Fluid core compressibility and the Earth's normal modes

Rieutord and Valdettaro (1997) study the inertial modes of a homogeneous, incompressible and viscous fluid shell. They show that as the fluid viscosity tends to zero the inertial modes of such a shell behave in a much more complicated way than those of a sphere. They infer from their work that, except for a set of special cases which have analytical solutions, no solutions exist, in the strict mathematical sense, for the inertial modes of a rotating homogeneous incompressible fluid shell in the asymptotic limit of zero viscosity. In this work we study the normal modes of self gravitating stratified compressible inviscid and rotating fluid sphere and spherical shell. We show that if the spherical model is neutrally stratified, its inertial modes behave much the same as those of a homogeneous and incompressible model. We will also show that robust numerical solutions can be found for (some of) the inertial modes of a compressible fluid shell proportional to the Earth's fluid core.