Open AccessCore dynamics: the two‐potential description and a new variational principle
Author(s) -
Wu WenJing,
Rochester M. G.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb05681.x
Subject(s) - variational principle , hydrostatic equilibrium , classical mechanics , compressibility , partial differential equation , calculus of variations , scalar field , physics , dissipation , primitive equations , mathematical analysis , mathematics , mechanics , numerical partial differential equations , quantum mechanics , thermodynamics
SUMMARY 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). The latter is simpler for computational purposes than the conventional VP involving four field variables. 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.