Internal oscillations in the Earth's fluid core

A formulation is given for the eigenvalue problem describing internal oscillations in the Earth's fluid core. The description is appropriate for either the Boussinesq or the subseismic approximations to the full system of governing equations for a rotating, compressible, inhomogeneous, selfgravitating thick shell of fluid. The depth distribution of the buoyancy frequency N , which measures the strength of the stratification in the core, is highly speculative, although physical observations constrain the maximum value of N . Theories have been proposed in which an outer layer of the fluid core is stably stratified (NZ > 0) whereas the inner regions are allowed to convect. The present mathematical model incorporates arbitrary variation of N with depth. The structure of the 'turning surfaces', which delineate the spatially wave-like from the exponentially decaying regimes of an internal mode, are examined for a particular functional choice for N that models a plausible stratification distribution in the core. The shapes of the regions in which the waves are trapped are dependent on the function N and the frequency X of the wave. This fact is used to suggest a mechanism by which hypothetical surface detection of internal waves in the core could be used to estimate both the value of N at the core-mantle boundary and the thickness of the layer of stable stratification.