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  \phi_0(z) e^{\mathrm{i} k x} \,
</math></center>
where <math>A </math> is the wave amplitude (in potential) <math>\mathrm{i} k </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>)
and
<center><math>
 \phi_0(z) =\frac{\cosh k(z+h)}{\cosh k h}
</math></center>