Anelastic approximation for a rotating barotropic star ($\nabla \cdot (\rho \mathbf{v})=0$)

For slow rotation and low-frequency inertial motion, neglect the time derivative of the Eulerian mass density perturbation relative to the mass-weighted velocity divergence. This filters acoustic compressibility while retaining background mass density variation. A spherical background mass density is often sufficient at leading order in rotation.