Environmental Engineering Reference
In-Depth Information
1000 kg, where A is the ocean
area and 1000 is the density of water in kg/m
3
. Thus,
P
Thus, P
¼
1/2M (1
0.1)
2
0.1, where M
¼
AD
10
3
m
2
=
A
¼
0
:
5
1000
¼
0
:
5W
=
;
compared to 0.155W/m
2
fromTable 1.1. We predict the total power in ocean waves is
181 TW, on this crude estimate, compared to 56 TW from Table 1.1.
This crude estimate is closer than one might have expected! (It is likely that the
typical frequency is higher, and the typical amplitude is smaller). The estimate also
helps us understand that the power is proportional to the square of the wave height
and the cube of the wave frequency. In fact, the trajectory of water particles as the
wave passes is not vertical but circular, and the wave is mathematically a trochoidal
wave rather than a sinusoidal wave. If one imagines a disk of radius R rolling, a
point on the radius r
¼
<
R
executes trochoidal motion. The model of sinusoidal motion is still useful (http://
hyperphysics.phy-astr.gsu.edu/hbase/waves/watwav2.html.).
The designs of devices, termed wave energy converters, WEC, to extract the wave
energy, are naturally adapted to a particular situation, such as at a given depth of water
beyond a shoreline, where waves are approaching land. The wave amplitude and
speed increase as the open water wave approaches land. Water depths in the range
40
-
100m are typical of present installations [13].
The potential extractable wave energy from the Paci
R experiences sinusoidal motion but a point at radius r
c west coast of the United
States is estimated [13] as 255 TWh per year, and in Europe about 280 TWh per year.
These numbers are equivalent to powers of 0.029 TW and 0.032 TW, respectively
(29 GW is an appreciable fraction, about 0.06, of electric power consumption in the
United States). It is not clear what the capital and operational costs of such extraction
would be, but at least one commercial device, the Pelamis, has been subsidized by the
government of Portugal and put into service.
Aplausible estimate of available wave power along a coastline is in terms of power
per unit length of the coastline. On the Atlantic coast of Great Britain this is
estimated [14] as 40 kW/m of exposed coastline. This estimate depends on the height
of the waves, which is a function of the windspeed and the unimpeded span of water
facing the coast over which the waves can collect energy from the wind. This estimate
might be compared to the estimate above for the Paci
c coast of the United States. If
that coastline is 1000 miles or 1.6 Mm, then we get, at 40 kW/m, the estimate 64 GW,
fairly close in agreement.
As waves approach land at depth d, the wave speed is
1
=
2
V
¼½ð
g
l=
2
pÞ
tan h
ð
2
p
d
=lÞ
:
ð
1
:
15
Þ
The Pelamis (the word means water snake) device is a linear array of four linked
pontoons, each 30m long, oriented perpendicular to the waves. The
flexing motion
occurring at the linking joints with wave passage is used to create electricity. Pelamis
devices totaling 2.25MW capacity have been installed in the sea near Portugal.
Vertically bobbing buoy devices anchored at modest depths are also practical. Devices
may also be based on trapping water from the tops of waves, extracting energy as that
water falls back into the sea.
