= Inertial modes of an incompressible disk
For $0<\omega^2<\kappa^2$, set $S=kH\omega/\sqrt{\kappa^2-\omega^2}$. Even-pressure modes satisfy $\omega^2=-\Omega_z^2S\tan S$, while odd-pressure modes satisfy $\omega^2=\Omega_z^2S\cot S$. In the case $\Omega_z>\kappa>0$, the branches approach $\kappa$ as $kH\to0$. For each fixed vertical order $n\geq1$ and large $kH$, $S\to n\pi/2$ and $\omega\sim\kappa n\pi/(2kH)$. Even orders have even <pressure> and odd orders odd <pressure>. The limiting <boundary condition> is zero normal derivative of <pressure> at both interfaces.
// Target: astrophysics.bigb
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