  We investigate the properties of forced inertial modes of a rotating fluid
inside a spherical shell. Our forcing is tidal like, but its main property is
that it is on the large scales. Our solutions first confirm some analytical
results obtained on a two-dimensional model by Ogilvie (2005). We also note
that as the frequency of the forcing varies, the dissipation varies drastically
if the Ekman number E is low (as is usually the case). We then investigate the
three-dimensional case and compare the results to the foregoing model. These
solutions show, like their 2D counterpart, a spiky dissipation curve when the
frequency of the forcing is varied; they also display small frequency intervals
where the viscous dissipation is independent of viscosity. However, we show
that the response of the fluid in these frequency intervals is crucially
dominated by the shear layer that is emitted at the critical latitude on the
inner sphere. The asymptotic regime is reached when an attractor has been
excited by this shear layer. This property is not shared by the two-dimensional
model. Finally, resonances of the three-dimensional model correspond to some
selected least-damped eigenmodes. Unlike their two-dimensional counter parts
these modes are not associated with simple attractors; instead, they show up in
frequency intervals with a weakly contracting web of characteristics. Besides,
we show that the inner core is negligible when its relative radius is less than
the critical value 0.4E^{1/5}. For these spherical shells, the full sphere
solutions give a good approximation of the flows (abridged abstract).
