[math]\displaystyle{
\Delta\phi=0, \, -h\lt z\lt 0,\,\,\,\mathbf{x} \in \Omega
}[/math]
[math]\displaystyle{
\partial_z\phi = 0, \, z=-h,
}[/math]
[math]\displaystyle{
\partial_z \phi = \alpha \phi,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
}[/math]
(note that the last expression can be obtained from combining the expressions:
[math]\displaystyle{
\partial_z \phi =\mathrm{i} \omega \zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
}[/math]
[math]\displaystyle{
\mathrm{i} \omega \phi = -g\zeta,\,z=0,\,\,\mathbf{x} \in \partial \Omega_{\mathrm{F}},
}[/math]
where [math]\displaystyle{ \alpha = \omega^2/g }[/math])
