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Recently, eigenmodes of rotating fluids, namely inertial modes, have receivedmuch attention in relation to their destabilization when coupled togravitational radiation within neutron stars. However, these modes have beenknown for a long time by fluid dynamicists. We give a short account of theirhistory and review our present understanding of their properties. Consideringthe case of a spherical container, we then give the exact solution of theboundary (Ekman) layer flow associated with inertial r-modes and show thatprevious estimations all underestimated the dissipation by these layers. Wealso show that the presence of an inner core has little influence on thisdissipation. As a conclusion, we compute the window of instability in theTemperature/rotation plane for a crusted neutron star when it is modeled by anincompressible fluid.Comment: 7 pages, 2 figures, revised version to appear in ApJ, March 1

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