Wave power 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.
- 1 Physical concepts
- 2 History
- 3 Modern technology
- 4 Potential
- 5 Challenges
- 6 Wave farms
- 7 Patents
- 8 See also
- 9 Notes
- 10 References
- 11 Further reading
- 12 External links
- 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, Te the wave energy period, ρ the water density and g the acceleration by gravity. The above formula states that wave power is proportional to the wave energy 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 energy 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.
The world's first marine energy test facility was established in 2003 to kick start the development of a wave and tidal energy industry in the UK. Based in Orkney, Scotland, the European Marine Energy Centre (EMEC) has supported the deployment of more wave and tidal energy devices than at any other single site in the world. EMEC provides a variety of test sites in real sea conditions. It's grid connected wave test site is situated at Billia Croo, on the western edge of the Orkney mainland, and is subject to the full force of the Atlantic Ocean with seas as high as 19 metres recorded at the site. Wave energy developers currently testing at the centre include Aquamarine Power, Pelamis Wave Power, ScottishPower Renewables and Wello.
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. 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. When evaluating wave energy as a technology type, it is important to distinguish between the four most common approaches: point absorber buoys, surface attenuators, oscillating water columns, and overtopping devices.
Point Absorber Buoy
This device floats on the surface of the water, held in place by cables connected to the seabed. Buoys use the rise and fall of swells to drive hydraulic pumps and generate electricity. EMF generated by electrical transmission cables and acoustic of these devices may be a concern for marine organisms. The presence of the buoys may affect fish, marine mammals, and birds as potential minor collision risk and roosting sites. Potential also exists for entanglement in mooring lines. Energy removed from the waves may also affect the shoreline, resulting in a recommendation that sites remain a considerable distance from the shore.
These devices act similarly to point absorber buoys, with multiple floating segments connected to one another and are oriented perpendicular to incoming waves. A flexing motion is created by swells that drive hydraulic pumps to generate electricity. Environmental effects are similar to those of point absorber buoys, with an additional concern that organisms could be pinched in the joints.
Oscillating Water Column
Oscillating water column devices can be located on shore or in deeper waters offshore. With an air chamber integrated into the device, swells compress air in the chambers forcing air through an air turbine to create electricity. Significant noise is produced as air is pushed through the turbines, potentially affecting birds and other marine organisms within the vicinity of the device. There is also concern about marine organisms getting trapped or entangled within the air chambers.
Overtopping devices are long structures that use wave velocity to fill a reservoir to a greater water level than the surrounding ocean. The potential energy in the reservoir height is then captured with low-head turbines. Devices can be either on shore or floating offshore. Floating devices will have environmental concerns about the mooring system affecting benthic organisms, organisms becoming entangled, or EMF effects produced from subsea cables. There is also some concern regarding low levels of turbine noise and wave energy removal affecting the nearfield habitat.
Oscillating Wave Surge Converter
These devices typically have one end fixed to a structure or the seabed while the other end is free to move. Energy is collected from the relative motion of the body compared to the fixed point. Oscillating wave surge converters often come in the form of floats, flaps, or membranes. Environmental concerns include minor risk of collision, artificial reefing near the fixed point, EMF effects from subsea cables, and energy removal effecting sediment transport. 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 2.5 MW. 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.|
|Crestwing||Crestwing ApS||Denmark||Surface-following attenuator||Offshore||Mechanical||2011||The device consists of two floats connected by a hinge. It uses atmospheric pressure acting on its large area to stick to the ocean surface. This allows it to follow the waves. Motion of the two floats relative to each other is transferred to electricity by a mechanical power take-off system. As of 2014, there is a 1:5 scale prototype that has been tested in the sea near Frederikshavn.|
|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||OWC||Nearshore & Offshore||air turbine||1997||Wave energy is captured with an Oscillating Water Column and electricity is generated by air flowing through a turbine. The third medium scale demonstration unit near Port Kembla, NSW, Australia, a medium scale system that was grid connected 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.|
|OWEL||Ocean Wave Energy Ltd||UK||Wave Surge Converter||Offshore||Air turbine||2013||The surging motion of long period waves compresses air in a tapered duct which is then used to drive an air turbine mounted on top of the floating vessel. The design of a full scale demonstration project was completed in Spring 2013, ready for fabrication.|
|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 at the European Marine Energy Centre's wave test site at Billia Croo in 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 was installed in 2004 at the European Marine Energy Center (EMEC) in Orkney. Here, it became the world's first offshore wave energy device to generate electricity into a national grid anywhere in the world. 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" 
|Squid/ WaveNET||AlbaTERN||UK (Scotland)||Multi-point absorber||Nearshore||Hydraulic?||2011||A 10 kW Squid prototype was tested at EMEC in 2011. The company have since secured funding through the WATERS2 project, to further develop the device including developing arrays.|
|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 SRI International.|
|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")|
|Wavepiston||Wavepiston ApS||Denmark||Oscillating wave surge converter||Nearshore||Pump-to-shore (hydro-electric turbine)||2013||The idea behind this concept is to reduce the mooring means for wave energy structures. Wavepiston systems use vertical plates to exploit the horizontal movement in ocean waves. By attaching several plates in parallel on a single structure the forces applied on the structure by the plates will tend to neutralize each other. This neutralization reduces the required mooring means. “Force cancellation” is the term used by the inventors of the technology to describe the neutralization of forces. Test and numerical models prove that force cancellation reduces the means for mooring and structure to 1/10. The structure is a steel wire stretched between two mooring points. The wire is a strong and flexible structure well suited for off shore use. The mooring is slack mooring. When the vertical plates move back and forth they produce pressurized water. The pressurized water is transported to a turbine through PE pipes. A central turbine station then converts it to electric power. Calculations on the current design show capital cost of EUR 0,89 per installed watt.|
|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.|
Common environmental concerns associated with marine energy developments include:
- The risk of marine mammals and fish being struck by tidal turbine blades;
- The effects of EMF and underwater noise emitted from operating marine energy devices;
- The physical presence of marine energy projects and their potential to alter the behavior of marine mammals, fish, and seabirds with attraction or avoidance;
- The potential effect on nearfield and farfield marine environment and processes such as sediment transport and water quality.
The Tethys database is an online knowledge management system that provides the marine energy community with access to information and scientific literature on environmental effects of marine energy developments.
The worldwide resource of wave energy 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.
- The Aguçadoura Wave Farm was the world's first wave farm. It was located 5 km (3 mi) offshore near Póvoa de Varzim, north of Porto, Portugal. 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.
- 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.
- Oceanlinx will deploy a commercial scale demonstrator off the coast of South Australia at Port MacDonnell before the end of 2013. This device, the greenWAVE, has a rated electrical capacity of 1MW. This project has been supported by ARENA through the Emerging Renewables Program. The greenWAVE device is a bottom standing gravity structure, that does not require anchoring or seabed preparation and with no moving parts below the surface of the water.
- 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 was scheduled for installation spring 2013. Project has ground to a halt because of legal and technical problems, August, 2013. See:-
- 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)
- 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.
- Here, the factor for random waves is 1⁄16, as opposed to 1⁄8 for periodic waves – as explained hereafter. 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.
- Christine Miller (August 2004). "Wave and Tidal Energy Experiments in San Francisco and Santa Cruz". Retrieved 2008-08-16.
- Joao Lima. Babcock, EDP and Efacec to Collaborate on Wave Energy Projects Bloomberg, September 23, 2008.
- Figure 6 from: Wiegel, R.L.; Johnson, J.W. (1950), "Elements of wave theory", Proceedings 1st International Conference on Coastal Engineering, Long Beach, California: ASCE, pp. 5–21
- Phillips, O.M. (1977). The dynamics of the upper ocean (2nd ed.). Cambridge University Press. ISBN 0-521-29801-6.
- Tucker, M.J.; Pitt, E.G. (2001). "2". In Bhattacharyya, R., McCormick, M.E. Waves in ocean engineering (1st ed. ed.). Oxford: Elsevier. pp. 35–36. ISBN 0080435661.
- "Wave Power". University of Strathclyde. Retrieved 2008-11-02.
- "Wave Energy Potential on the U.S. Outer Continental Shelf" (PDF). United States Department of the Interior. Retrieved 2008-10-17.
- Academic Study: Matching Renewable Electricity Generation with Demand: Full Report. Scotland.gov.uk.
- Goda, Y. (2000). Random Seas and Design of Maritime Structures. World Scientific. ISBN 978-981-02-3256-6.
- Holthuijsen, Leo H. (2007). Waves in oceanic and coastal waters. Cambridge: Cambridge University Press. ISBN 0-521-86028-8.
- Reynolds, O. (1877). "On the rate of progression of groups of waves and the rate at which energy is transmitted by waves". Nature 16: 343–44. Bibcode:1877Natur..16R.341.. doi:10.1038/016341c0.
Lord Rayleigh (J. W. Strutt) (1877). "On progressive waves". Proceedings of the London Mathematical Society 9 (1): 21–26. doi:10.1112/plms/s1-9.1.21. Reprinted as Appendix in: Theory of Sound 1, MacMillan, 2nd revised edition, 1894.
- R. G. Dean and R. A. Dalrymple (1991). Water wave mechanics for engineers and scientists. Advanced Series on Ocean Engineering 2. World Scientific, Singapore. ISBN 978-981-02-0420-4. See page 64–65.
- Clément et al. (2002). "Wave energy in Europe: current status and perspectives". Renewable and Sustainable Energy Reviews 6 (5): 405–431. doi:10.1016/S1364-0321(02)00009-6.
- "The Development of Wave Power" (PDF). Retrieved 2009-12-18.
- Morris-Thomas et al.; Irvin, Rohan J.; Thiagarajan, Krish P. (2007). "An Investigation Into the Hydrodynamic Efficiency of an Oscillating Water Column". Journal of Offshore Mechanics and Arctic Engineering 129 (4): 273–278. doi:10.1115/1.2426992.
- "Wave Energy Research and Development at JAMSTEC". Archived from the original on July 1, 2008. Retrieved 2009-12-18.
- Farley, F. J. M. and Rainey, R. C. T. (2006). "Radical design options for wave-profiling wave energy converters". International Workshop on Water Waves and Floating Bodies. Loughborough. Retrieved 2009-12-18.
- "Edinburgh Wave Energy Project" (PDF). University of Edinburgh. Retrieved 2008-10-22.
- Falnes, J. (2007). "A review of wave-energy extraction". Marine Structures 20 (4): 185–201. doi:10.1016/j.marstruc.2007.09.001.
- Embedded Shoreline Devices and Uses as Power Generation Sources Kimball, Kelly, November 2003
- McCormick, Michael E., and R. Cengiz Ertekin. Mechanical Engineering-CIME 131.5 (2009): 36. Expanded Academic ASAP. Web. October 5, 2009.
- Underwater Cable an Alternative to Electrical Towers, Matthew L. Wald, New York Times, 2010-03-16. Retrieved 2010-03-18.
- Anaconda WEC. Science Daily (July 7, 2008).
- Article about Anaconda on. Physics.org.
- Sustainable Business.com Finavera Renewables To Sell Ocean Energy Division. Sustainablebusiness.com.
- Stock Markets Review Finavera Renewables To Sell Finavera Renewables Ocean Energy – Quick Facts. Stockmarketsreview.com (July 2, 2010).
- Announcement of definitive agreement for sale of Finavera Ocean Energy Limited[dead link]
- "Finavera To Surrender Wave Energy Permits"
- "Wave device tested on Loch Ness". BBC News. Retrieved 17 November 2012.
- "Cromarty Firth test for Jumbo wings-sized wave device". BBC News. Retrieved 17 November 2012.
- "AWS Ocean Energy - AWS-III The story so far…". AWS Ocean. Retrieved 17 November 2012.
- "AWS Technology". AWS Ocean. Retrieved 17 November 2012.
- "CETO Overview". carnegiecorp.com.au. Retrieved 2008-11-03.
- Stephen Cauchi (October 5, 2008). "New wave of power in renewable energy market". The Age (Melbourne). Retrieved 2008-10-10.
- http://crestwing.dk/. Missing or empty
- Applied Ocean Research: Deep ocean wave energy conversion using a cycloidal turbine (April, 2011).
- Applied Ocean Research: Experimental wave termination in a 2D wave tunnel using a cycloidal wave energy converter (April, 2012)
- FlanSea "optimal for use in southern North Sea". Vliz.be.
- Image of FlanSea. Kw.rnews.be (December 1, 2010).
- FlanSea project page. Deme.be (December 1, 2010).
- "How it works: Wave power station". BBC News. November 20, 2000.
- Seenan, Gerard (September 14, 2000). "Islay pioneers harnessing of wave power". The Guardian (London).
- International Water Power and Dam Construction. Waterpowermagazine.com (January 16, 2008).
- Leijon, Mats et. al (April 9, 2008). "Wave Energy from the North Sea: Experiences from the lysekil Research site". Retrieved June 24, 2009.
- Leijon, Mats et. al (January–February 2009). "Catch the Wave to Electricity". IEEE power energy magazine 7 (1): 50–54. doi:10.1109/MPE.2008.930658. Retrieved June 29, 2009.
- Adee, Sally (October 21, 2009). "This Renewable Energy Source Is Swell". IEEE Spectrum Inside Technology. Retrieved 2009-10-22.
- "Oceanlinx told to clean-up [sic] sunken energy generator". ABC News. May 25, 2010. Retrieved 2012-08-28.
- "Oceanlinx 1MW Commercial Wave Energy Demonstrator". ARENA. Retrieved 27 November 2013.
- Ocean Energy press release. Oceanenergy.ie.
- "The Technology". Ocean Wave Energy Ltd. Retrieved 25 January 2014.
- "Completion of OWEL Marine Demonstrator design". 5 May 2013. Retrieved 25 January 2014.
- Heather Clancy (December 30, 2009). "Wave energy's new pearl: University begins testing Oyster tech off Scottish coast". ZDNet. Retrieved 2010-11-13.
- Jenny Haworth (September 24, 2008). "If Portugal can rule the waves, why not Scotland?". The Scotsman (Edinburgh). Retrieved 2008-10-09.
- "Update on EMEC activities, resource description, and characterisation of wave-induced velocities in a tidal flow". Retrieved 2010-12-03.
- "Making Waves". Scottish Government. Retrieved 2011-04-07.
- "Agreement to Develop Wave Power Park in Oregon". renewableeneregyaccess.com. Retrieved 2008-10-15.
- Johnson, Kirk (September 3, 2012). "Project Aims to Harness the Power of Waves". New York Times. Retrieved 2012-09-03.
- "Reedsport OPT Wave Park FERC Project No. 12713 Application for a Major License". Federal Energy Regulatory Commission. Retrieved 2010-02-15.
- "40South Energy assigned the 2011 UKTI Italy Research & Development Award". February 3, 2011.
- "40South Energy installs at sea the D100t full scale prototype". August 12, 2010.
- Theone Wilson (2011). "High achiever, Energy Engineering Magazine, Issue 33, page 51".
- "ReNews, Issue 198, page 15". 26 August 201.
- "40South Energy puts in operation the Y25t full scale prototype". August 12, 2010.
- "Real deal shapes up in Italy for 40South Energy, reNews, Issue 224, page 3". September 29, 2011.
- "40South Energy: preliminary agreement with two Italian developers for sale of machines, DECC REgional news: London".
- "Charging beneath the sea, Daily Telegraph Supplement, The Future of Energy". October 2010.
- Joseph Hincks (2011). "Energy Handbook 2011".
- "Italian wants front seat at Wave Hub, ReNews, Issue 195, page 2". July 1, 2010.
- Lewis Smith (November 17, 2008). "Searaser device in uphill battle for clean energy". The Sunday Times (London). Retrieved 2010-11-13.
- "Plans for sea energy device Searaser". BBC News. January 23, 2012.
- Shankleman, Jessica (18 May 2011). "Squid-like device aims to harness power of Scottish waves". BusinessGreen. Retrieved 25 January 2014.
- "AlbaTERN secures £617,000 of WATERS 2 support for their first WaveNET demonstrator array". AlbaTERN. 29 August 2012. Retrieved 25 January 2014.
- "SRI Demonstrates Ocean Wave-Powered Generator off California Coast" (Press release). SRI International. 2008-08-12. Retrieved 2013-07-10.
- Carolyn Said (December 14, 2008). "Researchers wring energy out of ocean waves". San Francisco Chronicle. Retrieved November 9, 2010.
- Susan Kraemer (November 3, 2009). "WaveRoller uses swinging door for underwater wave energy". Scientific American. Retrieved December 9, 2010.
- AW-Energy Oy. Aw-energy.com.
- Mats Renvall (November 27, 2011). "Danish WaveStar Energy retires the company’s old test plant – and plans a ten-fold expansion of the full-scale wave power plant". Retrieved 2012-01-05.
- Cruz J.; Gunnar M.; Barstow S.; Mollison D. (2008). Joao Cruz, ed. Green Energy and Technology, Ocean Wave Energy. Springer Science+Business Media. p. 93. ISBN 978-3-540-74894-6.
- Marine Renewable Energy Programme, NERC Retrieved 2011-08-01
- Steven Hackett:Economic and Social Considerations for Wave Energy Development in California CEC Report Nov 2008 Ch2, pp22-44 California Energy Commission|Retrieved 2008-12-14
- "First Electricity Generation in Portugal".
- "23 de Setembro de 2008". Government of Portugal. Retrieved 2008-09-24.
- Jha, Alok (September 25, 2008). "Making waves: UK firm harnesses power of the sea ... in Portugal". The Guardian (London). Retrieved 2008-10-09.
- "Pelamis Sinks Portugal Wave Power". cleantech.com. Retrieved 2009.
- Joao Lima (September 23, 2008). "Babcock, EDP and Efacec to Collaborate on Wave Energy Projects". Bloomberg Television. Retrieved 2008-09-24.
- Fyall, Jenny (May 19, 2010). "600ft 'sea snake' to harness power of Scotland". The Scotsman (Edinburgh). pp. 10–11. Retrieved 2010-05-19.
- James Sturcke (April 26, 2007). "Wave farm wins £21.5m grant". The Guardian (London). Retrieved 2009-04-08.
- "Tender problems delaying Wave Hub". BBC News. April 2, 2008. Retrieved 2009-04-08.
- "Go-ahead for £28m Cornish wave farm". The Guardian (London). September 17, 2007. Retrieved 2008-10-12.
- "Renewable Power from the Ocean's Waves". CETO Wave Power. Retrieved November 9, 2010.
- Keith Orchison (October 7, 2010). "Wave of the future needs investment". The Australian. Retrieved November 9, 2010.
- Lockheed Martin, Woodside, Ocean Power Technologies in wave power project, Portland Victoria Wave Farm
- America’s Premiere Wave Power Farm Sets Sail, Reedsport Wave Farm
-  US catching up with Europe - Forbes October 3, 2012
-  Reedsport project delayed due to early onset of winter weather - OregonLive Oct 2012
- 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.|
- Wave energy converters(a list of main types of wave energy converters, including animations)
- Wave energy developers (a database of known wave energy developers)
- "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"
- "Environmental Effects of Renewable Energy from the Sea" - Tethys