Inertial oscillations in the solar convection zone. II. A cylindrical model for equatorial regions

We present axisymmetric inertial oscillations found from a simplified, cylindrical model applicable to equatorial latitudes and compare these results with those obtained by numerical methods in Paper I for a spherical shell. The equations for the cylindrical model are solved using analytical methods. We derive analytically the asymptotic behavior of inertial mode frequencies in the limits of very large and very small axial (corresponding to latitudinal) wavenumber and show that inertial oscillations arise only when the angular momentum per unit mass increases outward. We also demonstrate how convection zone depth and differential rotation affect the different radial orders of inertial modes. As in the spherical case, we find that the deeper the layer, the closer together are successive radial orders. We find that in a convection zone 1.5 x 1010 cm in depth, rotation rate increasing inward leads to decreased oscillation frequency for a given radial order and axial wavenumber, the opposite of the result for the spherical shell. Deeper zones in the cylindrical case give increased frequencies for rotation rate either decreasing or increasing inward, unless the outermost part of the convection zone is removed from the model. In that case, the cylindrical and spherical shell results agree for deep convection zones. The differences in the results between spherical and cylindrical models are shown to be due to the different geometries