.

The 3 Rules for survival Training, training and
  • What should you watch for ?
  • Complex, multiple low pressure meteorological
  • Pressure lows traveling at the same speed as the
    waves they create (running fetch)
  • A sea state easier to handle than could have been
    expected from the winds strength
  • The time when the storms maximum is close ahead
  • The time when a cold front is close ahead

  • DesignRogue waves understanding is now far from
    being a priority, but they do occur (as
    statistically expected), and should not be
  • Forecast (the priority)No automatic rules, but
    it may not be impossible to train super-expert
    meteorologists to estimate the risks with good
    chances of success.NOT A METOFFICE ACCEPTED

Freak events do happen
The death of Aeschylus was not of his own will
. Having come out of the place where he lived
in Sicily, he sat under the sun. An eagle
carrying a tortoise happened to fly above him.
Mistaken by the whiteness of his bald head, it
let the tortoise fall on to it, as it would have
done to a stone, in order to break it and eat its
flesh. The blow took his life away from the poet
who first gave the most perfect form to tragedy.
Valerius Maximus, Factorum ac dictorum
memorabilium, IX 12, ca. 30 AD
THATS LIFE ! Thank you.