Environmental Engineering Reference
In-Depth Information
Fig. 2.24 Rayleigh distribution for wave heights; signi
cant wave height
is assumed that the significant wave height H
s
can be determined by the wave height H
1/3
in
the time domain, that is by the mean value of the 1/3-highest waves (centroid of area, see
Figure 2.24). The following applies:
p
m
0
p
m
0
z
M
S
¼ z
M
1
=
3
¼
2
and H
S
¼
H
1
=
3
¼
4
Also interesting in connection with the maxima statistics is the determination of the
average maxima per unit of time, that is the frequency of the maxima, or its inverse, the
average period of the maxima:
r
m
4
m
2
r
m
2
m
4
1
2
p
f
m
¼
and T
m
¼
2
p
Yet another aspect of interest for practical situations is the frequency of, or rather the time
intervals between, the zero points (
z
k
¼
0) in the same direction (zero-upcrossing/down-
crossing period):
r
m
2
m
0
r
m
0
m
2
1
2
p
f
0
¼
and T
0
¼
2
p
m
0
m
1
The choice of a function for the sea state spectrum is important for the application of the
statistical concept. The general form of the sea state spectrum, as Bretschneider shows
with the help of similarity mechanism observations, is
The average period is also often used: T
¼
2
p
5
4
S
z
ðÞ¼a v
exp
b v
The Pierson-Moskowitz spectrum is frequently recommended in deep water for a so-called
fully developed sea, that is when assuming a steady-state wind speed U and an unlimited
fetch [22]:
1
10
3
g
2
5
74
g
4
U
4
4
S
z
ðÞ¼
8
:
v
exp
0
:
v
