Editing Wave power (section)

=== 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]] 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>