= Zero-frequency balanced mode of an axisymmetric disk
{title2=$\omega=0,\quad U_x=0,\quad2\Omega U_y=ikc_s^2\sigma/\Sigma_0$}
Besides the two propagating <inertial-acoustic wave> branches, a uniform barotropic <Keplerian shearing sheet> has a stationary branch balancing <pressure> against <Coriolis acceleration>. For radial wavenumber $k\ne0$, setting $\omega=0$ in continuity gives $U_x=0$, and radial momentum gives the displayed azimuthal balance. The full determinant is proportional to $\omega(\omega^2-\Omega^2-c_s^2k^2)$. At $k=0$ the stationary branch is a uniform column-density change; it is not a travelling density wave.
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