Chapter 1: INTRODUCTION
2
rms
H
K
(1.115)
is related to the frequency spectrum as follows
2
0
d
K
Z Z
f
)
³
.
(1.116)
Significant wave height H S is defined as the mean of the highest one third of
the waves. In the absence of swell, it is related to H rms by
4
S
r m s
H
H .
(1.117)
The sea is fully developed when the waves have grown to their maximum
amplitude for a given wind speed. This implies that the shore is far away
(i.e., the sea is not fetch-limited) and the wind has been blowing for a long
time so that the wave spectrum has become saturated and no more energy
can be added.
In a fully developed sea the factors that are expected to be important for
describing the surface wave spectrum are the wave frequency Z, wind speed
a
U , and acceleration of gravity g (Kitaigorodskii, 1962). Standard
dimensional analysis leads to the following dependence:
3
5
1
/
/
a
a
g U
U
g
Z
I
Z
)
,
(1.118)
where I , is a universal function. Pierson and Moskowitz (1964) plotted
several field spectra for saturated conditions according to scaling (1.118) and
proposed an interpolation formula,
5
4
3
3
20
20
5
20
4.05 10
exp 0.74
g
U
U
U
g
g
Z
Z
Z
ª
º
)
§
·
§
·
u
«
»
¨
¸
¨
¸
«
»
©
¹
©
¹
¬
¼
(1.119)
where 20
U is the wind speed at 20 m height. The latter became known as the
Pierson-Moskowitz spectrum.
Two useful relations following from (1.119) are:
2
20
/
0.2
S
gH U
, and
(1.120)
20
/
0.88
p
U
g
Z
,
(1.121)
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