View source for Template:Incident plane wave 2d definition

<math>\phi^{\mathrm{I}}\,</math>  
is a plane wave travelling in the <math>x</math> direction,
<center><math>
\phi^{\mathrm{I}}(x,z)=A \left\{ \frac{\cos k_0(z+h)}{\cos k_0 h} \right\} e^{-k_0 x}
</math></center>
where <math>A </math> is the wave amplitude and <math>k_0 </math> is 
the positive imaginary solution of the [[Dispersion Relation for a Free Surface]]
(note we are assuming that the time dependence is of the form <math>\exp(\mathrm{i}\omega t) </math>).