The origin of Earth’s magnetism, i.e. how does the Earth sustain a magnetic field throughout all of Earth history (termed dynamo theory), remains one of the grand challenges of geophysics. Tremendous progress has been made in the last decades, primarily through computer simulations that solve the underlying differential equations governing momentum transfer, electromagnetic induction and heat transfer, such that one could say that we have a “theory” for planetary magnetism that is plausible. This theory is one that invokes thermal convection arising from planetary cooling as the source of fluid motions that are able to create magnetic fields, since motion of an electrical conductor through a magnetic field creates electric currents by Faraday’s law, and these currents create magnetic fields through Ampere’s law. Thus the picture is of a so-called self-exciting dynamo mechanism; but the status of this theory is very unsatisfactory at the present time because many aspects of the process have to be grossly approximated, as a result of computational constraints. Computer models suffer from effects of viscosity that are too large. In an effort to remedy this situation we propose to compute models in which viscosity is ignored. This problem was posed 55 years ago by Taylor, and has resisted solution.
The problem is relevant to society because the magnetic field provides a protective shield around the Earth that shields us from radiation. We wish to determine how the field changes in time and what the future holds.
Summary results:
One breakthrough is concerned with one of the work-packages concerned with the theory of plesio-geostrophy. In this package we are computing the normal modes (eigenmodes) associated with a background magnetic field when the fluid flow is columnar. This is a short time scale theory that is aimed at data assimilation and that prediction of magnetic field behaviour on time scales of tens to hundreds of years, relevant to humans. We have reformulated the theory of Jackson and Maffei (2020) that reduces the number of unknowns. A new paper is in development (Maffei et al 2025).
We have discovered normal modes in the presence of a dipolar poloidal background magnetic field that are in accord with three-dimensional calculations (plesio-geostrophy calculations are 2-D). This augurs well for our time-stepping development.
While the computational challenges are being addressed, we have continued with background ancillary work.
A major paper in Journal of Fluid Mechanics has addressed, for the first time, internally-heated convection in the whole sphere (Sternberg Marti & Jackson, 2025).
We demonstrated the existence of dynamos in the Early Earth, prior to the formation of the inner core. In these dynamos the magnetic field is driven by secular cooling.
