The structure and spectrum of inertial waves of an incompressible visc
ous fluid inside a spherical shell are investigated numerically. These
modes appear to be strongly featured by a web of rays which reflect o
n the boundaries. Kinetic energy and dissipation are indeed concentrat
ed on thin conical sheets, the meridional cross-section of which forms
the web of rays. The thickness of the rays is in general independent
of the Ekman number E but a few cases show a scaling with E-1/4 and st
atistical properties of eigenvalues indicate that high-wave number mod
es have rays of width 0(E-1/3). Such scalings are typical of Stewartso
n shear layers. It is also shown that the web of rays depends on the E
kman number and shows bifurcations as this number is decreased. This b
ehaviour also implies that eigenvalues do not evolve smoothly with vis
cosity. We infer that only the statistical distribution of eigenvalues
may follow some simple rules in the asymptotic limit of zero viscosit
y.