Numerical Simulation of Plumes and Small-Scale Dynamics in the Earth's Fluid Core

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Small-scale dynamics of the Earths corePI: Paul H. RobertsIt is generally accepted that the main magnetic field of the Earth is created in its core in much the same way that dynamos generate electric currents in power stations. Because the Earths mantle is a poor conductor of electricity, these currents do not reach the Earths surface, but the magnetic fields that inevitably accompany any flow of electricity do penetrate the mantle, and form the main geomagnetic field. A dynamo creates electric currents and magnetic fields by the motion of electrically conducting material across a magnetic field, by a process called `electromagnetic induction. When the induced magnetic field accompanying the electric currents is the same as the inducing magnetic field creating the currents, the dynamo is said to be `self-exciting. It is widely believed that the geodynamo is of this type. The required motions of the conductor are movements within the fluid core, which is plausibly a ferric alloy and therefore a good electrical conductor. The power consumed by the geodynamo is currently estimated to be about 1011 to 1012 watts. This has to be provided as kinetic energy to the core flow, otherwise motion would cease and the magnetic field would disappear in a few thousand years, in contradiction to paleomagnetic evidence that shows the geomagnetic field is as old as the Earth. There are several indications that the fluid core is in motion. Maps of the geomagnetic field at the Earths surface show growing and dying foci reminiscent of weather maps, though drifting in the reverse direction and evolving much more slowly . Also, successful models of the Earths interior require the fluid core to be in a nearly adiabatic state, which happens naturally if it is well mixed. Core stirring is most plausibly due to convective motions driven by small differences in the chemical composition and temperature of the fluid. Most likely these are the by-product of the continuing evolution of the Earth, in which the surface of the solid inner core gradually advances upwards, at a speed between 10-12 and 10-11 m/s, as fluid freezes onto it, releasing latent heat and light constituents of the ferric alloy as it does so. The release of heat and light material from the inner core boundary is probably far from uniform, taking the form of buoyant plumes that stir the fluid core. The fate of these plumes is uncertain, and two rival scenarios have been proposed. In the older `traditional scenario, the plumes quickly break up into ever smaller parcels that homogenize the fluid, so generating a slightly top-heavy state, the instability of which drives the large-scale convection powering the geodynamo. The newer Loper-Moffatt scenario, takes particular note of the low small diffusivities of heat and particularly of chemical inhomogeneities, which may allow a parcel to retain its buoyancy until it becomes really small. It is argued that the parcels and their debris will therefore linger for much longer than the traditional scenario recognizes, and will fill a stably stratified layer adjacent to the core surface. A main objective of this project is to model the mixing process computationally, and to determine which (if either) of the two scenarios is more relevant to the core. A fresh numerical technique is being used that allows geophysically more realistic diffusivities to be included, and particularly the small diffusivity of chemicalinhomogeneities. These calculations may clarify the small-scale dynamics of the core so that they can be better parameterized in future geodynamo simulations. The vast range of length and time scales of core dynamics makes parameterization unavoidable, but it is generally accepted that the parameterizations currently being used are unphysical. This constitutes one of the more serious deficiencies in geodynamo simulations today. Stated another way, current integrations of core magnetohydrodynamics and the geodynamo are unreasonably successful, bearing in mind their dubious basis. This success is sometimes called the the geodynamo paradox, and its resolution is an aim of this project.