Abstract

We carry out numerical and mathematical investigations of shear Alfvén waves inside of a rotating spherical shell filled with an incompressible conducting fluid (with finite conductivity), and bathed in a strong dipolar magnetic field. In particular, we are interested in studying inertial $r$-mode instability in rapidly rotating neutron stars. We considered the magneto-viscous Ekman layers at the core-crust interface and discussed the resulting damping mechanism for $r$-mode oscillations.