Inertial Waves and the Earth's Outer Core

The existence of wave solutions to the Poincaré equation for a rotating fluid confined between rigid spherical boundaries is investigated. This problem is ill-posed and there appear to be no continuous solutions. However experimental work indicates that solutions do exist under certain conditions and these experiments are at least partially interpreted by an approximate solution found by means of a variational principle. The Poincaré equation is of geophysical interest because it is central to the study of hydromagnetic waves in the Earth's outer core.