Dynamics of rotating fluids described by scalar potentials

The oscillatory dynamics of a rotating, self-gravitating, stratified, compressible, inviscid fluid body is simplified by an exact description in terms of three scalar fields which are constructed from the dilatation, and the perturbations in pressure and gravitational potential [Seyed-Mahmoud, B., 1994. Wobble/nutation of a rotating ellipsoidal Earth with liquid core: implementation of a new set of equations describing dynamics of rotating fluids M.Sc. Thesis, Memorial University of Newfoundland]. We test the method by applying it to compressible, but neutrally-stratified, models of the Earth’s liquid core, including a solid inner core, and compute the frequencies of some of the inertial modes. We conclude the method should be further exploited for astrophysical and geophysical normal mode computations.