Environmental Engineering Reference
In-Depth Information
with the following transformation factor
F
k
:
8
<
:
d
0
:
5
v
for
v
d
1
2
F
k
vðÞ¼
1
0
:
5
ð
2
v
d
Þ
for
1
< v
d
<
2
1
for
v
d
2
The result of using this approach is that deep-water conditions may be assumed for
v
d
2,
that is for d
g
T
2/
2
.
p
2.5.7 Long-term statistics for the sea state
The long-term behaviour of the sea state can be described by means of wave distribution
diagrams (scatter diagrams) which give the frequency of individual short-term sea
states. Figure 2.27 shows an example of a scatter diagram for the North Sea.
The significant wave height is denoted by H
s
(or H
1/3
), the wave period by T
z
(or T
0
); H
i
or H
j
specify the total of the relative frequencies of the sea states (duration generally
T
s0
¼
3 h [24]) of the respective class T
z
or H
s
. The time-related probability density for
the respective class is represented by f
i
and f
j
[23].
However, results from numerical studies can also be used, for example those developed
for the German Bight by Zielke et al. [18]. Such simulation computations can be used to
draw up, for example, wave distribution diagrams for any locations in the area under
investigation [6].
The evaluation of sea state data has shown that the long-term statistics for large extreme
values H
s
can be described with the help of a Gumbel distribution:
F
extr
H
ðÞ¼
exp
exp
a
H
s
u
f
½
ð
Þ
g
It is possible to calculate the following distribution parameters from the standard deviation
s
H,extr
(from the long-term statistics, e.g. Figure 2.27) and the modal value u:
a
¼
p
1
s
H
;
extr
¼
1
28255
s
H
;
extr
:
and m
H
;
extr
¼
u
þ
a
¼
u
þ
0
:
577216
a
p
Fig. 2.27 Scatter diagram for the open North Sea (after [21])
