Editing Wave power (section)

==== 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>
|}