  Recently, eigenmodes of rotating fluids, 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 by fluid dynamicists. 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 flow 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 influence 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 fluid.
