# Alpen Steel | Renewable Energy

## Wave power

Large storm waves pose a challenge to wave power developers

Wave power is the transport of energi by  and the capture of that energy to do useful — for example for , or the of water (into .

Wave power is distinct from the diurnal flux of and the steady gyre of  Wave power generation is not currently a widely employed commercia although there have been attempts at using it since at least 1890. The world's first commercial  is based in Portugal, at the  whic

consists of three 750 kilowot pelamis devices.

## Physical concepts

When an object bobs up and down on a  in a pond, it experiences an elliptical trajectory.
Motion of a particle in an ocean wave.
A = At deep water. The  motion of fluid particles decreases rapidly with increasing depth below the surface.
B = At shallow water (ocean floor is now at B). The elliptical movement of a fluid particle flattens with decreasing depth.
1 = Propagation direction.
2 = Wave crest.
3 = Wave trough.

Waves are generated by wind passing over the sea surface. 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 , as well as friction on the water surface by the wind  causes the growth of the waves.

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,, and wate

is highest at the surface and diminishes exponentially with depth. However, for  near a reflecting coast, wave energy is also present as pressure oscillations at great depth, producing 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. The mean transport rate of the wave energy through a vertical  of unit width, parallel to a wave  is called the wave energy  (or wave power, which must not be confused with the actual power generated by a wave power device).

### Wave power formula

In deep water where the water depth is larger than half the the wave energy flux is

$P = frac{rho g^2}{64pi} H_{m0}^2 T_{e} approx left(0.5 frac{text{kW}}{text{m}^3 cdot text{s}} right) H_{m0}^2; T_{e},$

where

• P the wave energy flux per unit wave crest length (kW/m);
• Hm0 is the  (meter), as measured by wave  and predicted by wave forecast models. By definition, Hm0 is four times the  of the water surface
• Te is the energy  (second);
• ρ is the of the water (kg/m3), and
• g is the (m/s2).

The above formula states that wave power is proportional to the wave period and to the  of the . 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  length.

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

$P approx 0.5 frac{text{kW}}{text{m}^3 cdot text{s}} (3 cdot text{m})^2 (8 cdot text{s}) approx 36 frac{text{kW}}{text{m}},$

meaning there are 36 kilowatts of power potential per meter of coastline.

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/m 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  the  density per unit area of  on the water surface is proportional to the wave height squared, according to linear wave theory:

$E=frac{1}{16}rho g H_{m0}^2,$

where E is the mean wave energy density per unit horizontal area (J/m2), the sum of and

density per unit horizontal area. The potential energy density is equal to the kinetic energy, both contributing half to the wave energy density E, as can be expected from the. In ocean waves, surface tension effects are negligible for  above a few

As the waves propagate, their energy is transported. The energy transport velocity is the As a result, the wave energy through a vertical plane of unit width perpendicular to the wave propagation direction, is equal to:

$P = E, c_g, ,$

with cg the group velocity (m/s). Due to the for water waves under the action of gravity, the group velocity depends on the  λ, or equivalently, on the wave 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:

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