## Formation and Description of Waves

Water waves are caused by the interaction of three forces, namely wind, surface tension and gravity. Wind causes air to pass over the surface of the sea, which in turn disturbs the position of the water surface. The wave is formed as a response to this disturbance, by surface tension on the small scale and gravity when dealing with larger disturbances. As the length of time or the length of water (called fetch) over which the wind has been acting increases, so too does the height and length of the resultant wave.

Although the visible evidence of waves is on the surface there is also energy being transferred within the sea body. The particles of fluid through which the wave is travelling follow an orbital path whose amplitude decreases exponentially as depth increases. It follows that 95% of the energy contained within a wave is to be found in the region between the mean water level and a depth of one quarter the wave length.

In deep water, defined as depth greater than half a wave length, the velocity (v) of a wave is dictated by its wave length as given by equation (1.1).

Where g = acceleration due to gravity (ms-2)

In the ocean, therefore, longer waves travel faster than shorter waves. As the crest of a longer, faster, wave passes the crest of a slower wave, the amplitude of the resulting wave will be equal to the sum of the two amplitudes. The converse happens if the trough of one interferes with the peak of another. Considering the real sea state, where there are many waves of different lengths, the displacement of the surface is hence a varying frequency varying amplitude signal. These variations highlight one of the difficulties with Wave Energy Converters (WECs), namely the requirement of adaptability to different sea states. A device which is optimised for a given amplitude and frequency must be capable of surviving in much rougher conditions if it is to have a credible lifetime. The net result is the need to over engineer structures relative to their rated capacity, a factor which increases the cost.

To calculate the mean energy contained within a given sea state it is necessary to use not the instant height of a wave but Hs, the significant wave height. This is defined as the average height of the highest third of the waves passing a site and is used in Equation (1.2) to derive power.

Where P = mean power (W) T = time period (S) p = density = 1025 kg/m3 for sea water W = width of wave front (m)

The power contained within a wave is therefore proportional to its period and the square of its significant wave height.

One further description of real wave conditions is the zero upcross time, defined as the time interval between subsequent occasions when the water surface crosses the mean water height in an upward direction. It hence gives an insight to the predominant wave frequency.

These definitions may be used to further highlight the sizing difficulties for WECs. A typical site may have a most likely sea state of 0.75 m height and 6.5 seconds period, giving power levels of just 3.6 kW per metre wave front, yet a device sited there to extract this will also be expected to survive in states of 5 m height and 12 seconds period corresponding to almost 300 kW per m wave front: two orders of magnitude greater.

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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