= Axisymmetric waves of a homogeneous incompressible disk
In a thin constant-density disk with <free surfaces> $z=\pm H$, neglect slow radial gradients and let <perturbations> vary as $e^{ikr-i\omega t}$. With $h=p'/\rho$, the local inviscid equations are $-i\omega u-2\Omega v=-ikh$, $-i\omega v+\kappa^2u/(2\Omega)=0$, $-i\omega w=-h_z$ and $iku+w_z=0$. Eliminating <velocity> gives $h_{zz}=k^2\omega^2h/(\omega^2-\kappa^2)$. This local <WKB approximation> assumes $H/r\ll1$ and $|kr|\gg1$ and has both surface and <inertial wave> branches.
// Target: astrophysics.bigb
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