Inertial oscillations in a spherical shell

It has previously been shown that inertial oscillations in spherical shells exhibit internal shear layers, which may be triggered by the breakdown of the Ekman layers. We consider the influence of the boundary conditions imposed at the inner and outer boundaries on these inertial oscillations and their internal shear layers. We show that although the pattern of the shear layers is determined primarily by the presence of the inner boundary, the precise boundary conditions imposed there are largely irrelevant. In contrast, changing the boundary conditions imposed at the outer boundary can have an effect on the details of the mode, even though the overall pattern is still determined by the inner boundary.