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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 at using it since at least 1890.^[1] In 2008, the first experimental wave farm was opened in Portugal, at the Aguçadoura Wave Park.^[2]

Physical concepts[link]

When an object bobs up and down on a ripple in a pond, it experiences an elliptical trajectory.

Motion of a particle in an ocean wave.
A = At deep water. The orbital 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.

Photograph of the water particle orbits under a – progressive and periodic – surface gravity wave in a wave flume. The wave conditions are: mean water depth d = 2.50 ft (0.76 m), wave height H = 0.339 ft (0.103 m), wavelength λ = 6.42 ft (1.96 m), period T = 1.12 s.^[3]

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.^[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[link]

In deep water where the water depth is larger than half the wavelength, the wave energy flux is^{[A 1]}

Failed to parse (Missing texvc executable; please see math/README to configure.): P = \frac{\rho g^2}{64\pi} H_{m0}^2 T \approx \left(0.5 \frac{\text{kW}}{\text{m}^3 \cdot \text{s}} \right) H_{m0}^2\; T,

with P the wave energy flux per unit of wave-crest length, H_m0 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 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

Failed to parse (Missing texvc executable; please see math/README to configure.): 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 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[link]

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]

Failed to parse (Missing texvc executable; please see math/README to configure.): E=\frac{1}{16}\rho g H_{m0}^2,

[A 2][9]

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]

Failed to parse (Missing texvc executable; please see math/README to configure.): P = E\, c_g, \, \

with c_g 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]

Deep water characteristics and opportunities[link]

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 twenty times the water depth, as found quite often near the coast, the group velocity is equal to the phase velocity.^[11]

The regularity of deep-water ocean swells, where "easy-to-predict long-wavelength oscillations" are typically seen, offers the opportunity for the development of energy harvesting technologies that are potentially less subject to physical damage by near-shore cresting waves.^[12]

History[link]

The first known patent to utilize energy from ocean waves dates back to 1799 and was filed in Paris by Girard and his son.^[13] 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.^[14] It appears that this was the first Oscillating Water Column type of wave energy device.^[15] From 1855 to 1973 there were already 340 patents filed in the UK alone.^[13]

Modern scientific pursuit of wave energy was however pioneered by Yoshio Masuda's experiments in the 1940s.^[16] 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.^[17]

A renewed interest in wave energy was motivated by the oil crisis in 1973. A number of university researchers reexamined the potential of generating 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, John Newman and Chiang C. Mei from MIT.

Stephen Salters 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.^[18]

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.^[19]

Modern technology[link]

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,^[20] 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.^[21] 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.^[22] The table contains descriptions of some wave power systems:

Device	Proponent	Country of Origin	Capture Method Category	Location Category	Power take off Category	Year Announced	Notes
ProteanTM Energy Wave Energy Converter	Protean Energy Ltd	Australia	Point-absorber wave-buoy device	Offshore	Direct drive energy conversion	2004	The Protean™ WEC technology is a unique type of wave buoy or point absorber. When deployed, it sits on the ocean surface where the energy density is the highest. The Protean™ WEC technology works on a buoy and tethering system. The buoy converts relative movement between the static ocean floor and the floating buoy into energy. The innovative tension mooring system uses a combination of cables running from an ocean floor mounted clump weight to the WEC buoy on the ocean surface. The Protean™ technology has no exposed turbines or moving parts that are dangerous to marine life and each unit has a small environmental File:Footprint. Protean Energy Wave Energy Converter prototype trial being conducted in the ocean off the coast of Western Australia in 2008.
SurgeDrive	AquaGen Technologies	Australia	Buoy	Offshore	Tension transfer	2007	This technology captures wave energy from point absorber buoyancy units and transfers the pure wave forces out of the water via tension transfer elements. The ‘out-of-water’ Energy Conversion Module then converts the wave forces into electricity or desalinated water. This technology removes the more complex equipment of the system from the water.[23] With less equipment in the water, expensive subsea maintenance is reduced thus reducing the cost of the electricity produced.[24] The system also incorporates a storm survival system whereby the buoyancy units are automatically pulled under the water in a storm.
PowerBuoy	Ocean Power Technologies	US	Buoy	Offshore	Hydroelectric turbine	1997	In the United States, the Pacific Northwest Generating Cooperative is funding construction of a commercial wave-power park at Reedsport, Oregon that will utilize this technology which consists of modular, ocean-going buoys.[25] The rise and fall of the waves moves hydraulic fluid within the buoy and spins a generator. The electricity is transmitted to shore over a submerged transmission line. A 150 kW buoy has a diameter of 36 feet (11 m) and is 145 feet (44 m) tall, with approximately 30 feet of the unit rising above the ocean surface. Using a three-point mooring system, they are designed to be installed one to five miles (8 km) offshore in water 100 to 200 feet (60 m) deep.[26] PB150 PowerBuoy with peak-rated power output of 150 kW.
Pelamis Wave Energy Converter	Pelamis Wave Power	UK (Scottish)	Surface-following attenuator	Offshore	Hydraulic	1998	The Pelamis machine consists of a series of semi-submerged cylindrical sections linked by hinged joints. As waves pass along the length of the machine, the sections move relative to one another. The wave-induced motion of the sections is resisted by hydraulic cylinders which pump high pressure oil through hydraulic motors via smoothing hydraulic accumulators. The hydraulic motors drive electrical generators to produce electricity.[27] Pelamis Wave Power first tested and grid connected a Pelamis machine in 2004 at the European Marine Energy Center.[28] The first of a second generation of machines, the P2 started grid connected tests off Orkney in 2010, the machine is owned by E.ON.[29] Pelamis prototype machine at EMEC, Scotland in 2004.
Wave Dragon	Erik Friis-Madsen	Denmark	Surface-following attenuator	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. Wave Dragon seen from reflector, prototype 1:4½
Anaconda Wave Energy Converter	Checkmate SeaEnergy.[25]	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.[30][31]
AquaBuOY	Finavera Wind Energy, later SSE Renewables Limited	Ireland-Canada-Scotland	Buoy	Offshore	xxx	2003	In 2009 Finavera Renewables surrendered its wave energy permits from FERC.[27] 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.[32][33][34][35]
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.[31][32][33] It works by means of a cable that due to the bobbing effect of the buoy, generates electricity.[36][37][38]
SeaRaser	Alvin Smith (Dartmouth Wave Energy)	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.[39][40]
CETO Wave Power	Carnegie	Australia	Buoy	Offshore	Pump-to-shore	1999	Currently being tested off Fremantle, Western Australia,[35] 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.[41][42] CETO Buoyant Actuator during the installation process
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.[43][44]
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 ccean-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")
Oyster wave energy converter	Aquamarine Power	UK (Scots-Irish)	Oscillating wave surge converter	Nearshore	Pump-to-shore (hydro-electric turbine)	2005	The wave energy device captures the energy found in nearshore waves and converts it into electricity. The systems consists of a hinged mechanical flap connected to the seabed at around 10m depth. Each passing wave moves the flap which drives hydraulic pistons to deliver high pressure water via a pipeline to an onshore turbine which generates electricity. In November 2009, the first full-scale demonstrator Oyster began producing power when it was launched at the European Marine Energy Centre (EMEC) on Orkney.[45]
OE buoy	Ocean Energy	Ireland	Buoy	Offshore	xxx	2006	In September 2009 completed a 2-year sea trial in one quarter scale form. The OE buoy has only one moving part.[46]
Lysekil Project	Uppsala University	Sweden	Buoy	Offshore	Linear generator	2002	Direct driven linear generator placed on the seabed. The generator is connected to a buoy at the surface via a line. The movements of the buoy will drive the translator in the generator. The advantage of this setup is a less complex mechanical system with potentially a smaller need for maintenance. One drawback is a more complicated electrical system.[47][48]
Oceanlinx	Oceanlinx	Australia	Buoy	Offshore	Hydroelectric turbine	1997	An Australian firm is developing this deep-water technology to generate electricity from, ostensibly, easy-to-predict long-wavelength ocean swell oscillations. Oceanlinx recently began installation of a third and final demonstration-scale, grid-connected unit near Port Kembla, near Sydney, Australia, a 2.5 MWe system that is expected to go online in early 2010, when its power will be connected to the Australian grid. The company's much smaller first-generation prototype unit, in operation since 2006, was since disassembled.[12]
SDE Sea Waves Power Plant	SDE Energy Ltd.	Israel	Buoy	Inshore	Hydroelectric turbine	xxx	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.
WaveRoller	AW-Energy Oy	Finland	Surface-following attenuator	Offshore	Pump-to-shore	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.[49][50]
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 have 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 place in Hanstholm which has produced electricity to the grid since September 2009.[51]
Islay LIMPET	Islay LIMPET	Scotland	oscillating water column	Onshore	air turbine	1991	Islay LIMPET is a 500 kW shoreline device uses an oscillating water column to drive air in and out of a pressure chamber through a Wells turbine.[52][53][54] The chamber of the LIMPET is an inclined concrete tube with its opening below the water level. As external wave action causes the water level in the chamber to oscillate, the variation in water level alternately compresses and decompresses the trapped air above, causing air to flow backwards and forwards through a pair of contra-rotating turbines.
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.[55] A first generation full scale prototype for this solution was tested offshore in 2010,[56][57][58] and a second generation full scale prototype was tested offshore during 2011.[59] In 2012 the first units were sold to clients in various countries, for delivery within the year.[60][61] The first reduced scale prototypes were tested offshore during 2007, but the company decided to remain in a "stealth mode" until May 2010[62] and is now recognized as one of the technological innovators in the sector.[63] The company initially considered installing at Wave Hub in 2012,[64] 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.
bioWAVE[TM]	BioPower	Australia	ocean swell waves	depth of 30-45m	capture and conversion process	2011	The bioWAVETM is being developed for utility-scale power production from ocean waves. Its nature-inspired design (biomimicry) combines high conversion efficiency with the ability to avoid excessive wave forces, enabling supply of grid-connected electricity at a competitive price per MWh. The bioWAVETM is designed to operate in ocean swell waves, absorbing energy both at the surface and below. It is a bottom-mounted pitching device, which spans the full depth. The bioWAVETM prototype currently under development will operate at a depth of 30m, while the planned 1MW commercial model will operate where the depth is 40-45m. The energy capture and conversion process for bioWAVETM has been confirmed through peer reviewed scientific research, extensive device testing at model-scale, and by measured results from dry-tests on our full-scale grid-connected O-DriveTM test module. An ocean-based 250kW bioWAVETM demonstration project is currently under development at a grid-connected site with further plans in place to develop a 1MW demonstration, followed by multi-unit wave energy farms. [65] CETO Buoyant Actuator during the installation process

Potential[link]

The realistically usable worldwide resource has been estimated to be greater than 2 TW.^[66][67] 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.

Challenges[link]

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.^[6] Other biophysical impacts (flora and fauna, sediment regimes and water column structure and flows) of scaling up the technology is being studied.^[68] 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.^[69] Waves generate about 2,700 gigawatts of power. Of those 2,700 gigawatts, only about 500 gigawatts can be captured with the current technology.^[21]

Wave farms[link]

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 Oporto in 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^[70] and was officially opened on the 23rd of September 2008, by the Portuguese Minister of Economy.^[71][72] 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.^[73] A second phase of the project planned to increase the installed capacity to 21 MW using a further 25 Pelamis machines^[74] is in doubt following Babcock's financial collapse.

Funding for a 3 MW wave farm in Scotland was announced on 20 February 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.^[75]

Funding has also been announced for the development of a Wave hub off the north coast of Cornwall, England. 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.^[76][77]

The scientists have calculated that wave energy gathered at Wave Hub will be enough to power up to 7,500 households. Savings that the Cornwall wave power generator will bring are significant: about 300,000 tons of carbon dioxide in the next 25 years.^[78]

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.^{[citation needed] [79][80]}

Patents[link]

• 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  — 2004 Wave energy converters utilizing pressure differences (src)

See also[link]

• CETO Wave Power
• Ocean thermal energy conversion
• World energy resources and consumption

Notes[link]

1. ^ The energy flux is Failed to parse (Missing texvc executable; please see math/README to configure.): P = \tfrac{1}{16} \rho g H_{m0}^2 c_g, with Failed to parse (Missing texvc executable; please see math/README to configure.): c_g 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 Failed to parse (Missing texvc executable; please see math/README to configure.): c_g=\tfrac{g}{4\pi}T , 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.
2. ^ For a small-amplitude sinusoidal wave Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle \eta=a\,\cos\, 2\pi\left(\frac{x}{\lambda}-\frac{t}{T}\right) with wave amplitude Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle a,\, the wave energy density per unit horizontal area is Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle E=\frac{1}{2}\rho g a^2, or Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle E=\frac{1}{8}\rho g H^2 using the wave height Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle H\,=\,2\,a\, for sinusoidal waves. In terms of the variance of the surface elevation Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle m_0=\sigma_\eta^2=\overline{(\eta-\bar\eta)^2}=\frac{1}{2}a^2, the energy density is Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle E=\rho g m_0\, . Turning to random waves, the last formulation of the wave energy equation in terms of Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle m_0\, is also valid (Holthuijsen, 2007, p. 40), due to Parseval's theorem. Further, the significant wave height is defined as Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle H_{m0}=4\sqrt{m_0} , leading to the factor ¹⁄₁₆ in the wave energy density per unit horizontal area.
   
3. ^ 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.

References[link]

Further reading[link]

• 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.

External links[link]

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. http://www.nytimes.com/2008/09/23/business/23tidal.html?em. Retrieved 2008-10-09. 
• "Wave Power: The Coming Wave" from the Economist, June 5, 2008
• "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"

v t e Ocean energy Wave power Australia New Zealand Tidal power New Zealand Annapolis Royal Generating Station Other Marine current power Offshore construction Ocean thermal energy conversion Pelamis wave energy converter SDE Sea Waves Power Plant Wind power (offshore) Wave farm Portals: Energy Renewable energy Sustainable development

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Lee Ritenour
Ritenour at the Stockholm Jazz Festival in 2009.
Background information
Birth name	Lee Mack Ritenour
Also known as	Captain Fingers
Born	(1952-01-11) January 11, 1952 (age 60) Los Angeles, California, United States
Genres	Jazz, jazz-funk, jazz fusion, smooth jazz
Occupations	Musician, composer, producer
Instruments	Guitar, SynthAxe
Years active	1975–present
Labels	Epic, Elektra, GRP, PolyGram, Decca, Peak, Concord
Website	leeritenour.com
Notable instruments
Gibson ES-335 Gibson L-5

Lee Mack Ritenour (born January 11, 1952) is an American jazz guitarist who has recorded over 42 albums, appeared on over 3000 sessions, and has charted over 30 instrumental and vocal contemporary jazz hits since 1976.^[1] One of his most popular songs was the smash hit, “Is It You” in 1981. Ritenour is considered to be a pioneer in the Contemporary Jazz and jazz-funk genres of music.^{[citation needed]}. Guitar Player Magazine awarded him with a Lifetime Achievement Award for the year 2010. His highly acclaimed and popular 2010 hit album Lee Ritenour's 6 String Theory had numerous awards in 2011 including, Guitar Album of the Year – Guitar International Magazine. UK’s Guitarist Magazine: The #1 Best 50 Guitar Albums of 2010. JAZZIZ Magazine Publisher’s Album of the Year. Top Albums of 2010 from Canada’s “The Guardian”. Lee was awarded at the 2011 Echo Awards in Germany (the German Grammy awards) for Best International Instrumentalist (Guitar) in conjunction with the album, 6 String Theory)

Biography[link]

Ritenour was born January 11, 1952 in Los Angeles, California. He played his first session when he was 16 with the Mamas & the Papas and given the moniker, "Captain Fingers", because of his manual dexterity on the guitar. Ritenour was a sought-after session guitarist by the mid-1970s, and won Guitar Player Magazine's Best Studio Guitarist twice in the 1970s. He is noted for playing his red Gibson ES-335 and his Gibson L5 guitars.

Ritenour in 2007.

One of his most notable influences is the pioneering jazz guitarist Wes Montgomery among others like Joe Pass, Kenny Burrell and John McLaughlin. His prolific career includes a Grammy Award for the collaborative work Harlequin (1985), and 19 other Grammy nominations. Ritenour also holds the distinction of having two of the promotional videos for his songs "Is It You" and "Mr. Briefcase" being played during MTV's first day. Ritenour has been at the top of many guitar polls throughout the world.

Throughout his career, Ritenour has experimented with different styles of music. A true fusionist, he has often incorporated elements of funk, pop, rock, blues, Brazilian and most recently with Amparo (2008), classical music with jazz. In the early 1980s, Ritenour was given his own Ibanez signature model guitar, the LR-10. The LR-10 was produced from 1981 to 1987. It can be heard exclusively on his album Rit. Currently, Ritenour plays the Gibsons that he first played in the 1970s (the ES-335 and L5), and now also plays his signature Lee Ritenour Model archtop guitar made by Gibson.

Style[link]

Ritenour's solo career began in 1975 with the recording of his album First Course. Released in 1976, the album gave a strong representation of the mid-1970s L.A. Jazz/Funk sound. Critics did, however, complain that his first album was "lightweight." So Lee countered this with his strongly crossover-based follow up, Captain Fingers. This was followed by two more crossover efforts—The Captain's Journey (1978) and Feel The Night (1979). On these albums, Ritenour primarily used something of a rich, yet rock-oriented distorted guitar sound, coming from his Gibson ES-335 guitar. In other instances on these albums, clean sounds were heard coming from his Gibson L5 and classical acoustic guitars (he played his classical acoustic guitars almost exclusively on his album Rio in 1979). In the 1970s, Ritenour would often use effects like wah-wah, phasers, chorus, and flangers on his electric instruments. Also, during the late 1970s, Ritenour can be heard using the 360 Systems guitar synthesizer (he is pictured sitting in front of it on the back cover of his Captain Fingers album). He can be heard using the synthesizer on the track Captain Fingers (from the album with the same title), and can also be heard playing solo with the synthesizer on the song "What Do You Want?" from The Captain's Journey.

In 1979, Ritenour "was brought in to beef up one of Pink Floyd's The Wall's heaviest rock numbers, "Run Like Hell"."^[2] He also played "uncredited rhythm guitar" on "One Of My Turns".^[3][4]

As the 1980s began, Ritenour began to add stronger elements of pop to his music, beginning with Rit in 1981. For this, he kept with his distorted sound, now using his Ibanez LR-10 signature model guitar. One of tracks from "Rit", entitled, "Is It You" featuring vocals from Eric Tagg became a hit reaching number fifteen on the pop chart and number twenty-seven on the soul chart.^[5] He continued with the pop-oriented music for two albums after Rit (Rit/2 in 1982 and Banded Together in 1984), while releasing a slick, yet more crossover-styled, Direct-Disk instrumental album in 1983 called On The Line. He also provided rhythm guitar on Tom Browne's hit, Funkin' for Jamaica.

In 1985, he recorded his first album for GRP with Dave Grusin, entitled Harlequin. It featured Lee primarily on his classical acoustic guitar and also featured Brazilian singer/songwriter Ivan Lins. Up to this point, this album along with Rio arguably gave the strongest representation of Lee's Brazilian influences.

The following year, 1986, Ritenour released the album Earth Run, which featured him using the then-newly designed SynthAxe guitar. He used nine different guitars on the album, most notably the SynthAxe, his Valley Arts guitar, and his Gibson Chet Atkins acoustic. The album also featured long-time collaborator Phil Perry for the first time, on the track "If I'm Dreaming, Don't Wake Me" — a song also featuring David Foster and Maurice White. He also produced songs and played guitar on Deniece Williams's LP Hot on the Trail during that same year.

Ritenour continued in a direction strongly featuring other artists in 1987, with Portrait. The album itself has something of a strong smooth-jazz sound, and Ritenour can be heard here playing with The Yellowjackets, Djavan, and Kenny G.^{[citation needed]}!

In 1988, his smooth jazz-influenced Brazilian music came to the forefront with Festival — another album strongly featuring his work on nylon-string acoustic guitars. The following album, Color Rit, continued with a similar mood. He did however, change direction completely again with his straight-ahead jazz album Stolen Moments. Sounding similar to Wes Montgomery, Ritenour played alongside long-time collaborator, saxophonist Ernie Watts, pianist Alan Broadbent, bassist John Patitucci (playing only acoustic) and drummer Harvey Mason. Continuing in a Wes Montgomery mood, Ritenour paid tribute to the man himself in 1992, with his album Wes Bound. The album featured a number of covers of Montgomery compositions, as well as some seemingly tributary pieces from Ritenour himself.

Also seen in this decade was a 1994 collaboration album with guitarist Larry Carlton called Larry & Lee.

In 1991 Lee Ritenour, together with keyboard player Bob James, formed the Grammy-nominated contemporary jazz group Fourplay. Lee left the hugely successful group in 1998 to continue with his own solo works. He was replaced by Larry Carlton.

2002 saw the release of his album, Rit's House.

In February 2004, Ritenour completed a project looking back on his career involving musicians he has worked with throughout his career called Overtime. Overtime was recorded live in a studio in front of a small audience. It was released in early 2005, and is currently available as a singular audio CD, double-DVD set or singular HD DVD. Some of the musicians featured include Dave Grusin, Patrice Rushen, Harvey Mason, Alex Acuna, Taylor Dayne, Nathan East, Chris Botti, Anthony Jackson, Melvin Lee Davis, and Ernie Watts, amongst many others.

His album entitled Smoke n' Mirrors was released in late August 2006. His son Wesley makes his debut appearance as a drummer on the album at the age of 13. This album contains Ritenour's version of Bill Withers' 1978 hit "Lovely Day".

Ritenour joined the 10th annual Independent Music Awards judging panel to assist independent musicians' careers.^{[6] [7] [8]} He was also a judge for the 8th and 9th Independent Music Awards.^[9]

In June 2010, in order to celebrate his fifty years as a guitarist, Lee Ritenour released the album 6 String Theory (in reference to 6 musical areas covered by the use of guitar).^[10] The album featured famous guitarists such as Steve Lukather, Neal Schon, John Scofield, Slash, Pat Martino, Mike Stern, George Benson and B.B.King, but also younger players such as Andy McKee, Joe Robinson and Guthrie Govan. Ritenour, YamahaCorporation, The Berklee College of Music, Concord Records, Monster Cable, and D'Addario Strings collaborated to create the 2010 Yamaha 6 String Theory Guitar Competition. The winner of that international competition, that included guitarists from over 45 countries, was 16-year-old Canadian classical guitarist Shon Boublil. The competition in 2011 is continuing.

Discography[link]

As sideman[link]

This section requires expansion.

With Brass Fever

• Brass Fever (Impulse!, 1975)
• Time Is Running Out (Impulse!, 1976)

With Dizzy Gillespie

• Free Ride (Pablo, 1977) composed and arranged by Lalo Schifrin

With Alphonse Mouzon

• Mind Transplant (Blue Note, 1974)
• The Man Incognito (Blue Note, 1975)

With Lalo Schifrin

• Rollercoaster (soundtrack) (MCA, 1977)

References[link]

External links[link]

• Lee Ritenour official site
• Lee Ritenour
• Lee Ritenour Guitar Licks