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{{short description|Transport of energy by wind waves, and the capture of that energy to do useful work}}
{{about|transport and capture of energy in ocean waves|other aspects of waves in the ocean|Wind wave|other uses of wave or waves|Wave (disambiguation)}}
{{Use mdy dates|date=August 2019}}{{Renewable energy sources}}
{{Sustainable energy}}'''Wave power''' is the capture of energy of [[wind wave]]s to do useful [[mechanical work|work]] – for example, [[electricity generation]], [[desalination]], or [[pump]]ing water. A machine that exploits wave [[power (physics)|power]] is a '''wave energy converter''' ('''WEC''').

Waves are generated primarily by wind passing over the sea's surface and also by tidal forces, temperature variations, and other factors. As long as the waves propagate slower than the wind speed just above, energy is transferred from the wind to the waves. Air pressure differences between the windward and leeward sides of a wave [[crest (physics)|crest]] and surface friction from the wind cause [[shear stress]] and wave growth.<ref name="Phillips">{{cite book |last=Phillips |first=O.M. |title=The dynamics of the upper ocean |publisher=Cambridge University Press |year=1977 |isbn=978-0-521-29801-8 |edition=2nd |author-link=Owen Martin Phillips}}</ref>

Wave power as a descriptive term is different from [[tidal power]], which seeks to primarily capture the energy of the current caused by the gravitational pull of the Sun and Moon. However, wave power and tidal power are not fundamentally distinct and have significant cross-over in technology and implementation.  Other forces can create [[ocean currents|currents]], including [[wave breaking|breaking waves]], [[wind]], the [[Coriolis effect]], [[cabbeling]], and [[temperature]] and [[salinity]] differences.

As of 2023, wave power is not widely employed for commercial applications, after a long series of trial projects. Attempts to use this energy began in 1890 or earlier,<ref>{{cite web|url=http://www.outsidelands.org/wave-tidal3.php|title=Wave and Tidal Energy Experiments in San Francisco and Santa Cruz|author=Christine Miller|access-date=August 16, 2008|date=August 2004|archive-url=https://web.archive.org/web/20081002203245/http://www.outsidelands.org/wave-tidal3.php|archive-date=October 2, 2008|url-status=live}}</ref> mainly due to its high [[power density]].  Just below the ocean's water surface the wave energy flow, in time-average, is typically five times denser than the wind energy flow 20 m above the sea surface, and 10 to 30 times denser than the solar energy flow.<ref name="Falnes1999">{{cite web |date=June 1, 1999 |title=Wave energy and its utilization |url=https://www.slideshare.net/JrgenHalsTodalshaug/wave-energy-and-its-utilization-257609652 |website=Slideshare |access-date=April 28, 2023}}</ref>

In 2000 the world's first commercial wave power device, the [[Islay LIMPET]] was installed on the coast of [[Islay]] in Scotland and connected to the [[National Grid (Great Britain)|UK national grid]].<ref>{{Cite web | url=https://www.edie.net/news/0/Worlds-first-commercial-wave-power-station-activated-in-Scotland/3492/ | title=World's first commercial wave power station activated in Scotland | access-date=June 5, 2018 | archive-url=https://web.archive.org/web/20180805172514/https://www.edie.net/news/0/Worlds-first-commercial-wave-power-station-activated-in-Scotland/3492/ | archive-date=August 5, 2018 | url-status=live }}</ref> In 2008, the first experimental multi-generator [[wave farm]] was opened in Portugal at the [[Aguçadoura Wave Farm]].<ref>Joao Lima. [https://www.bloomberg.com/apps/news?pid=21070001&sid=aSsaOB9qbiKE Babcock, EDP and Efacec to Collaborate on Wave Energy projects] {{Webarchive|url=https://web.archive.org/web/20150924065943/http://www.bloomberg.com/apps/news?pid=21070001&sid=aSsaOB9qbiKE |date=September 24, 2015 }} ''Bloomberg'', September 23, 2008.</ref> Both projects have since ended. For a list of other wave power stations see [[List of wave power stations]].

Wave energy converters can be classified based on their working principle as either:<ref>{{Cite journal |last=Falcão |first=António F. de O. |date=2010-04-01 |title=Wave energy utilization: A review of the technologies |url=https://www.sciencedirect.com/science/article/pii/S1364032109002652 |journal=Renewable and Sustainable Energy Reviews |language=en |volume=14 |issue=3 |pages=899–918 |doi=10.1016/j.rser.2009.11.003 |bibcode=2010RSERv..14..899F |issn=1364-0321}}</ref><ref>{{Citation |last1=Madan |first1=D. |date=2020-10-21 |url=http://dx.doi.org/10.1007/978-981-15-4739-3_91 |pages=1057–1072 |place=Singapore |publisher=Springer Singapore |isbn=978-981-15-4738-6 |access-date=2022-06-02 |last2=Rathnakumar |first2=P. |last3=Marichamy |first3=S. |last4=Ganesan |first4=P. |last5=Vinothbabu |first5=K. |last6=Stalin |first6=B.|title=Advances in Industrial Automation and Smart Manufacturing |chapter=A Technological Assessment of the Ocean Wave Energy Converters |series=Lecture Notes in Mechanical Engineering |doi=10.1007/978-981-15-4739-3_91 |s2cid=226322561 }}</ref>

* oscillating water columns (with air turbine)
* oscillating bodies (with hydroelectric motor, hydraulic turbine, linear electrical generator)
* overtopping devices (with low-head hydraulic turbine)
{{Toclimit}}

== History ==

The first known patent to extract energy from ocean waves was in 1799, filed in Paris by [[Pierre-Simon Girard]] and his son.<ref name="cle2002">{{cite journal |author=Clément, A. |year=2002 |title=Wave energy in Europe: current status and perspectives |journal=Renewable and Sustainable Energy Reviews |volume=6 |issue=5 |pages=405–431 |doi=10.1016/S1364-0321(02)00009-6|bibcode=2002RSERv...6..405C |display-authors=etal}}</ref> An early device was constructed around 1910 by Bochaux-Praceique to power his house in [[Royan]], France.<ref>{{cite web |url=http://www.mech.ed.ac.uk/research/wavepower/0-Archive/EWPP%20archive/1976%20Leishman%20and%20Scobie%20NEL.pdf |title=The Development of Wave Power|access-date=December 18, 2009|archive-url=https://web.archive.org/web/20110727162538/http://www.mech.ed.ac.uk/research/wavepower/0-Archive/EWPP%20archive/1976%20Leishman%20and%20Scobie%20NEL.pdf |archive-date=July 27, 2011}}</ref> It appears that this was the first oscillating water-column type of wave-energy device.<ref name="morris2007">{{cite journal |last1=Morris-Thomas |first1=Michael T. |year=2007 |title=An Investigation Into the Hydrodynamic Efficiency of an Oscillating Water Column |journal=Journal of Offshore Mechanics and Arctic Engineering |volume=129 |issue=4 |pages=273–278 |doi=10.1115/1.2426992 |last2=Irvin |first2=Rohan J. |last3=Thiagarajan |first3=Krish P. |display-authors=etal}}</ref> From 1855 to 1973 there were 340 patents filed in the [[UK]] alone.<ref name="cle2002" />

Modern pursuit of wave energy was pioneered by [[Yoshio Masuda]]'s 1940s experiments.<ref>{{cite web |url=http://www.jamstec.go.jp/jamstec/MTD/Whale/ |title=Wave Energy Research and Development at JAMSTEC|access-date=December 18, 2009 |archive-url = https://web.archive.org/web/20080701162330/http://www.jamstec.go.jp/jamstec/MTD/Whale/ |archive-date = July 1, 2008}}</ref> He tested various concepts, constructing hundreds of 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 Masuda proposed in the 1950s.<ref name="ey2006">{{cite conference |author1=Farley, F. J. M. |author2=Rainey, R. C. T. |name-list-style=amp |year=2006 |title=Radical design options for wave-profiling wave energy converters |book-title=International Workshop on Water Waves and Floating Bodies |location=Loughborough |url=http://www.iwwwfb.org/Abstracts/iwwwfb21/iwwwfb21_15.pdf |access-date=December 18, 2009 |url-status=live |archive-url=https://web.archive.org/web/20110726200118/http://www.iwwwfb.org/Abstracts/iwwwfb21/iwwwfb21_15.pdf |archive-date=July 26, 2011}}</ref>

The [[1973 oil crisis|oil crisis in 1973]] renewed interest in wave energy. Substantial wave-energy development programmes were launched by governments in several countries, in particular in the UK, Norway and Sweden.<ref name="Falnes1999" />  Researchers re-examined waves' potential to extract energy, notably [[Stephen Salter]], [[Johannes Falnes]], [[Kjell Budal]], [[Michael E. McCormick]], [[David Evans (mathematician)|David Evans]], Michael French, [[John Nicholas Newman|Nick Newman]], and [[C. C. Mei]].

Salter's [[1974 in science|1974 invention]] became known as [[Salter's duck]] or ''nodding duck'', officially the Edinburgh Duck. In small-scale tests, the Duck's curved [[Cam (mechanism)|cam]]-like body can stop 90% of wave motion and can convert 90% of that to electricity, giving 81% efficiency.<ref>{{cite web |url=http://www.mech.ed.ac.uk/research/wavepower/EWPP%20archive/duck%20efficiency%20&%20survival%20notes.pdf |title=Edinburgh Wave Energy Project|publisher=[[University of Edinburgh]]|access-date=October 22, 2008|archive-url=https://web.archive.org/web/20061001110556/http://www.mech.ed.ac.uk/research/wavepower/EWPP%20archive/duck%20efficiency%20%26%20survival%20notes.pdf|archive-date=October 1, 2006|url-status=dead}}</ref>  In the 1980s, several other first-generation prototypes were tested, but as oil prices ebbed, wave-energy funding shrank. [[Climate change]] later reenergized the field.<ref name="falnes2007">{{cite journal |author=Falnes, J. |year=2007 |title=A review of wave-energy extraction |journal=Marine Structures |volume=20 |issue=4 |pages=185–201 |doi=10.1016/j.marstruc.2007.09.001 |bibcode=2007MaStr..20..185F }}</ref><ref name="Falnes1999" />

The world's first wave energy test facility was established in [[Orkney]], Scotland in 2003 to kick-start the development of a wave and tidal energy industry. The [[European Marine Energy Centre|European Marine Energy Centre(EMEC)]] has supported the deployment of more wave and tidal energy devices than any other single site.<ref>{{cite web|url=https://www.emec.org.uk/about-us/emec-history/ |title=Our history |access-date=April 28, 2023}}</ref>  Subsequent to its establishment test facilities occurred also in many other countries around the world, providing services and infrastructure for device testing.<ref name="Aderinto2019">{{cite journal |author=Aderinto, Tunde |author2=Li, Hua |year=2019 |title=Review on power performance and efficiency of wave energy converters |journal=Energies |volume=12 |issue=22 |page=4329 |doi=10.3390/en12224329 |doi-access=free }}</ref>

The £10 million Saltire prize challenge was to be awarded to the first to be able to generate 100 GWh from wave power over a continuous two-year period by 2017 (about 5.7 MW average).<ref>{{Cite web |date=September 7, 2012 |title=Ocean Energy Teams Compete for $16 Million Scotland Prize |url=https://www.nationalgeographic.com/pages/article/120907-scotland-wave-energy-saltire-prize |archive-url=https://web.archive.org/web/20220911165125/https://www.nationalgeographic.com/pages/article/120907-scotland-wave-energy-saltire-prize |url-status=dead |archive-date=September 11, 2022 |website=National geographic}}</ref>  The prize was never awarded.  A 2017 study by [[Strathclyde University]] and [[Imperial College]] focused on the failure to develop "market ready" wave energy devices – despite a UK government investment of over £200 million over 15 years.<ref>{{cite news |author=Scott Macnab |date=November 2, 2017 |title=Government's £200m wave energy plan undermined by failures |newspaper=The Scotsman |url=https://www.scotsman.com/news/environment/government-s-200m-wave-energy-plan-undermined-by-failures-1-4602617 |url-status=live |access-date=December 5, 2017 |archive-url=https://web.archive.org/web/20171205194623/https://www.scotsman.com/news/environment/government-s-200m-wave-energy-plan-undermined-by-failures-1-4602617 |archive-date=December 5, 2017}}</ref>

Public bodies have continued and in many countries stepped up the research and development funding for wave energy during the 2010s.  This includes both EU, US and UK where the annual allocation has typically been in the range 5-50 million USD.<ref>[http://www.renewableenergyworld.com/articles/2007/06/wave-energy-bill-approved-by-u-s-house-science-committee-48984.html Wave Energy Bill Approved by U.S. House Science Committee] {{Webarchive|url=https://web.archive.org/web/20180525063553/https://www.renewableenergyworld.com/articles/2007/06/wave-energy-bill-approved-by-u-s-house-science-committee-48984.html |date=May 25, 2018 }} June 18, 2007</ref><ref>[http://uaelp.pennnet.com/Articles/Article_Display.cfm?Section=ONART&PUBLICATION_ID=22&ARTICLE_ID=341078&C=ENVIR&dcmp=rss  DOE announces first marine renewable energy grants] {{Webarchive|url=https://web.archive.org/web/20040727181853/http://uaelp.pennnet.com/Articles/Article_Display.cfm?Section=OnArt|date=2004-07-27}} September 30, 2008</ref><ref>{{cite web |title=Ocean energy|url=https://research-and-innovation.ec.europa.eu/research-area/energy/ocean-energy_en |access-date=28 April 2023}}</ref><ref>{{cite web |title=Projects to unlock the potential of marine wave energy |date=March 24, 2021 |url=https://www.ukri.org/news/projects-to-unlock-the-potential-of-marine-wave-energy/ |access-date=28 April 2023}}</ref><ref>{{cite web |title=Wave energy Scotland |url=https://www.waveenergyscotland.co.uk/ |access-date=28 April 2023}}</ref>  Combined with private funding, this has led to a large number of ongoing wave energy projects (see [[List of wave power projects]]).

== Physical concepts ==
{{Main|Airy wave theory}}
Like most fluid motion, the interaction between ocean waves and energy converters is a high-order nonlinear phenomenon. It is described using the [[Incompressible navier-stokes equations|incompressible Navier-Stokes equations]]
<math display="block">\begin{align}
\frac{\partial\vec{u}}{\partial t}+(\vec{u}\cdot\vec{\nabla})\vec{u}&=\nu\Delta\vec{u}+\frac{\vec{F_\text{ext}}-\vec{\nabla}p}{\rho} \\
\vec{\nabla}\cdot\vec{u}&=0
\end{align}
</math>where <math display="inline">\vec u(t, x, y, z)</math> is the fluid velocity, <math display="inline">p

</math> is the [[pressure]], <math display="inline">\rho

</math> the [[density]], <math display="inline">\nu

</math> the [[viscosity]], and <math display="inline">\vec{F_\text{ext}}

</math> the net external force on each fluid particle (typically [[gravity]]). Under typical conditions, however, the movement of waves is described by [[Airy wave theory]], which posits that

* fluid motion is roughly [[irrotational]],
* pressure is approximately constant at the water surface, and
* the [[seabed]] depth is approximately constant.

In situations relevant for energy harvesting from ocean waves these assumptions are usually valid.

=== Airy equations ===
The first condition implies that the motion can be described by a [[velocity potential]] <math display="inline"> \phi(t,x,y,z)</math>:<ref>{{Cite book |title=Numerical modelling of wave energy converters : state-of-the-art techniques for single devices and arrays |date=2016 |first=Matt |last=Folley |isbn=978-0-12-803211-4 |publisher=Academic Press |location=London, UK |oclc=952708484}}</ref><math display="block"> {\vec{\nabla}\times\vec{u}=\vec{0}}\Leftrightarrow{\vec{u}=\vec{\nabla}\phi}\text{,}</math>which must satisfy the [[Laplace's equation|Laplace equation]],<math display="block"> \nabla^2\phi=0\text{.}</math>In an ideal flow, the viscosity is negligible and the only external force acting on the fluid is the earth gravity <math> \vec{F_\text{ext}}=(0,0,-\rho g)</math>. In those circumstances, the [[Navier–Stokes equations|Navier-Stokes equations]] reduces to <math display="block">{\partial\vec\nabla\phi \over\partial t}+{1 \over2}\vec \nabla\bigl(\vec\nabla\phi\bigr)^2=
-{1 \over \rho}\cdot\vec\nabla p +{1 \over \rho}\vec\nabla\bigl(\rho gz\bigr),

</math>which integrates (spatially) to the [[Bernoulli Equation|Bernoulli conservation law]]:<math display="block">{\partial\phi \over\partial t}+{1 \over2}\bigl(\vec\nabla\phi\bigr)^2
+{1 \over \rho} p + gz=(\text{const})\text{.}

</math>

=== Linear potential flow theory ===
[[File:Wave motion-i18n-mod.svg|thumb|Motion of a particle in an ocean wave.<br />
'''A''' = At deep water. The [[circular motion]] magnitude of fluid particles decreases exponentially with increasing depth below the surface.<br />
'''B''' = At shallow water (ocean floor is now at B). The elliptical movement of a fluid particle flattens with decreasing depth.<br />
'''1''' = Propagation direction. <br />
'''2''' = Wave crest.<br />
'''3''' = Wave trough.]]
When considering small amplitude waves and motions, the quadratic term <math display="inline">\left(\vec{\nabla}\phi\right)^2

</math> can be neglected, giving the linear Bernoulli equation,<math display="block">{\partial\phi \over\partial t}+{1 \over \rho} p + gz=(\text{const})\text{.}

</math>and third Airy assumptions then imply<math display="block">\begin{align}
&{\partial^2\phi \over\partial t^2} + g{\partial\phi \over\partial z}=0\quad\quad\quad(\text{surface}) \\
&{\partial\phi \over\partial z}=0\phantom{{\partial^2\phi \over\partial t^2}+{}}\,\,\quad\quad\quad(\text{seabed})
\end{align}
</math>These constraints entirely determine [[sinusoidal]] wave solutions of the form <math display="block">\phi=A(z)\sin{\!(kx-\omega t)}\text{,}

</math>where <math>k

</math> determines the [[wavenumber]] of the solution and <math>A(z)

</math> and <math>\omega

</math> are determined by the boundary constraints (and <math>k

</math>). Specifically,<math display="block">\begin{align}
&A(z)={gH \over 2\omega}{\cosh(k(z+h)) \over \cosh(kh)} \\
&\omega=gk\tanh(kh)\text{.}
\end{align}
</math>The surface elevation <math>\eta

</math> can then be simply derived as <math display="block">\eta=-{1 \over g}{\partial \phi \over \partial t}={H \over 2}\cos(kx-\omega t)\text{:}
</math>a plane wave progressing along the x-axis direction.

==== Consequences ====
[[Ocean surface wave#Science of waves|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 [[microseism]]s.<ref name="Phillips" /> Pressure fluctuations at greater depth are too small to be interesting for wave power conversion.

The behavior of Airy waves offers two interesting regimes: water deeper than half the wavelength, as is common in the sea and ocean, and shallow water, with wavelengths larger than about twenty times the water depth. Deep waves are [[Dispersion (water waves)|dispersionful]]: Waves of long wavelengths propagate faster and tend to outpace those with shorter wavelengths. Deep-water group velocity is half the [[phase velocity]]. Shallow water waves are dispersionless: group velocity is equal to phase velocity, and [[wavetrain]]s propagate undisturbed.<ref name="Phillips" /><ref name="Dean_Dalrymple">{{cite book |author1=R. G. Dean |title=Water wave mechanics for engineers and scientists |author2=R. A. Dalrymple |publisher=World Scientific, Singapore |year=1991 |isbn=978-981-02-0420-4 |series=Advanced Series on Ocean Engineering |volume=2 |name-list-style=amp}} See page 64–65.</ref><ref name="Goda" />

The following table summarizes the behavior of waves in the various regimes:
{| class="wikitable collapsible collapsed" style="width:65%; text-align:center;"

|+ Airy gravity waves on the surface of deep water, shallow water, or intermediate depth<!-- Data is not present -->
|-
! style="width:10%;" | quantity
! style="width:7%;" | symbol
! style="width:7%;" | units
! style="width:15%;" | deep water<br>(''h'' > {{1/2}} ''λ'')
! style="width:25%;" | shallow water<br>(''h'' < 0.05 ''λ'')
! style="width:25%;" | intermediate depth<br>(all ''λ'' and ''h'')
|- style="height:120px"
! [[phase velocity]]
| <math> c_p=\frac{\lambda}{T}=\frac{\omega}{k}</math>
|| m / s
|| <math>\frac{g}{2\pi} T</math>
|| <math>\sqrt{g h}</math>
|| <math>\sqrt{\frac{g\lambda}{2\pi}\tanh\left(\frac{2\pi h}{\lambda}\right)}</math>
|- style="height:120px"
! [[group velocity]]{{efn|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''.}}
| <math> c_g= c_p^2 \frac{\partial\left(\lambda/c_p\right)}{\partial\lambda}=\frac{\partial\omega}{\partial k}</math>
|| m / s
|| <math>\frac{g}{4\pi} T</math>
|| <math>\sqrt{g h}</math>
|| <math>\frac{1}{2} c_p \left( 1 + \frac{4\pi h}{\lambda}\frac{1}{\sinh\left( \frac{4\pi h}{\lambda}\right)} \right)</math>
|- style="height:120px"
! ratio
| <math> \frac{c_g}{c_p}</math>
|| –
|| <math>\frac{1}{2}</math>
|| <math> 1</math>
|| <math>\frac{1}{2} \left( 1 + \frac{4\pi h}{\lambda}\frac{1}{\sinh\left( \frac{4\pi h}{\lambda}\right)} \right)</math>
|- style="height:120px"
! wavelength 
| <math>\lambda</math>
|| m
|| <math>\frac{g}{2\pi} T^2</math>
|| <math>T \sqrt{g h}</math>
|| for given period ''T'', the solution of:<br>&nbsp;<br><math> \left(\frac{2\pi}{T}\right)^2=\frac{2\pi g}{\lambda}\tanh\left(\frac{2\pi h}{\lambda}\right)</math>
|-
! colspan="6" | general
|- style="height:80px"
! wave energy density
| <math> E</math>
| J&nbsp;/&nbsp;m<sup>2</sup>
| colspan="3" | <math>\frac{1}{16} \rho g H_{m0}^2</math>
|- style="height:80px"
! wave energy [[flux]]
| <math> P</math>
| W&nbsp;/&nbsp;m
| colspan="3" | <math> E\;c_g</math>
|- style="height:80px"
! angular [[frequency]]
| <math> \omega</math>
| [[radian|rad]]&nbsp;/&nbsp;s
| colspan="3" | <math>\frac{2\pi}{T}</math>
|- style="height:80px"
! [[wavenumber]]
| <math> k</math>
| rad&nbsp;/&nbsp;m
| colspan="3" | <math>\frac{2\pi}{\lambda}</math>
|}

=== Wave power formula ===

[[File:Orbital wave motion-Wiegel Johnson ICCE 1950 Fig 6.png|thumb|Photograph of the elliptical trajectories of water particles under a – progressive and periodic – [[surface gravity wave]] in a [[wave flume]]. The wave conditions are: mean water depth ''d''&nbsp;=&nbsp;{{convert|2.50|ft|m|abbr=on}}, [[wave height]] ''H''&nbsp;=&nbsp;{{convert|0.339|ft|m|abbr=on}}, wavelength λ&nbsp;=&nbsp;{{convert|6.42|ft|m|abbr=on}}, [[period (physics)|period]] ''T''&nbsp;=&nbsp;1.12&nbsp;s.<ref>Figure 6 from: {{cite book |last1=Wiegel |first1=R.L. |title=Proceedings 1st International Conference on Coastal Engineering |url=https://repository.tudelft.nl/record/uuid:5c12e11b-a0fc-4245-a23f-4bbc75571c33 |pages=5–21 |date=October 1950 |chapter=Elements of wave theory |location=Long Beach, California |publisher=[[American Society of Civil Engineers|ASCE]] |last2=Johnson |first2=J.W. |editor-last=Johnson |editor-first=J.W. |series=Coastal Engineering Proceedings |volume=1 |doi=10.9753/icce.v1.2 |doi-access=free }}</ref>]]
In deep water where the water depth is larger than half the [[wavelength]], the wave [[energy flux]] is{{efn|The energy flux is <math>P = \tfrac{1}{16} \rho g H_{m0}^2 c_g,</math> with <math>c_g</math> the group velocity,<ref>{{Cite book
| publisher = McGraw-Hill Professional
| isbn = 978-0-07-134402-9
| last = Herbich
| first = John B.
| title = Handbook of coastal engineering
| year = 2000
| no-pp = yes
|page=A.117, Eq. (12)
}}</ref> The group velocity is <math>c_g=\tfrac{g}{4\pi}T</math>, 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 "''[[#Energy and energy flux|Wave energy and wave energy flux]]''" below.}}

:<math>
  P = \frac{\rho g^2}{64\pi} H_{m0}^2 T_e
    \approx \left(0.5 \frac{\text{kW}}{\text{m}^3 \cdot \text{s}} \right) H_{m0}^2\; T_e,
</math>

with ''P'' the wave energy flux per unit of wave-crest length, ''H''<sub>''m0''</sub> the [[significant wave height]], ''T''<sub>''e''</sub> the wave energy [[period (physics)|period]], ''ρ'' the water [[density]] and ''g'' the [[Earth's gravity|acceleration by gravity]]. The above formula states that wave power is proportional to the wave energy period and to the [[Square (algebra)|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.<ref>{{cite book |title=Waves in ocean engineering |year=2001 |publisher=Elsevier |location=Oxford |isbn=978-0080435664 |pages=35–36 |author=Tucker, M.J. |edition=1st |author2=Pitt, E.G. |editor=Bhattacharyya, R. |editor2=McCormick, M.E. |chapter=2}}</ref><ref>{{cite web |title=Wave Power |publisher=[[University of Strathclyde]] |url=http://www.esru.strath.ac.uk/EandE/Web_sites/01-02/RE_info/wave%20power.htm |access-date=November 2, 2008 |archive-url=https://web.archive.org/web/20081226032455/http://www.esru.strath.ac.uk/EandE/Web_sites/01-02/RE_info/wave%20power.htm |archive-date=December 26, 2008 |url-status=live}}</ref><ref name="ocs">{{cite web |url=http://www.ocsenergy.anl.gov/documents/docs/OCS_EIS_WhitePaper_Wave.pdf|title=Wave Energy Potential on the U.S. Outer Continental Shelf |publisher=[[United States Department of the Interior]] |access-date=October 17, 2008 |archive-url=https://web.archive.org/web/20090711052514/http://ocsenergy.anl.gov/documents/docs/OCS_EIS_WhitePaper_Wave.pdf |archive-date=July 11, 2009}}</ref><ref>[http://www.scotland.gov.uk/Publications/2006/04/24110728/10 Academic Study: Matching Renewable Electricity Generation with Demand: Full Report] {{Webarchive|url=https://web.archive.org/web/20111114015028/http://www.scotland.gov.uk/Publications/2006/04/24110728/10 |date=November 14, 2011 }}. Scotland.gov.uk.</ref>

For 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 s. Solving for power produces

:<math>
  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}},
</math>

or 36 kilowatts of power potential per meter of wave crest.

In major storms, the largest offshore sea states have significant wave height of about 15 meters and energy period of about 15 seconds. According to the above formula, such waves carry about 1.7&nbsp;MW of power across each meter of wavefront.

An effective wave power device captures a significant portion of the wave energy flux. As a result, wave heights diminish in the region behind the device.

=== Energy and energy flux ===

In a [[sea state]], the [[Arithmetic mean|mean]] [[energy density]] per unit area of [[gravity wave]]s on the water surface is proportional to the wave height squared, according to linear wave theory:<ref name="Phillips" /><ref name="Goda">{{cite book | first=Y. | last=Goda | title=Random Seas and Design of Maritime Structures | year=2000 | publisher=World Scientific | isbn=978-981-02-3256-6 }}</ref>

:<math>E=\frac{1}{16}\rho g H_{m0}^2,</math>{{efn|Here, the factor for random waves is {{frac|1|16}}, as opposed to {{frac|1|8}} for periodic waves – as explained hereafter. For a small-amplitude sinusoidal wave <math display="inline"> \eta = a \cos 2\pi\left(\frac{x}{\lambda}-\frac{t}{T}\right)</math> with wave amplitude <math> a,</math> the wave energy density per unit horizontal area is <math display="inline"> E=\frac{1}{2}\rho g a^2,</math> or <math display="inline"> E=\frac{1}{8}\rho g H^2</math> using the wave height <math display="inline"> H = 2a</math> for sinusoidal waves. In terms of the variance of the surface elevation <math display="inline"> m_0 = \sigma_\eta^2 = \overline{(\eta-\bar\eta)^2} = \frac{1}{2}a^2,</math> the energy density is <math display="inline"> E=\rho g m_0</math>. Turning to random waves, the last formulation of the wave energy equation in terms of <math display="inline"> m_0</math> is also valid (Holthuijsen, 2007, p. 40), due to [[Parseval's theorem]]. Further, the [[significant wave height]] is ''defined'' as <math display="inline"> H_{m0} = 4\sqrt{m_0}</math>, leading to the factor {{frac|1|16}} in the wave energy density per unit horizontal area.}}<ref>{{Cite book
 | last = Holthuijsen
 | first = Leo H.
 | year = 2007
 | title = Waves in oceanic and coastal waters
 | publisher = Cambridge University Press
 | isbn = 978-0-521-86028-4
 | location = Cambridge
}}</ref>

where ''E'' is the mean wave energy density per unit horizontal area (J/m<sup>2</sup>), the sum of [[kinetic energy|kinetic]] and [[potential energy]] density per unit horizontal area. The potential energy density is equal to the kinetic energy,<ref name="Phillips" /> both contributing half to the wave energy density ''E'', as can be expected from the [[Equipartition theorem#Potential energy and harmonic oscillators|equipartition theorem]].

The waves propagate on the surface, where crests travel with the phase velocity while the energy is transported horizontally with the [[group velocity]]. The mean transport rate of the wave energy through a vertical [[plane (mathematics)|plane]] of unit width, parallel to a wave crest, is the energy [[flux]] (or wave power, not to be confused with the output produced by a device), and is equal to:<ref>{{cite journal | last=Reynolds |first=O. | author-link=Osborne Reynolds | year=1877 |title=On the rate of progression of groups of waves and the rate at which energy is transmitted by waves | journal=Nature | volume=16 |issue=408 | pages=343–44 | doi = 10.1038/016341c0 |bibcode = 1877Natur..16R.341. | doi-access=free }}<br>{{cite journal | title=On progressive waves | author=Lord Rayleigh (J. W. Strutt) | author-link=Lord Rayleigh | year=1877 | journal=Proceedings of the London Mathematical Society | volume=9 | issue=1 | pages=21–26 | doi=10.1112/plms/s1-9.1.21 | url=https://zenodo.org/record/1447762 }} Reprinted as Appendix in: ''Theory of Sound'' '''1''', MacMillan, 2nd revised edition, 1894.</ref><ref name="Phillips" />

:<math>P = E\, c_g, </math> with ''c<sub>g</sub>'' the group velocity (m/s).

Due to the [[dispersion (water waves)|dispersion relation]] for waves under gravity, the group velocity depends on the wavelength ''λ'', or equivalently, on the wave [[period (physics)|period]] ''T''.

[[Wave height]] is determined by wind speed, the length of time the wind has been blowing, fetch (the distance over which the wind excites the waves) and by the [[bathymetry]] (which can focus or disperse the energy of the waves). A given wind speed has a matching practical limit over which time or distance do not increase wave size. At this limit the waves are said to be "fully developed". In general, larger waves are more powerful but wave power is also determined by [[wavelength]], water [[density]], water depth and acceleration of gravity.

== Wave energy converters ==
[[File:WECs-2020.png|thumb|upright=2|Generic wave energy concepts: 1.&nbsp;Point absorber, 2.&nbsp;Attenuator, 3.&nbsp;Oscillating wave surge converter, 4.&nbsp;Oscillating water column, 5.&nbsp;Overtopping device, 6.&nbsp;Submerged pressure differential, 7.&nbsp;Floating in-air converters.]]

Wave energy converters (WECs) are generally categorized by the method, by location and by the [[power take-off]] system. Locations are shoreline, nearshore and offshore. Types of power take-off include: [[hydraulic ram]], [[Peristaltic pump|elastomeric hose pump]], pump-to-shore, [[Hydroelectricity|hydroelectric turbine]], air turbine,<ref>[https://web.archive.org/web/20060523114110/http://classes.engr.oregonstate.edu/eecs/fall2003/ece441/groups/g12/White_Papers/Kelly.htm Embedded Shoreline Devices and Uses as Power Generation Sources] ''Kimball, Kelly, November 2003''</ref> and [[Linear alternator|linear electrical generator]]. 
[[File:Wave energy power take-off alternatives.png|thumb|upright=1.35|Different conversion routes from wave energy to useful energy in terms or electricity or direct use.]]

The four most common approaches are:

* point absorber buoys
* surface attenuators
* oscillating water columns
* overtopping devices

=== Point absorber buoy ===

This device floats on the surface, held in place by cables connected to the seabed. The point-absorber has a device width much smaller than the incoming wavelength λ. Energy is absorbed by radiating a wave with destructive interference to the incoming waves. Buoys use the swells' rise and fall to generate electricity directly via [[linear alternator|linear generators]],<ref name="Seabased">{{cite web|title=Seabased AB wave energy technology|work=Seabased |url=http://www.seabased.com/en/technology/seabased-wave-energy |access-date=October 10, 2017|archive-url=https://web.archive.org/web/20171010211446/http://www.seabased.com/en/technology/seabased-wave-energy|archive-date=October 10, 2017|url-status=live}}</ref> generators driven by mechanical linear-to-rotary converters,<ref name="PowerBuoy">{{cite web |title=PowerBuoy Technology |publisher=Ocean Power Technologies |url=http://www.oceanpowertechnologies.com/powerbuoy-technology/ |access-date=October 10, 2017|archive-url=https://web.archive.org/web/20171010213214/http://www.oceanpowertechnologies.com/powerbuoy-technology/|archive-date=October 10, 2017|url-status=live}}</ref> or hydraulic pumps.<ref name="CETO">{{cite web|title=Perth Wave Energy Project – Carnegie's CETO Wave Energy technology |url=https://arena.gov.au/projects/perth-wave-energy-project/|access-date=October 10, 2017|archive-url=https://web.archive.org/web/20171011072056/https://arena.gov.au/projects/perth-wave-energy-project/|archive-date=October 11, 2017|url-status=live}}</ref> Energy extracted from waves may affect the shoreline, implying that sites should remain well offshore.<ref name="Tethys">{{cite web|title=Tethys |url=http://tethys.pnnl.gov/technology-type/wave|access-date=April 21, 2014|url-status=live|archive-url=https://web.archive.org/web/20140520003234/http://tethys.pnnl.gov/technology-type/wave|archive-date=May 20, 2014}}</ref>

One point absorber design tested at commercial scale by [[CorPower Ocean|CorPower]] features a negative spring that improves performance and protects the buoy in very large waves. It also has an internal pneumatic cylinder that keeps the buoy at a fixed distance from the seabed regardless of the state of the tide. Under normal operating conditions, the buoy bobs up and down at double the wave amplitude by adjusting the phase of its movements. It rises with a slight delay from the wave, which allows it to extract more energy. The firm claimed a 300% increase (600&nbsp;kW) in power generation compared to a buoy without phase adjustments in tests completed in 2024.<ref>{{Cite web |last=Blain |first=Loz |date=2024-03-07 |title=Video: Wave-amplifying generator bounces twice as high as the swells |url=https://newatlas.com/energy/corpower-wavespring/ |access-date=2024-04-12 |website=New Atlas |language=en-US}}</ref>

=== Surface attenuator ===

These devices use multiple floating segments connected to one another. They are oriented perpendicular to incoming waves. A flexing motion is created by swells, and that motion drives hydraulic pumps to generate electricity. The [[Pelamis Wave Energy Converter]] is one of the more well-known attenuator concepts, although this is no longer being developed.<ref name="admin2014">{{cite news |date=21 November 2014 |title=Wave power firm Pelamis calls in administrators |url=https://www.bbc.co.uk/news/uk-scotland-scotland-business-30151276 |access-date=2024-04-13 |work=BBC News |publisher=}}</ref>

=== 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. Converters often come in the form of floats, flaps, or membranes. Some designs incorporate [[parabolic reflector]]s to focus energy at the point of capture. These systems capture energy from the rise and fall of waves.<ref name="Renewable Sea Power">{{cite journal| last1=McCormick |first1=Michael E. |first2=R. Cengiz |last2=Ertekin |title=Renewable sea power: Waves, tides, and thermals – new research funding seeks to put them to work for us |journal=Mechanical Engineering |publisher=ASME |volume=131 |issue=5 |year=2009 |pages=36–39|doi=10.1115/1.2009-MAY-4 |doi-access=free }}</ref>

=== Oscillating water column ===

[[Oscillating Water Column|Oscillating water column]] devices can be located onshore or offshore. Swells compress air in an internal chamber, forcing air through a turbine to create [[electricity]].<ref name="“grnflea">{{cite web|title=Extracting Energy From Ocean Waves |url=http://grnflea.com/extracting-energy-from-ocean-waves/|access-date=April 23, 2015|archive-url=https://web.archive.org/web/20150815152057/http://grnflea.com/extracting-energy-from-ocean-waves/|archive-date=August 15, 2015}}</ref> Significant noise is produced as air flows through the turbines, potentially affecting nearby [[birds]] and [[marine organisms]]. Marine life could possibly become trapped or entangled within the air chamber.<ref name="Tethys" /> It draws energy from the entire water column.<ref name=":1">{{Cite web |last=Blain |first=Loz |date=2022-08-01 |title=Blowhole wave energy generator exceeds expectations in 12-month test |url=https://newatlas.com/energy/blowhole-wave-energy-generator/ |access-date=2022-08-08 |website=New Atlas |language=en-US}}</ref>

=== Overtopping device ===

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 captured with low-head turbines. Devices can be on- or offshore.

=== Submerged pressure differential ===
Submerged pressure differential based converters<ref>{{Cite journal |last1=Kurniawan |first1=Adi |author-link2=Deborah Greaves |last2=Greaves |first2=Deborah |last3=Chaplin |first3=John |date=December 8, 2014 |title=Wave energy devices with compressible volumes |journal=Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences |volume=470 |issue=2172 |pages=20140559 |issn=1364-5021 |doi=10.1098/rspa.2014.0559 |pmc=4241014 |pmid=25484609 |bibcode=2014RSPSA.47040559K}}</ref> use flexible (typically reinforced rubber) membranes to extract wave energy. These converters use the difference in pressure at different locations below a wave to produce a pressure difference within a closed power take-off hydraulic system. This pressure difference is usually used to produce flow, which drives a turbine and electrical generator. Submerged pressure differential converters typically use flexible membranes as the working surface between the water and the power take-off. Membranes are pliant and low mass, which can strengthen coupling with the wave's energy. Their pliancy allows large changes in the geometry of the working surface, which can be used to tune the converter for specific wave conditions and to protect it from excessive loads in extreme conditions.

A submerged converter may be positioned either on the seafloor or in midwater. In both cases, the converter is protected from water impact loads which can occur at the [[free surface]]. Wave loads also diminish in [[Nonlinear system|non-linear]] proportion to the distance below the free surface. This means that by optimizing depth, protection from extreme loads and access to wave energy can be balanced.

=== Floating in-air converters ===
[[File:Wellenkraftwerk.JPG|thumb|Wave power station using a pneumatic chamber]]
[[File:Wave power station.gif|alt=Simplified design of wave power station|thumb|upright|Simplified design of wave power station]]
Floating in-air converters potentially offer increased reliability because the device is located above the water, which also eases inspection and maintenance. Examples of different concepts of floating in-air converters include:

* roll damping energy extraction systems with turbines in compartments containing sloshing water
* horizontal axis pendulum systems
* vertical axis pendulum systems

===Submerged wave energy converters===
In early 2024, a fully submerged wave energy converter using point absorber-type wave energy technology was approved in Spain.<ref name=InterestingEngineering_20240418/> The converter includes a buoy that is moored to the bottom and situated below the surface, out of sight of people and away from storm waves.<ref name=InterestingEngineering_20240418>{{cite news |last1=Paleja |first1=Ameya |title=Spain set to get table-top-like submerged sea wave energy converter |url=https://interestingengineering.com/energy/spain-submerged-wave-energy-converter |work=Interesting Engineering |date=18 April 2024 |archive-url=https://web.archive.org/web/20240422020251/https://interestingengineering.com/energy/spain-submerged-wave-energy-converter |archive-date=22 April 2024 |url-status=live }}</ref>

== Environmental effects ==

{{further|Environmental impact of electricity generation}}

Common environmental concerns associated with [[marine energy]] include:

* The effects of [[electromagnetic field]]s and underwater noise;
* Physical presence's potential to alter the behavior of marine mammals, fish, and [[seabird]]s with attraction, avoidance, entanglement
* Potential effect on marine processes such as [[sediment transport]] and [[water quality]].
* Foundation/mooring systems can affect [[benthic organism]]s via entanglement/entrapment
* [[Electromotive force]] effects produced from [[subsea power cable]]s.
* Minor collision risk 
* Artificial reef accumulation near fixed installations 
* Potential disuption to roosting sites

The [[Tethys (database)|Tethys database]] provides access to scientific literature and general information on the potential environmental effects of ocean current energy.<ref>{{cite web|title=Tethys |url=https://tethys.pnnl.gov/|website=Tethys |publisher=PNNL}}</ref>

== Potential ==

Wave energy's worldwide theoretical potential has been estimated to be greater than 2 TW.<ref>{{cite journal |last1=Gunn |first1=Kester |last2=Stock-Williams |first2=Clym |date=August 2012 |title=Quantifying the global wave power resource |journal=Renewable Energy |publisher=[[Elsevier]] |volume=44 |pages=296–304 |doi=10.1016/j.renene.2012.01.101 |bibcode=2012REne...44..296G }}</ref> 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.

[[File:World wave energy resource map.png|thumb|upright=1.35|World wave energy resource map]]

The [[National Renewable Energy Laboratory]] (NREL) estimated the theoretical wave energy potential for various countries. It estimated that the US' potential was equivalent to 1170 TWh per year or almost 1/3 of the country's electricity consumption.<ref name=":0">{{Cite web |url=https://www.boem.gov/Ocean-Wave-Energy/ |title=Ocean Wave Energy |website=BOEM|access-date=March 10, 2019 |archive-url=https://web.archive.org/web/20190326062254/https://www.boem.gov/Ocean-Wave-Energy/|archive-date=March 26, 2019|url-status=live}}</ref> The Alaska coastline accounted for ~50% of the total.

The technical and economical potential will be lower than the given values for the theoretical potential.<ref>{{Cite web |url=https://www.nrel.gov/gis/re-econ-potential.html |title=Renewable Energy Economic Potential |website=www.nrel.gov |access-date=May 2, 2023}}</ref><ref>{{cite book |last1=Teske |first1=S. |last2=Nagrath |first2=K. |last3=Morris |first3=T. |last4=Dooley |first4=K. |date=2019 |title=Achieving the Paris Climate Agreement Goals |chapter=Renewable Energy Resource Assessment |pages=161–173 |editor-last=Teske |editor-first=S. |publisher=Springer |doi=10.1007/978-3-030-05843-2_7 |isbn=978-3-030-05842-5 |s2cid=134370729 }}</ref>

== Challenges ==
{{Expand section|what are the main technical difficulties?|date=February 2023}}
Environmental impacts must be addressed.<ref name="ocs"/><ref>[http://www.nerc.ac.uk/research/programmes/mre/background.asp Marine Renewable Energy Programme] {{Webarchive|url=https://web.archive.org/web/20110803183744/http://www.nerc.ac.uk/research/programmes/mre/background.asp |date=August 3, 2011 }}, [[Natural Environment Research Council|NERC]] Retrieved August 1, 2011</ref> Socio-economic challenges include the displacement of commercial and recreational fishermen, and may present navigation hazards.<ref>[[Steven Hackett]]:''Economic and Social Considerations for Wave Energy Development in California'' [http://www.energy.ca.gov/2008publications/CEC-500-2008-083/CEC-500-2008-083.PDF CEC Report Nov 2008] {{Webarchive|url=https://web.archive.org/web/20090526062018/http://www.energy.ca.gov/2008publications/CEC-500-2008-083/CEC-500-2008-083.PDF |date=May 26, 2009 }} Ch2, pp22-44 [[California Energy Commission]]|Retrieved December 14, 2008</ref> Supporting infrastructure, such as grid connections, must be provided.<ref>{{Cite journal|last=Gallucci|first=M.|date=December 2019|title=At last, wave energy tech plugs into the grid - [News]|journal=IEEE Spectrum|volume=56|issue=12|pages=8–9|doi=10.1109/MSPEC.2019.8913821|issn=1939-9340|doi-access=free}}</ref> Commercial WECs have not always been successful. In 2019, for example, Seabased Industries AB in Sweden was liquidated due to "extensive challenges in recent years, both practical and financial".<ref>{{cite web |title=Seabased Closes Production Facility in Sweden |url=https://marineenergy.biz/2019/01/17/seabased-closes-production-facility-in-sweden/ |publisher=marineenergy.biz |access-date=12 December 2019 |date=January 2019}}</ref>

Current wave power generation technology is subject to many technical limitations.<ref>{{Cite journal |last1=Singh |first1=Rajesh |last2=Kumar |first2=Suresh |last3=Gehlot |first3=Anita |last4=Pachauri |first4=Rupendra |date=February 2018 |title=An imperative role of sun trackers in photovoltaic technology: A review |url=https://linkinghub.elsevier.com/retrieve/pii/S1364032117313953 |journal=Renewable and Sustainable Energy Reviews |language=en |volume=82 |pages=3263–3278 |doi=10.1016/j.rser.2017.10.018|bibcode=2018RSERv..82.3263S }}</ref> These limitations stem from the complex and dynamic nature of ocean waves, which require robust and efficient technology to capture the energy. Challenges include designing and building wave energy devices that can withstand the corrosive effects of saltwater, harsh weather conditions, and extreme wave forces.<ref>{{Cite journal |last1=Felix |first1=Angélica |last2=V. Hernández-Fontes |first2=Jassiel |last3=Lithgow |first3=Débora |last4=Mendoza |first4=Edgar |last5=Posada |first5=Gregorio |last6=Ring |first6=Michael |last7=Silva |first7=Rodolfo |date=July 2019 |title=Wave Energy in Tropical Regions: Deployment Challenges, Environmental and Social Perspectives |journal=Journal of Marine Science and Engineering |language=en |volume=7 |issue=7 |pages=219 |doi=10.3390/jmse7070219 |issn=2077-1312 |doi-access=free |bibcode=2019JMSE....7..219F }}</ref> Additionally, optimizing the performance and efficiency of wave energy converters, such as oscillating water column (OWC) devices, point absorbers, and overtopping devices, requires overcoming engineering complexities related to the dynamic and variable nature of waves.<ref>{{Cite journal |last1=Xamán |first1=J. |last2=Rodriguez-Ake |first2=A. |last3=Zavala-Guillén |first3=I. |last4=Hernández-Pérez |first4=I. |last5=Arce |first5=J. |last6=Sauceda |first6=D. |date=April 2020 |title=Thermal performance analysis of a roof with a PCM-layer under Mexican weather conditions |url=https://linkinghub.elsevier.com/retrieve/pii/S0960148119319561 |journal=Renewable Energy |language=en |volume=149 |pages=773–785 |doi=10.1016/j.renene.2019.12.084|bibcode=2020REne..149..773X |s2cid=213903662 }}</ref> Furthermore, developing effective mooring and anchoring systems to keep wave energy devices in place in the harsh ocean environment, and developing reliable and efficient power take-off mechanisms to convert the captured wave energy into electricity, are also technical challenges in wave power generation.<ref>{{Citation |last1=Røe |first1=Oluf Dimitri |title=Malignant Pleural Mesothelioma: History, Controversy, and Future of a Man-Made Epidemic |date=2017 |url=http://link.springer.com/10.1007/978-3-319-53560-9_4 |work=Asbestos and Mesothelioma |pages=73–101 |editor-last=Testa |editor-first=Joseph R. |access-date=2023-04-18 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-53560-9_4 |isbn=978-3-319-53558-6 |last2=Stella |first2=Giulia Maria|series=Current Cancer Research |hdl=11250/2628134 |hdl-access=free }}</ref> As the wave energy dissipation by a submerged flexible mound breakwater is greater than that of a rigid submerged structure, greater wave energy dissipation is expected due to highly deformed shape of the structure.<ref>Jafarzadeh, E., Kabiri-Samani, A., Mansourzadeh, S., & Bohluly, A. (2021). Experimental modeling of the interaction between waves and submerged flexible mound breakwaters. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 235(1), 127-141.</ref>

== Wave farms ==
A wave farm (wave power farm or wave energy park) is a group of colocated wave energy devices. The devices interact hydrodynamically and electrically, according to the number of machines, spacing and layout, wave climate, coastal and benthic geometry, and control strategies. The design process is a multi-[[optimization problem]] seeking high power production, low costs and limited power fluctuations.<ref>{{Cite journal |last1=Giassi |first1=Marianna |last2=Göteman |first2=Malin |date=April 2018 |title=Layout design of wave energy parks by a genetic algorithm |journal=Ocean Engineering |volume=154 |pages=252–261 |doi=10.1016/j.oceaneng.2018.01.096 |bibcode=2018OcEng.154..252G |s2cid=96429721 |issn=0029-8018 |url=http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-346695}}</ref> Nearshore wave farms have substantial impact on beach dynamics. For instance, wave farms significantly reduce erosion which demonstrates that this synergy between coastal protection and energy production enhances the economic viability of wave energy.<ref>{{Cite journal |last1=Abanades |first1=J. |last2=Greaves |first2=D. |last3=Iglesias |first3=G. |date=2014-09-01 |title=Coastal defence through wave farms |journal=Coastal Engineering |volume=91 |pages=299–307 |doi=10.1016/j.coastaleng.2014.06.009 |bibcode=2014CoasE..91..299A |hdl=10026.1/4556 |s2cid=35664931 |issn=0378-3839|hdl-access=free }}</ref> Additional research finds that wave farms located near lagoons can potentially provide effective coastal protection during maritime spatial planning.<ref>{{Cite journal |last1=Onea |first1=Florin |last2=Rusu |first2=Liliana |last3=Carp |first3=Gabriel Bogdan |last4=Rusu |first4=Eugen |date=March 2021 |title=Wave Farms Impact on the Coastal Processes—A Case Study Area in the Portuguese Nearshore |journal=Journal of Marine Science and Engineering |language=en |volume=9 |issue=3 |pages=262 |doi=10.3390/jmse9030262 |doi-access=free |bibcode=2021JMSE....9..262O |issn=2077-1312}}</ref>

==Gallery of wave energy installations==
{{Gallery
|File:Pelamis at EMEC.jpg 
|[[Pelamis Wave Energy Converter]] on site at the [[European Marine Energy Centre]] (EMEC), in 2008.
|File:Sunburst edited.jpg 
|[[Azura wave power device|Azura]] at the US Navy’s Wave Energy Test Site (WETS) on [[Oahu]].
|File:AMOG Wave Energy Converter.png
|The AMOG Wave Energy Converter (WEC), in operation off SW England (2019).
|File:Bombora_mWave_Converter.jpg
|The mWave converter by Bombora Wave Power.
|File:CalWave x1 WEC Pilot Unit.jpg
|[[CalWave Power Technologies, Inc]]. wave energy converter in California.
}}

== Patents ==
*[https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2016032360&redirectedID=true WIPO patent application WO2016032360] — 2016 ''Pumped-storage system'' – "Pressure buffering hydro power" patent application
*{{US patent|8806865}} — 2011 ''Ocean wave energy harnessing device'' – Pelamis/Salter's Duck Hybrid patent
*{{US patent|3928967}} — 1974 ''Apparatus and method of extracting wave energy'' – The original "Salter's Duck" patent
*{{US patent|4134023}} — 1977 ''Apparatus for use in the extraction of energy from waves on water'' – Salter's method for improving "duck" efficiency
*{{US patent|6194815}} — 1999 ''Piezoelectric rotary electrical energy generator''
*{{US patent|1930958}} — 1932 ''Wave Motor'' - Parsons Ocean Power Plant - Herring Cove Nova Scotia - March 1925. The world's first commercial plant to convert ocean wave energy into electrical power. Designer - Osborne Havelock Parsons - born in 1873 Petitcodiac, New Brunswick. 
*[https://patents.google.com/patent/US20040217597 Wave energy converters utilizing pressure differences US 20040217597 A1] — 2004 ''Wave energy converters utilizing pressure differences''<ref>{{cite web |date=April 11, 2004 |title=Wave energy converters utilizing pressure differences |website=FreePatentsOnline.com |url=http://www.freepatentsonline.com/y2004/0217597.html |archive-url=https://web.archive.org/web/20141031000016/http://www.freepatentsonline.com/y2004/0217597.html |archive-date=October 31, 2014 |url-status=live}}</ref>

A UK-based company has developed a Waveline Magnet that can achieve a [[levelized cost of electricity]] of £0.01/kWh with minimal levels of maintenance.<ref>{{cite web |url=https://www.independent.co.uk/tech/wave-magnet-renewable-energy-swel-b2156572.html?amp|title=Wave magnets offer 'cheapest clean energy ever'|date=August 31, 2022|work=[[The Independent]]}}</ref>

==See also==
* [[List of wave power projects]]
* [[List of wave power stations]]
* [[Wave power in Australia]]
* [[Wave power in New Zealand]]
* [[Wave power in Scotland]]
* [[Wave power in the United States]]
* [[Wave power ship]]
* [[WavePiston]]
* [[Marine energy]]
* [[Tidal power]]
* [[Ocean thermal energy conversion]]
* [[Osmotic power]]
* [[Office of Energy Efficiency and Renewable Energy]] (OEERE)
* [[World energy consumption]]

==Notes==
{{Notelist}}

==References==
{{Reflist|30em}}

==Further reading==
*{{Cite book| title=Ocean Wave Energy – Current Status and Future Prospects| first=Joao| last=Cruz| publisher=Springer| year=2008| isbn=978-3-540-74894-6}}, 431 pp.
*{{Cite book| title=Ocean Waves and Oscillating Systems| first=Johannes| last=Falnes| publisher=Cambridge University Press| year=2002| isbn=978-0-521-01749-7}}, 288 pp.
*{{Cite book|title=Ocean Wave Energy Conversion| first=Michael| last=McCormick| publisher=Dover| year=2007| isbn=978-0-486-46245-5}}, 256 pp.
*{{Cite book| title=Renewable Energy Resources| first1=John| last1=Twidell| first2=Anthony D.| last2= Weir| first3=Tony| last3=Weir| publisher=Taylor & Francis| year=2006| isbn=978-0-419-25330-3}}, 601 pp.

==External links==
{{Commons category}}
* [https://openei.org/wiki/PRIMRE Portal and Repository for Information on Marine Renewable Energy] A network of databases providing broad access to marine energy information.
* [https://openei.org/wiki/PRIMRE/Basics/Wave_Energy Marine Energy Basics: Wave Energy] Basic information about wave energy.
* [https://openei.org/wiki/PRIMRE/Databases/Projects_Database Marine Energy Projects Database] A database that provides up-to-date information on marine energy deployments in the U.S. and around the world.
* [https://tethys.pnnl.gov Tethys Database] A database of information on potential environmental effects of marine energy and offshore wind energy development.
* [https://tethys-engineering.pnnl.gov Tethys Engineering Database] A database of information on technical design and engineering of marine energy devices.
* [https://mhkdr.openei.org/ Marine and Hydrokinetic Data Repository] A database for all data collected by marine energy research and development projects funded by the U.S. Department of Energy.
*{{YouTube|id=EPFGQy4Bnjc|title=Wave Swell Energy video}}
*{{cite news | title=Power From the Restless Sea Stirs the Imagination | author=Kate Galbraith | date=September 22, 2008 |work=The New York Times | url=https://www.nytimes.com/2008/09/23/business/23tidal.html?em | access-date=October 9, 2008 }}
*[http://www.economist.com/search/displaystory.cfm?story_id=11482565 "Wave Power: The Coming Wave"] from the Economist, June 5, 2008

{{Ocean energy}}
{{physical oceanography}}
{{subject bar|portal1=Renewable energy|portal2=Energy|portal3=Oceans}}

[[Category:Wave power| ]]
[[Category:Bright green environmentalism]]
[[Category:Energy conversion]]
[[Category:Power station technology]]
[[Category:Sustainable technologies]]