Physics
Scientific paper
Dec 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990geoji.103..697w&link_type=abstract
Geophysical Journal International (ISSN 0955-419X), vol. 103, Dec. 1990, p. 697-706.
Physics
13
Earth Core, Geodynamics, Variational Principles, Elastic Deformation, Liquid Phases, Mathematical Models, Partial Differential Equations, Seismic Waves
Scientific paper
The general variational principle based on the equation derived by Johnson and Smylie (1977) is used to study the long-period oscillations of the earth which are largely, but not totally, confined to the liquid core. The mathematical description of the normal modes of the rotating self-gravitating stratified compressible liquid core is shown (in the absence of dissipation) to rest exactly on only two scalar fields. These two potentials are governed by a coupled pair of second-order linear partial differential equations which follow from a new variational principle (VP). One of the two new equations reduces to the subseismic wave equation (SSWE) when the effect of flow pressure on compression is neglected. A VP for the SSWE exists only when the earth model is further constrained, but the VP for the two-potential formulation of core dynamics is valid, without approximation, for any core stratified in accord with hydrostatic equilibrium, with elastically deformable oblate boundaries.
Rochester Michael G.
Wu Wen-Jing
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