Axisymmetric compressible shearing-sheet waves
= Axisymmetric compressible shearing-sheet waves
{title2=$\omega^4-(\Omega^2+c^2k^2)\omega^2+\Omega^2c^2k_z^2=0$}
In an unstratified <Keplerian shearing sheet> with <sound speed> $c$, the four linear velocity-density equations yield $\omega^4-(\Omega^2+c^2k^2)\omega^2+\Omega^2c^2k_z^2=0$. The lower-frequency branch approaches the <inertial wave> relation $\omega^2=\Omega^2k_z^2/k^2$ for $ck\gg\Omega$; the upper branch is predominantly acoustic.