Ekman Layers and the Damping of Inertial r ‐Modes in a Spherical Shell: Application to Neutron Stars

Abstract

Recently, eigenmodes of rotating Ñuids, namely, inertial modes, have received much attention in relation to their destabilization when coupled to gravitational radiation within neutron stars. However, these modes have been known for a long time in Ñuid dynamics. We give a short account of their history and review our present understanding of their properties. Considering the case of a spherical container, we then give the exact solution of the boundary (Ekman) layer Ñow associated with inertial r-modes and show that previous estimations all underestimated the dissipation by these layers. We also show that the presence of an inner core has little inÑuence on this dissipation. As a conclusion, we compute the window of instability in the temperature/rotation plane for a crusted neutron star when it is modeled by an incompressible Ñuid.