INERTIAL WAVES IN A ROTATING SPHERICAL-SHELL

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.