A THERMODYNAMIC FORMULATION OF THE EQUATIONS OF MOTION AND BUOYANCY FREQUENCY FOR EARTHS FLUID OUTER CORE

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.