Application Example 12
(Functions of random variables and reliability analysis)
DISTRIBUTION OF WAVES AND WAVE LOADS IN A
RANDOM SEA
The Ocean Surface and the Distribution of Wave Height
The elevation of the sea surface during a storm is adequately described by what is called
a normal (or Gaussian) random function.
This means that, at a generic location and time,
the sea surface elevation has with good approximation a normal distribution around the
mean sea elevation. Considerations from the theory of normal random functions lead to a
distribution of wave height H of the Rayleigh type, with CDF
F
H
(h)
=
1
−
e
−
2(h / H
s
)
2
(1)
where the parameter H
S
, called the significant wave height, is four times the standard
deviation of the sea surface elevation at a generic point. H in Eq. 1 has mean value 0.627
H
S
and standard deviation 0.328 H
S
.
Curve (a) in Figure 1 is a plot of the Rayleigh probability density
f
X
(x)
=
xe
−
x
2
/2
of the normalized variable
X
=
2H /H
s
. Our main interest is in the upper tail of the
distribution of H, because the larger waves are those that pose threat to ships, offshore
structures and marine operations in general.
Maximum Wave Height in a Storm
F
H
(h) in Eq. 1 is the probability that a wave chosen at random in a sea state with
parameter H
S
has height less than h. Consider now a storm with 1000 waves (this number
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 Fall '07
 DonHill
 Normal Distribution, Probability distribution, Probability theory, probability density function, Cumulative distribution function

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