Environmental Engineering Reference
In-Depth Information
expressed as
gH
2
8
=
ρ
Wave energy/area
(7.20)
The wave energy of equation (7.20) is propagated in the direction of motion of the wave, which
is generally the direction of the wind, at the group velocity of an ocean wave. The latter equals half
the phase velocity
c
,or
g
f
. The flux of wave energy, or power, per unit of distance normal to
the direction of wave propagation, is the product of the energy per unit area and the group velocity:
/
4
π
g
2
H
2
16
g
3
/
2
H
2
1
/
2
ρ
)
=
ρ
λ
Wave power/length
=
(7.21)
/
(
2
π
f
16
(
2
π)
1
2
Unlike the wave energy, the wave power depends upon the wavelength, albeit as the half power of
the wavelength.
Depending upon the wind speed, the surface of the ocean is covered with a random collection
of waves of differen
t he
ight and wavelength. As the speed
V
of the wind increases, b
ot
h the mean
square wave height
H
2
and the mean wavelength increase and the mean frequency
f
decreases.
Oceanographers have measured these quantities as a function of wind speed and found them to be
empirically related by the following formulas
26
:
V
4
g
2
H
2
=
2
.
19E
(
−
2
)
(7.22)
0
.
70
g
V
2
π
f
=
(7.23)
Substituting these relations into equations (7.20) and (7.21) for wave energy and power, we find
that
V
4
g
)
ρ
Wave energy/area
=
2
.
74E
(
−
3
(7.24)
V
5
g
)
ρ
Wave power/length
=
3
.
89E
(
−
3
(7.25)
For example, a wind speed of 20 knots (10.29 m/s) will generate an energy density of 3.13 kJ/m
2
,
a wave power of 45.8 kW/m, an average wave height of 1.6 m, and an average wave frequency of
0.106 Hz, which is a wave period of 9.4 s.
The dependence of wave power on wind speed,
V
5
, is steeper than that for wind power,
V
3
.
As a consequence, most of the wave power available at a site is collectible only when the wind
exceeds its average value, as can be seen in Figure 7.26, showing the probability distribution of
wave power with wind speed, assuming the wind speed probability distribution of Figure 7.19.
Figure 7.26 contrasts sharply with Figure 7.19 for the distribution of wind speed. The average
wave power for t
he
distribution of Figure 7.26 is 60
2
/π
=
6
.
08 times the power available at the
mean wind speed
V
.
26
These relations hold under conditions where the wind duration is long enough over a sufficiently great
unimpeded fetch of ocean surface.
