Wave power
Wave power is the transport of energy
by ocean surface waves, and the capture of that
energy is to do useful work –
for example, electricity generation, water desalination, or the pumping of water
(into reservoirs). Machinery able to exploit wave power is generally known as a wave
energy converter (WEC).
Wave power is distinct from the diurnal
flux of tidal power and the steady gyre of ocean
currents. Wave-power generation is not currently a widely employed
commercial technology, although there have been attempts to use it since at
least 1890.[1] In
2008, the first experimental wave farm was
opened in Portugal, at the Aguçadoura Wave Park.[2] The
major competitor of wave power is offshore wind power.
Physical
concepts
Waves are generated by wind passing
over the surface of the sea. As long as the waves propagate slower than the
wind speed just above the waves, there is an energy transfer from the wind to
the waves. Both air pressure differences between the upwind and the lee side of
a wave crest, as well as friction on the water
surface by the wind, making the water to go into the shear stress causes
the growth of the waves.[4]
Wave height is
determined by wind speed, the duration of time the wind has been blowing, fetch
(the distance over which the wind excites the waves) and by the depth and
topography of the seafloor (which can focus or disperse the energy of the
waves). A given wind speed has a matching practical limit over which time or
distance will not produce larger waves. When this limit has been reached the
sea is said to be "fully developed".
In
general, larger waves are more powerful but wave power is also determined by
wave speed, wavelength, and water density.
Oscillatory
motion is highest at
the surface and diminishes exponentially with depth. However, for standing waves (clapotis)
near a reflecting coast, wave energy is also present as pressure oscillations
at great depth, producing microseisms.[4] These
pressure fluctuations at greater depth are too small to be interesting from the
point of view of wave power.
The
waves propagate on the ocean surface, and the wave energy is also transported
horizontally with the group velocity. The mean transport rate of the
wave energy through a vertical plane of unit width, parallel to a wave
crest, is called the wave energy flux (or wave power, which must not be
confused with the actual power generated by a wave power device).
Wave power formula
with P the wave energy flux per unit of wave-crest length, Hm0 the significant wave height, T the wave period, ρ the water density and g theacceleration by gravity. The above formula states that wave power is proportional to the wave period and to the square of the wave height. When the significant wave height is given in meters, and the wave period in seconds, the result is the wave power in kilowatts (kW) per meter of wavefront length.[5][6][7]
Example: Consider moderate ocean swells,
in deep water, a few kilometers off a coastline, with a wave height of 3 meters
and a wave period of 8 seconds. Using the formula to solve for power, we get
meaning there are 36 kilowatts of power
potential per meter of wave crest.
In major storms, the largest waves
offshore are about 15 meters high and have a period of about 15 seconds.
According to the above formula, such waves carry about 1.7 MW of power across
each meter of wavefront.
An effective wave power device captures as
much as possible of the wave energy flux. As a result the waves will be of
lower height in the region behind the wave power device.
Wave energy and wave-energy flux
In a sea state, the average energy density per unit area of gravity waves on the water surface is proportional to the wave height squared, according
to linear wave theory:[4][8]
where E is the mean wave energy density per unit
horizontal area (J/m2), the sum of kinetic and potential energy density per
unit horizontal area. The potential energy density is equal to the kinetic
energy,[4] both contributing half to the wave energy density E, as can be expected from the equipartition theorem.
In ocean waves, surface tension effects are negligible for wavelengths above a
few decimetres.
As the waves propagate, their energy is
transported. The energy transport velocity is the group velocity. As a result, the wave energy flux,
through a vertical plane of unit width perpendicular to the wave propagation
direction, is equal to:[10][4]
with cg the group
velocity (m/s). Due to the dispersion relation for water waves
under the action of gravity, the group velocity depends on the wavelength λ, or equivalently, on the wave period T. Further, the dispersion relation is a
function of the water depth h. As a result, the group velocity behaves
differently in the limits of deep and shallow water, and at intermediate
depths:[4][8]
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