Tidal dissipation in rotating fluid bodies: a simplified model

We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid. Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces. The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases with the size of the core. In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction. We discuss the results with reference to wave attractors, critical latitudes and other features of the propagation of inertial waves within the fluid, and comment on their relevance for tidal dissipation in planets and stars.