Inertial waves in a rotating spherical shell: Attractors and asymptotic spectrum (Q2731238)

The aim is to present the asymptotic limit of inertial modes for fluid flow in a rotating spherical shell when viscosity tends to zero. First, the authors study the trajectories of characteristics of governing hyperbolic equation in a meridional plane of the shell, and derive a relation between these trajectories and eigenfunctions in two and three dimensions. The authors present the main features of the solutions when viscosity is omitted. In the second part the authors investigate the influence of viscosity, and examine the structure of shear layers which arise. By studying the behaviour of a wave packet, it is shown how eigenvalues and eigenmodes may be computed in the asymptotic limit of small viscosity. The authors also discuss the distribution of eigenvalues in complex plane.