Microsoft Word Report 11 02 Wave Power final ex appendix doc

m
H
m
=
where 
m0
is derived through 
∫
=
n
n
n
df
f
S
f
m
0
)
(
where 
f
is the frequency and 
S(f)
is the spectral density function. The wave 
energy period, 
Te
, is also derived trough spectral moments,
0
1
m
m
T
e
−
=
Figure 2.1 Anticlockwise from top: Surface plot of directional spectrum – 2D 
spectrum from directional spectrum (303 degrees) – Resulting 2D spectrum 
of the whole 3D spectrum.
Figure 2.1 shows various spectra from a buoy off the Norwegian coast. From 
the 2D spectrum in the lower right corner e.g. the Hs can be calculated to 
1.71 m. 

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ELFORSK 
7 
Once the Hm0 (or Hs) and Te have been calculated, the energy flux per meter 
wave front, also referred to as the wave climate (J), can be established with 
the following formula valid for deep waters. 
2
0
2
0
2
64
m
e
m
e
H
kT
H
T
g
J
=
=
π
ρ
[kW/m]
However, when the 2D spectrum is used for deriving various statistical 
parameters the directional information about the sea state is obviously lost, 
and sea states are rarely perfectly unidirectional. As mentioned earlier in this 
chapter, waves seen on the ocean surface are as a result of different weather 
systems. An oceanic swell might enter from one direction, whilst the wind in a 
local weather system might create waves with a completely other direction. 
The result is a crossed sea with waves traveling in different directions, and for 
e.g. WEC stability reasons etc. this could be of utmost importance. 
When the waves travel into the nearshore one need to take notice of the 
changing physical setting. As mentioned, the sea floor influences the waves, 
resulting in the particle paths becoming more elliptical. In the shallow water 
regime the linear theory is no longer valid and a more complex non-linear 
theory is needed to describe the waves. The non-linear wave theory will not 
be presented here, instead it is concluded that waves loose energy as they 
travel into shallower water due to sea-floor interactions and that the surge 
component of the particle motion increases relatively.
2.3
Wave energy absorption 
In wave energy, the term absorption refers to the conversion of the incoming 
wave energy flux to mechanical power. Wave energy absorption is best 
explained by considering the example given in Falnes et al
3
(1978), re-
produced here in Figure 2.2. Figure 2.2a shows an undisturbed incident wave. 
Curve b shows the wave radiation pattern by a wave energy converter 
oscillating in heave while curve c shows the wave radiation patter by a wave 
energy converter oscillating in surge. Curve d shows the resultant wave field 
after the superposition of all three waves, curves a, b and c. It can be seen 
that in order to absorb a wave it is necessary to generate a wave. Hence the 
paradoxical statement “that to destroy a wave means to absorb a wave”
3
Falnes, J and Budal, K: Wave-power conversion by point absorbers. Norwegian 
Maritime Research, Vol.6, No.4, pp.2-11 (1978) 

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ELFORSK 
8