Editing Wave power (section)

=== 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.