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The cause for the damping of the Earth's free core nutation (FCN) and the free inner core nutation eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid outer core, where important energy dissipation mechanisms can take place. We present a fully 3D numerical model for the FCN capable of describing accurately viscous and Ohmic dissipation processes taking place in the bulk of the fluid core as well as in the boundary layers. We find an asymptotic regime, appropriate for Earth's parameters, where viscous and Ohmic processes contribute to the total damping, with the dissipation taking place almost exclusively in the boundary layers. By matching the observed nutational damping, we infer an enhanced effective viscosity matching and validating methods from previous studies. We suggest that turbulence caused by the Earth's precession can be a source for the enhanced viscosity. Plain Language Summary: Gravitational pull from the Sun and the moon (tidal forces) cause small periodic changes in the orientation of the Earth's spin axis, which can be measured very precisely by using radiotelescope observations of very distant quasars around the sky. It turns out that there is a small time delay between the tidal force and the Earth's spin axis response indicating that there is some process inside the Earth that is dissipating energy. Here we perform a numerical simulation to see if there is energy being lost inside the fluid outer core of the Earth. We find that there is minimal energy lost in the bulk of the core and that most of the energy is being lost at the interface between the fluid core and the Earth's mantle. Previous studies have assumed without proper justification that energy dissipates only at the fluid‐solid interface. Thus our study validates such assumption. Key Points: We establish asymptotic scaling laws for the free core nutation (FCN)'s Ohmic and viscous dissipation in the fluid coreMost of the energy dissipation associated with the FCN takes place in the boundary layersOur work validates inferences from previous studies that assumed the flow in the outer core as a uniform vorticity flow [ABSTRACT FROM AUTHOR]