Magnetism is everywhere, in planets, stars and galaxies. Usually it is the by-product of electric currents created in the same way as in a commercial power plant, i.e., by dynamo action. This is the name given to the process through which the motion of an electrical conductor across a magnetic field creates electric currents that can maintain that magnetic field against energy losses through electrical resistance. Dynamos require an energy source to offset those losses. For the geodynamo operating in the Earth's liquid core there are two main possibilities: buoyancy and the luni-solar precession.
Buoyancy is created by the release of latent heat and light constituents as core fluid solidifies onto the surface of the solid inner core in the general cooling of the Earth, the buoyant power release being proportional to the rate of solidification and therefore to the rate of growth of the solid core. Precession is the name given to the motion of the Earth's polar axis round a cone with a semi-angle of about 23.5 degrees; it sweeps out the complete cone approximately every 26,000 years. Precession is caused by the gravitational torques that the Sun, Moon and planets exert on the equatorial bulge of the Earth. The Earth's mantle and core are coupled by viscosity and topography, the topographic torque existing because of the slight oblateness of the core-mantle interface. Through this coupling, precession creates fluid motions in the core. Of the two mechanisms, the buoyancy explanation is the better studied and the more widely accepted. Nevertheless, there is a difficulty: the power requirements of the geodynamo imply such a rapid growth of the inner core that it is, on current estimates, at most about 2 billion years old. Paleomagnetism has established however that the geomagnetic field has existed at about its present strength for more than 3.4 billion years. The precessional explanation does not encounter this particular difficulty but it may face others. This will not be known until the precessional dynamo has been studied in greater detail than has so far been attempted. This is the main objective of this project.
There is a subsidiary objective too, that of understanding better the flows generated in planets such as Mercury and satellites such as Europa by their libration. This is the term used when a body does not keep the same face towards another body about which it orbits. For example, the Moon does not present exactly the same face towards the Earth as it orbits about it. Librationally-driven motions are being actively studied experimentally at UCLA, and our techniques for solving precessionally-driven flows can be easily modified to apply to these experiments and to librating bodies in the solar system.
Most studies of dynamo action in large naturally-occurring bodies have had to assume that those bodies are spherical. A radically new method is required to study precessionally-driven flows in non-spherical bodies. We have recently developed and tested a numerical technique for solving the equations of magnetohydrodynamics, governing fluid flow and magnetic field, in an oblate spheroidal container. The computer code advances the flow in time using finite differences on overlapping grids; in this way the grids map the spheroidal container and the numerical difficulty known as the pole problem is completely avoided. Already some unexpected, and so far inexplicable, results have been obtained. We intend to carry out many exploratory studies to try to elucidate these flows in order to determine how important precession is in driving motions in Earth's core and in creating the main magnetic field of the Earth.
A dynamo is a device that converts mechanical energy into electrical energy by inducing electric current to flow by moving an electrical conductor across a magnetic field. The electrical current creates its own induced magnetic field. The dynamo is self-excited when the induced and inducing magnetic fields are the same. A similar self-excited process creates geomagnetism and the north- seeking property of the magnetic compass needle. The associated electric currents flow in Earth's core, a nearly spherical mass of liquid iron, of radius 2,200 miles, surrounding Earth's center. Because of this conducting fluid's motion, Earth's core is a gigantic electric generator, called 'the geodynamo'. But a dynamo needs a power source to keep it moving and to maintain its production of electricity. What maintains the geodynamo? Over past decades many possibilities have been proposed and dismissed. By now they have narrowed to two: convection and precession. This project focussed on the latter. Most people have seen how the axis of a spinning top may slowly describe a cone about the vertical, a motion called 'precession'. Earth is a giant top spinning about an axis that precesses about the perpendicular to the ecliptic, which is the plane of Earth's orbit around the Sun, so named because eclipses may happen when the Moon passes through that plane. Earth's rotation axis is at angle of about 23.4 degrees to the normal to the ecliptic, and it moves completely around its cone in about 26,000 years. This is called `the lunisolar precession', as it is created by the Moon and Sun. These can exert the necessary torques through the flatening of Earth at its poles caused by its daily rotation. The precessional motion of Earth is transmitted topographically to the fluid in its core, through the oblateness of the core's surface. One intellectual merit of our project was the creation of the first model of a topographically-driven dynamo. This required the development of a computational method for magnetohydrodynamic flow in a core that is oblate rather a spherical. This method potentially will have a broad impact. A subsidiary objective of our research aimed to understand flows generated in the cores of planets, such as Mercury, and in satellites such as Europa, by their libration. Libration is the term used when a body does not keep the same face towards another body about which it orbits. For example, Earth's Moon does not present exactly the same face towards the Earth as it circles around it. We could use our computational method for precession to elucidate libration, and could show for the first time that librationally-driven flow could maintain a dynamo. Our findings on libration were published at the same time as those of a group at Hong Kong University, but where results overlapped they agreed. During our tenure of this grant, we also published papers on general dynamo theory, and also on core-mantle coupling. The latter will hopefully have a broad geophysical impact.
