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PosGeo
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A geosciences blog
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Fluid Mechanics , Geomagnetism
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Solving the geodynamo problem
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Date: June 28, 2019 Author: posgeo 0 Comments
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Our understanding and knowledge of the Earth’s magnetic field has progressed much over the last few centuries. The property of a compass needle pointing North has been used in navigation for millennia, but scientific investigation into the origin of the magnetic field has been a comparably recent venture.
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The first major investigation on the phenomenon of magnetism was conducted by William Gilbert, natural philosopher and physician to Queen Elizabeth I. In his 1600 treatise on magnetic experimental studies, De Magnete , he concluded the global field had the same form as a bar magnet:
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“Magnus magnes ipse est globus terrestris.”
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[The Earth itself is a great magnet.]
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– De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, William Gilbert, (1600).
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About two hundred years later in 1835, this problem attracted the attention of the famous mathematician, Carl Friedricht Gauss. Using observatory data and his new invention of least squares regression, he proved that the field had a source that originated inside the Earth. In addition he determined the field was, to a good approximation, a dipole. This reinforced Gilbert’s hypothesis that the origin of the Earth’s magnetic field lay in a permanent magnet at the Earth’s centre.
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However, this theory was promptly put into question by inconsistent observations. At the time in the 19 th century, there was a great deal of interest in the magnetic field for navigation. Maps of how the magnetic field declines and inclines at different latitude and longitudes were commonly used to estimate longitude on ships traversing oceans.
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image_jpeg Terrestrial magnetism by Colonel Edward Sabine, R.A.V.P.R.S. Engraved by W. & A.K. Johnston. William Blackwood & Sons, Edinburgh & London. (1856) (Source: David Rumsey Map Collection, http://www.davidrumsey.com , USA; Images copyright © 2000 by Cartography Associates).
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Over the century, to the surprise of navigators and scientists alike, it was discovered that these maps became less accurate as the century progressed: the magnetic field seemed to be changing with time. Another blow came to the permanent magnet theory in 1895, when French physicist Pierre Curie discovered that materials lose their permanent magnetic properties at high temperature. Surely the centre of the Earth would be too hot to sustain a permanent magnet. As the century tuned, work by seismologists–such as Richard Dixon Oldham and later by Beno Gutenberg–indicated that the Earth had a compositionally distinct liquid core. This set the stage for new theories on the origin of the magnetic field.
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In 1919, Irish physicist Sir Joseph Larmor proposed that if the core held a conducting fluid, then motions of the fluid through a weak magnetic field would generate an electric field. That electric field would then produce its own magnetic field. If this “dynamo” process was self-sustaining, then perhaps this could explain the origin of the global magnetic field. The question then became the task of determining if self-regenerating fields were possible in Earth-like geometries.
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Screen Shot 2019-06-25 at 20.12.01 Illustration of magnetic field distortion inside a rotating conducting core. Adapted from Field generation in electrically conducting fluids. Moffatt, H. K. (1978). Cambridge University Press
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Unfortunately, the next few decades of research yielded many negative results in the form of “anti-dynamo theories”. The most extreme examples of this came in 1934, when English mathematician Thomas George Cowling proved that simple 2D dynamos are impossible: the geodynamo problem requires more complicated 3D fields. This and other results worried many scientists and mathematicians for decades.
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“[Cowling’s] theorem had led to the suspicion that a self-excited fluid dynamo might not explain the existence of a geomagnetic field.”
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-Quote by George Backus. In Disagreements over continental drift, ocean floor evolution, and mantle convection continue, Frankel, H. (2012). , 1963–1965. In The Continental Drift Controversy (pp. 148-232). Cambridge: Cambridge University Press.
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Working at Scrips university in the 1960s, geophysicists George Backus and Robert Parker worked on the mathematical problem of the geodynamo.
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“In the early days of dynamo theory the failure of axisymmetric systems to perform as hoped led to a belief that perhaps all dynamos were impossible because of a yet-to-be-discovered general antidynamo theorem; then, of course, the source of the geomagnetic field would have to be sought elsewhere. It was therefore most important to establish mathematically the existence of a working dynamo as a matter of principle, no matter how artificial the motions.”
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-Quote by George Backus. In Foundations of geomagnetism . Backus, G., George, B., Parker, R. L., Parker, R., & Constable, C. (1996). Cambridge University Press.
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At the time, Parker supposedly would “test the intelligence” of new graduate students by asking them to find a solution for the self-sustaining dynamo problem. The sooner they returned to him exclaiming “It’s impossible!”, the smarter he judged they were!
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Backus did eventually find a solution, however it required unrealistic flows with periods of activity and stasis. More realistic solutions based on so called magnetohydrodynamics (MHD) were sought after. These are solutions where energy sources driving the fluid flow are specified, and the fluid flow and magnetic field are determined simultaneously by solving the full MHD equations. Unfortunately these equations are notoriously unintuitive and difficult to solve. For solutions to be found, the problem had to be numerically solved on large computers.
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Nowadays, modern supercomputers can model the 3D structure and time-dependence of temperature, fluid flow, and magnetic field inside the core. By exploring the possibilities of different boundary conditions, parameters, and resolutions, our understanding of the dynamics of the core have become deeper and broader.
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external_f_006 Simulation results of the Earth’s magnetic field, showing the radial component of the non-dipole field at the core-mantle boundary, projected to the Earth’s surface. Own work.
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However there is a limit to how far we can push the bounds of these simulations. A combination very low viscosity of core material and (relatively) rapid rotation of the Earth causes flows to have details on length scales below one meter. If we were to truly model the whole core up to this length scale, we would have to store over 1000 billion billion numbers. Even on the fastest computers in the world, calculations would take an inordinately long time–much longer than the age of the universe many times over.
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So how will the problem be solved in the future? Is it even necessary to push these simulations to extreme parameters? How do magnetic reversals fit into this picture? What about other planetary magnetic fields, such as Jupiter of Saturn? Answering these fundamental questions is the task of current and future geophysicists, and with continuing advances into both analytical and numerical studies of the core–along with new observations and data–we hope to uncover the elusive nature of the deep Earth.
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Related
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Geomagnetic reversals and marine magnetic anomalies May 31, 2018 In "Geomagnetism"
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Why is the geodynamo so complicated? December 1, 2021 In "Geomagnetism"
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Reversals and low ADM observations July 25, 2021 In "Geomagnetism"
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Published by posgeo
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My name is William Davis. I am a geophysics and data researcher at Scripps Institution of Oceanography. This is a blog about projects I am working on. View all posts by posgeo
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My name is William Davis. I am the Miles postdoctoral fellow at the Institute of Geophysics and Planetary Physics at UC San Diego. This blog is a place where I post about projects and other interests.
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