  A magneto-hydrodynamic model of boundary layers at the Core-Mantle Boundary
(CMB) is derived and used to compute the viscous and electromagnetic torques
generated by the Earth's nutation forcing. The predicted electromagnetic torque
alone cannot account for the dissipation estimated from the observations of the
free core nutation. The presence of a viscous boundary layer in the
electromagnetic skin layer at the CMB, with its additional dissipative torques,
may explain the geodetic data. An apparent Ekman number at the top of the core
between 3 and $5 10^{-11}$ is inferred depending on the electrical conductivity
of the mantle.
