Wave energy is the transport of energy by ocean surface waves, and the capture of that energy 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. In 2008, the first experimental wave farm was opened in Portugal, at the Aguçadoura Wave Park. The major competitor of wave power is offshore wind power.
Physical concepts 
- See energy, power and work for more information on these important physical concepts. see wind wave for more information on ocean waves.
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.
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".
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. 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 the acceleration 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 metres, and the wave period in seconds, the result is the wave power in kilowatts (kW) per metre of wavefront length.
Example: Consider moderate ocean swells, in deep water, a few km off a coastline, with a wave height of 3 m 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 metre 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 
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, 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:
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:
|Properties of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory|
( h > ½ λ )
( h < 0.05 λ )
( all λ and h )
|phase velocity||m / s|
|group velocity[c]||m / s|
|wavelength||m||for given period T, the solution of:
|wave energy density||J / m2|
|wave energy flux||W / m|
|angular frequency||rad / s|
|wavenumber||rad / m|
Deep-water characteristics and opportunities 
Deep water corresponds with a water depth larger than half the wavelength, which is the common situation in the sea and ocean. In deep water, longer-period waves propagate faster and transport their energy faster. The deep-water group velocity is half the phase velocity. In shallow water, for wavelengths larger than about twenty times the water depth, as found quite often near the coast, the group velocity is equal to the phase velocity.
The first known patent to use energy from ocean waves dates back to 1799 and was filed in Paris by Girard and his son. An early application of wave power was a device constructed around 1910 by Bochaux-Praceique to light and power his house at Royan, near Bordeaux in France. It appears that this was the first oscillating water-column type of wave-energy device. From 1855 to 1973 there were already 340 patents filed in the UK alone.
Modern scientific pursuit of wave energy was pioneered by Yoshio Masuda's experiments in the 1940s. He has tested various concepts of wave-energy devices at sea, with several hundred units used to power navigation lights. Among these was the concept of extracting power from the angular motion at the joints of an articulated raft, which was proposed in the 1950s by Masuda.
A renewed interest in wave energy was motivated by the oil crisis in 1973. A number of university researchers re-examined the potential to generate energy from ocean waves, among whom notably were Stephen Salter from the University of Edinburgh, Kjell Budal and Johannes Falnes from Norwegian Institute of Technology (now merged into Norwegian University of Science and Technology), Michael E. McCormick from U.S. Naval Academy, David Evans from Bristol University, Michael French from University of Lancaster, Nick Newman and C. C. Mei from MIT.
Stephen Salter's 1974 invention became known as Salter's duck or nodding duck, although it was officially referred to as the Edinburgh Duck. In small scale controlled tests, the Duck's curved cam-like body can stop 90% of wave motion and can convert 90% of that to electricity giving 81% efficiency.
In the 1980s, as the oil price went down, wave-energy funding was drastically reduced. Nevertheless, a few first-generation prototypes were tested at sea. More recently, following the issue of climate change, there is again a growing interest worldwide for renewable energy, including wave energy.
Modern technology 
Wave power devices are generally categorized by the method used to capture the energy of the waves, by location and by the power take-off system. Method types are point absorber or buoy; surfacing following or attenuator oriented parallel to the direction of wave propagation; terminator, oriented perpendicular to the direction of wave propagation; oscillating water column; and overtopping. Locations are shoreline, nearshore and offshore. Types of power take-off include: hydraulic ram, elastomeric hose pump, pump-to-shore, hydroelectric turbine, air turbine, and linear electrical generator. Some of these designs incorporate parabolic reflectors as a means of increasing the wave energy at the point of capture. These capture systems use the rise and fall motion of waves to capture energy. Once the wave energy is captured at a wave source, power must be carried to the point of use or to a connection to the electrical grid by transmission power cables. The table contains descriptions of some wave power systems:
|Device||Proponent||Country of origin||Capture method||Location||Power take off||Year build||Notes|
|Anaconda Wave Energy Converter||Checkmate SeaEnergy.||UK||Surface-following attenuator||Offshore||Hydroelectric turbine||2008||In the early stages of development, the device is a 200 metres (660 ft) long rubber tube which is tethered underwater. Passing waves will instigate a wave inside the tube, which will then propagates down its walls, driving a turbine at the far end.|
|AquaBuOY||Finavera Wind Energy, later SSE Renewables Limited||Ireland-Canada-Scotland||Buoy||Offshore||Hydroelectric turbine||2003||In 2009 Finavera Renewables surrendered its wave energy permits from FERC. In July 2010 Finavera announced that it had entered into a definitive agreement to sell all assets and intellectual property related to the AquaBuOY wave energy technology.|
|AWS-iii||AWS Ocean Energy||UK (Scotland)||Surface-following attenuator?||Offshore||Air turbine||2010||The AWS-III is a floating toroidal vessel. It has rubber membranes on the outer faces which deform as waves pass, moving air inside chambers which in turn drive air-turbines to generate electricity. AWS Ocean tested a 1/9 scale model in Loch Ness in 2010, and are now working on a full sized version which will be 60m across and should generate 2.5MW. It is envisage these will be installed in offshore farms moored in around 100m depth of water.|
|CETO Wave Power||Carnegie||Australia||Buoy||Offshore||Pump-to-shore||1999||As of 2008, the device is being tested off Fremantle, Western Australia, the device consists of a single piston pump attached to the sea floor with a float (buoy) tethered to the piston. Waves cause the float to rise and fall, generating pressurized water, which is piped to an onshore facility to drive hydraulic generators or run reverse osmosis water desalination.|
|Cycloidal Wave Energy Converter||Atargis Energy Corporation||USA||Fully Submerged Wave Termination Device||Offshore||Direct Drive Generator||2006||In the tank testing stage of development, the device is a 20 metres (66 ft) diameter fully submerged rotor with two hydrofoils. Numerical studies have shown greater than 99% wave power termination capabilities. These were confirmed by experiments in a small 2D wave flume as well as a large offshore wave basin.|
|FlanSea (Flanders Electricity from the Sea)||FlanSea||Belgium||Buoy||Offshore||Hydroelectric turbine||2010||A point absorber buoy developed for use in the southern North Sea conditions. It works by means of a cable that due to the bobbing effect of the buoy, generates electricity.|
|Islay LIMPET||Islay LIMPET||Scotland||oscillating water column||Onshore||Air turbine||1991||500 kW shoreline device uses an oscillating water column to drive air in and out of a pressure chamber through a Wells turbine.|
|Lysekil Project||Uppsala University||Sweden||Buoy||Offshore||Linear generator||2002||Direct driven linear generator placed on the seabed, connected to a buoy at the surface via a line. The movements of the buoy will drive the translator in the generator.|
|Oceanlinx||Oceanlinx||Australia||Buoy||Offshore||Hydroelectric turbine||1997||To generate electricity from long-wavelength ocean swell oscillations. The third and final demonstration-scale, grid-connected unit near Port Kembla, near Sydney, Australia, a 2.5 MWe system that went online in early 2010.|
|OE buoy||Ocean Energy||Ireland||Buoy||Offshore||Air turbine||2006||In September 2009 completed a 2-year sea trial in one quarter scale form. The OE buoy has only one moving part.|
|Oyster wave energy converter||Aquamarine Power||UK (Scots-Irish)||Oscillating wave surge converter||Nearshore||Pump-to-shore (hydro-electric turbine)||2005||A hinged mechanical flap attached to the seabed captures the energy of nearshore waves. It drives hydraulic pistons to deliver high pressure water to an onshore turbine which generates electricity. In November 2009, the first full-scale demonstrator Oyster began producing power on Orkney.|
|Pelamis Wave Energy Converter||Pelamis Wave Power||UK (Scottish)||Surface-following attenuator||Offshore||Hydraulic||1998||As waves pass along a series of semi-submerged cylindrical sections linked by hinged joints, the sections move relative to one another. This motion activates hydraulic cylinders which pump high pressure oil through hydraulic motors which drive electrical generators. The first working Pelamis machine in 2004 was at the European Marine Energy Center. The later P2, owned by E.ON, started grid connected tests off Orkney in 2010.|
|PowerBuoy||Ocean Power Technologies||US||Buoy||Offshore||Hydroelectric turbine||1997||The Pacific Northwest Generating Cooperative is funding construction of a commercial wave-power park at Reedsport, Oregon using buoys. The rise and fall of the waves moves a rack and pinion within the buoy and spins a generator. The electricity is transmitted by a submerged transmission line. The buoys are designed to be installed one to five miles (8 km) offshore in water 100 to 200 feet (60 m) deep.|
|R38/50 kW, R115/150 kW||40South Energy||UK||Underwater attenuator||Offshore||Electrical conversion||2010||These machines work by extracting energy from the relative motion between one Upper Member and one Lower Member, following an innovative method which earned the company one UKTI Research & Development Award in 2011. A first generation full scale prototype for this solution was tested offshore in 2010, and a second generation full scale prototype was tested offshore during 2011. In 2012 the first units were sold to clients in various countries, for delivery within the year. The first reduced scale prototypes were tested offshore during 2007, but the company decided to remain in a "stealth mode" until May 2010 and is now recognized as one of the technological innovators in the sector. The company initially considered installing at Wave Hub in 2012, but that project is on hold for now. The R38/50 kW is rated at 50 kW while the R115/150 kW is rated at 150 kW.|
|SDE Sea Waves Power Plant||SDE Energy Ltd.||Israel||Buoy||Nearshore||Hydroelectric turbine||2010||A breakwater-based wave energy converter, this device is built close to the shore and utilizes the vertical motion of buoys for creating hydraulic pressure which in turn operates the system's generators. In 2010 it began construction of a new 250 kWh model in the port of Jaffa, Tel Aviv and preparing to construct its standing orders for a 100 MWh power plants in the islands of Zanzibar and Kosrae, Micronesia.|
|SeaRaser||Alvin Smith (Dartmouth Wave Energy)\Ecotricity||UK||Buoy||Nearshore||Hydraulic ram||2008||Consisting of a piston pump(s) attached to the sea floor with a float (buoy) tethered to the piston. Waves cause the float to rise and fall, generating pressurized water, which is piped to resoviors onshore which then drive hydraulic generators.
It is currently "undergoing extensive modelling ahead of a sea trial" 
|Unnamed Ocean Wave-Powered Generator||SRI International||US||Buoy||Offshore||Electroactive polymer artificial muscle||2004||A type of wave buoys, built using special polymers, is being developed by Stanford Research Institute.|
|Wavebob||Wavebob||Ireland||Buoy||Offshore||Direct Drive Power Take off||1999||Wavebob have conducted some ocean trials, as well as extensive tank tests. It is an ocean-going heaving buoy, with a submerged tank which captures additional mass of seawater for added power and tunability, and as a safety feature (Tank "Venting")|
|Wave Dragon||Erik Friis-Madsen||Denmark||Overtopping device||Offshore||Hydroelectric turbine||2003||With the Wave Dragon wave energy converter large wing reflectors focus waves up a ramp into an offshore reservoir. The water returns to the ocean by the force of gravity via hydroelectric generators.|
|WaveRoller||AW-Energy Oy||Finland||Oscillating wave surge converter||Nearshore||Hydraulic||1994||The WaveRoller is a plate anchored on the sea bottom by its lower part. The back and forth movement of surge moves the plate. The kinetic energy transferred to this plate is collected by a piston pump. Full-scale demonstration project built off Portugal in 2009.|
|Wave Star||Wave Star A/S||Denmark||Multi-point absorber||Offshore||Hydroelectric turbine||2000||The Wavestar machine draws energy from wave power with floats that rise and fall with the up and down motion of waves. The floats are attached by arms to a platform that stands on legs secured to the sea floor. The motion of the floats is transferred via hydraulics into the rotation of a generator, producing electricity. Wave Star has been testing a 1:10 machine since 2005 in Nissum Bredning, Denmark, it was taken out of duty in November 2011. A 1:2 Wave Star machine is in place in Hanstholm which has produced electricity to the grid since September 2009.|
The realistically usable worldwide resource has been estimated to be greater than 2 TW. Locations with the most potential for wave power include the western seaboard of Europe, the northern coast of the UK, and the Pacific coastlines of North and South America, Southern Africa, Australia, and New Zealand. The north and south temperate zones have the best sites for capturing wave power. The prevailing westerlies in these zones blow strongest in winter.
There is a potential impact on the marine environment. Noise pollution, for example, could have negative impact if not monitored, although the noise and visible impact of each design varies greatly. Other biophysical impacts (flora and fauna, sediment regimes and water column structure and flows) of scaling up the technology is being studied. In terms of socio-economic challenges, wave farms can result in the displacement of commercial and recreational fishermen from productive fishing grounds, can change the pattern of beach sand nourishment, and may represent hazards to safe navigation. Waves generate about 2,700 gigawatts of power. Of those 2,700 gigawatts, only about 500 gigawatts can be captured with the current technology.
Wave farms 
- The Aguçadoura Wave Farm was the world's first wave farm. It was located 5 km (3 mi) offshore near Póvoa de Varzim, Portugal north of Oporto. The farm was designed to use three Pelamis wave energy converters to convert the motion of the ocean surface waves into electricity, totalling to 2.25 MW in total installed capacity. The farm first generated electricity in July 2008 and was officially opened on September 23, 2008, by the Portuguese Minister of Economy. The wave farm was shut down two months after the official opening in November 2008 as a result of the financial collapse of Babcock & Brown due to the global economic crisis. The machines were off-site at this time due to technical problems, and although resolved have not returned to site and were subsequently scrapped in 2011 as the technology had moved on to the P2 variant as supplied to Eon and Scottish Power Renewables. A second phase of the project planned to increase the installed capacity to 21 MW using a further 25 Pelamis machines is in doubt following Babcock's financial collapse.
United Kingdom 
- Funding for a 3 MW wave farm in Scotland was announced on February 20, 2007 by the Scottish Executive, at a cost of over 4 million pounds, as part of a £13 million funding package for marine power in Scotland. The first of 66 machines was launched in May 2010.
- A facility known as Wave hub has been constructed off the north coast of Cornwall, England to facilitate wave energy development. The Wave hub will act as giant extension cable, allowing arrays of wave energy generating devices to be connected to the electricity grid. The Wave hub will initially allow 20 MW of capacity to be connected, with potential expansion to 40 MW. Four device manufacturers have so far expressed interest in connecting to the Wave hub. The scientists have calculated that wave energy gathered at Wave Hub will be enough to power up to 7,500 households. The site has the potential to save greenhouse gas emissions of about 300,000 tons of carbon dioxide in the next 25 years.
- A CETO wave farm off the coast of Western Australia has been operating to prove commercial viability and, after preliminary environmental approval, is poised for further development.
- Ocean Power Technologies (OPT Australasia Pty Ltd) is developing a wave farm connected to the grid near Portland, Victoria through a 19 MW wave power station. The project has received an AU $66.46 million grant from the Federal Government of Australia.
United States 
- Reedsport, Oregon – a commercial wave park on the west coast of the United States located 2.5 miles offshore near Reedsport, Oregon. The first phase of this project is for ten PB150 PowerBuoys, or 1.5 megawatts. The Reedsport wave farm is now scheduled for installation spring 2013.
- U.S. Patent 3,928,967 — 1974 Apparatus and method of extracting wave energy – The original "Salter's Duck" patent
- U.S. Patent 4,134,023 — 1977 Apparatus for use in the extraction of energy from waves on water – Salter's method for improving "duck" efficiency
- U.S. Patent 6,194,815 — 1999 Piezoelectric rotary electrical energy generator
- US application 20,040,217,597 [dead link] — 2004 Wave energy converters utilizing pressure differences (src)
See also 
- The energy flux is with the group velocity, see Herbich, John B. (2000). Handbook of coastal engineering. McGraw-Hill Professional. p. A.117, Eq. (12). ISBN 978-0-07-134402-9. The group velocity is , see the collapsed table "Properties of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory" in the section "Wave energy and wave energy flux" below.
- For a small-amplitude sinusoidal wave with wave amplitude the wave energy density per unit horizontal area is or using the wave height for sinusoidal waves. In terms of the variance of the surface elevation the energy density is . Turning to random waves, the last formulation of the wave energy equation in terms of is also valid (Holthuijsen, 2007, p. 40), due to Parseval's theorem. Further, the significant wave height is defined as , leading to the factor 1⁄16 in the wave energy density per unit horizontal area.
- For determining the group velocity the angular frequency ω is considered as a function of the wavenumber k, or equivalently, the period T as a function of the wavelength λ.
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Further reading 
- Cruz, Joao (2008). Ocean Wave Energy – Current Status and Future Prospects. Springer. ISBN 3-540-74894-6., 431 pp.
- Falnes, Johannes (2002). Ocean Waves and Oscillating Systems. Cambridge University Press. ISBN 0-521-01749-1., 288 pp.
- McCormick, Michael (2007). Ocean Wave Energy Conversion. Dover. ISBN 0-486-46245-5., 256 pp.
- Twidell, John; Weir, Anthony D.; Weir, Tony (2006). Renewable Energy Resources. Taylor & Francis. ISBN 0-419-25330-0., 601 pp.
|Wikimedia Commons has media related to: Wave power|
|Wikimedia Commons has media related to: Renewable energy|
- "Ocean waves – our new electricity supplier" Archived 7 January 2010 at the Wayback Machine (Uppsala university 2010)
- Kate Galbraith (September 22, 2008). "Power From the Restless Sea Stirs the Imagination". New York Times. Retrieved 2008-10-09.
- "Wave Power: The Coming Wave" from the Economist, June 5, 2008
- Russian Company Develops Mobile Wave Energy Generator
- "The untimely death of Salter's Duck"
- "Ocean Power Fights Current Thinking"
- "Wave energy in New Zealand"
- Wave technologies: types of devices (LORC Knowledge 2011)
- "How it works: Wave power station"