= Sectoral inertial mode of a slowly rotating barotropic star
{title2=$W=zR^m,\quad\sigma=2\Omega/(m+1)$}
= Sectoral stellar r-mode
{synonym}
For spherical <mass density> in the <anelastic approximation for a rotating barotropic star>, the displayed <pressure> amplitude gives <velocity> proportional to $(-izR^{m-1},zR^{m-1},iR^m)$. This <velocity> is divergence free and tangent to spherical shells, so its mass-weighted divergence vanishes for every spherical <mass density> profile. It is an inertial r-mode driven by <Coriolis acceleration>; with phase $e^{i\omega t+im\phi}$ its inertial frequency is $\omega=-(m-1)(m+2)\Omega/(m+1)$.
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