On the motion of an iron-alloy core containing a slurry. II. A simple model

Abstract

This is the second in a series of papers intended to develop a practical theory for the motion of an iron-alloy core containing a slurry. We have developed a simplified theory based upon the general theory developed in the first paper (Loper and Roberts, 1978) and have solved completely a relatively simple problem to verify that our theory is complete and solvable and o illustrate some of its basic features. These features include diffusion of material driven by the hydrostatic pressure gradient and solidification of material onto a moving boundary of unknown position. The solution includes a linear stability analysis for the onset of convection driven by compositional buoyancy and the resulting nonlinear steady state which occurs in the long wavelength limit. Two important ideas emerged from the analysis of the strongly nonlinear convective state which occurs far above critical. First, the motions mix the fluid vigorously, producing a state of nearly constant composition. Second, two distinct timescales occur: a long evolutionary time and a short convective time.