Dynamics of a fluid core with inward growing boundaries
In both physical and mathematical models of the Earth's core it has been difficult, so far, to discuss all the terms in the magneto-hydrodynamic energy equation under one unifying theory and to relate all the physical mechanisms involved in a specific model. The reason for this is mainly the uncertainty about the energy sources, or, when they could be accounted for, with uncertainty about their location. In the following article we deduce and examine a model of the Earth's core which can be regarded as a sequel to theories of the formation of a fluid core in the course of the Earth's thermal evolution. General cooling and pressure-freezing cause the formation of solid phases at the boundaries of the fluid core, leading to a solid inner core (IC) and a lower mantle shell (Bullen's D" layer) from slow overgrowth at the mantle-core (MC) boundary. For simplicity, the core fluid is assumed to consist of two major phases, one conducive to solid metallic core formation, and the other to crystallization of a lower mantle phase from "solution" in a metal "solvent." The presence of a third, minor constituent, by selective partitioning between phases, acts as a solid phase growth regulator. On the basis of this model the energy available for fluid core motion and thereby for maintenance of the magnetic field, is related directly to the time rate of change of the growth of the solid phases at the IC and MC boundaries. Most of the available energy is gravitational and is associated with density and concentration currents which offset density inhomogeneities caused by selective acceptance and rejection of the fluid core constituents by the two solid phases. A very conservative estimate of the net gain per second in gravitational potential energy resulting from the mass redistribution via density currents and solid phase formation is 2.6 x 10" W which may become available in different forms. The fraction which is converted into kinetic energy associated with differential circulatory motion around the rotation axis amounts to 3.4 x 10" W, based on radial interchange with respect to the Earth's centre. The heat liberated as a result of IC solidification is 2.7 x loL1 W, assuming that the metallic phase is mainly iron. Since our ideas of other constituents of the core fluid are less definite we can draw only very general conclusions about the MC boundary. If silicates and oxides are likely candidates, it is possible that in the crystallization of the mantle phase from the core fluid, heat is being absorbed, thus creating a heat sink at the MC boundary. An estimate of the net strain energy associated with compression of IC material by about 1.4% and expansion of MC material by, on the average, 0.4% gives 1.5 x 10'' W. Magnetic polarity reversals might be explained as due to epochs during which the solid phase growth rate which dominates the fluid motion shifts from the IC to the MC boundary and vice versa. Intensity changes might be due to significant variations in the ratio of the radial and horizontal velocity components of the fluid motion.