K. Johnk et B. Svendsen, A THERMODYNAMIC FORMULATION OF THE EQUATIONS OF MOTION AND BUOYANCY FREQUENCY FOR EARTHS FLUID OUTER CORE, Continuum mechanics and thermodynamics, 8(2), 1996, pp. 75-101
This work presents a precise formulation of the balance and constituti
ve relations appropriate to the modeling of the motion of the fluid ou
ter core, including a full thermodynamic analysis and derivation of th
e buoyancy frequency, its role in the equations of motion for the flui
d outer core, and the dependence of this equation on the thermodynamic
state of the outer core. It is shown that the equation of motion is c
ontrolled by a single parameter, the buoyancy frequency. Its definitio
n is general, so as to include also thermodynamic effects in various f
orms. The dependence on concentration or entropy-gradients is of impor
tance for motions on longer time scales but also influences core under
tones, the oscillations of the Earth's outer core, in regions of stron
g concentration gradients. By appropriate scaling a variety of differe
nt approximations arise from this formulation using the thermodynamic
definiton of the buoyancy frequency. Special interest is put on the sc
aling for the outer core eigenmodes yielding consistent formulations f
or the Boussinesq- and the subseismic approximation.