Periodic Reporting for period 4 - UEMHP (Unravelling Earth’s magnetic history and processes)
Okres sprawozdawczy: 2024-04-01 do 2025-03-31
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.
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.
Work has proceeded on various avenues and so far a total of 27 peer-reviewed research papers have been published. We envisage another 10-15 papers will appear in the next 1-2 years.
A host of new results have been published that arose through pure serendipity. The ability to build a first-class research team led to unexpected results, because of the synergies that occurred during team meetings.
We develop 3-D models of convectively driven dynamos under the magnetostrophic approximation. This has required major code development and new associated mathematics. We have developed a new Jones-World transform for the whole sphere, published as Marti & Jackson (2021). We have used the code to compute convective solutions in a whole sphere and have discovered large scale vortices, never before seen, published in Lin & Jackson (2021).
We have made a breakthrough in the theory underpinning the magnetostrophic approximation by carrying out a normal mode analysis of the small oscillations that can exist in the core.
This is published as Luo & Jackson (2022a, b).
An unforeseen opportunity arose to develop short-timescale modes of the core's dynamics. We call these Plesio-Geostrophic models and they are optimal for describing the evolution of the field over decades. Thus the prediction problem may have a new method of solution, as we aspire to contribute to the production of future International Geomagnetic Reference Field models, which are produced every 5 years by the international community. This is published as Jackson & Maffei (2020).
A general theme in our work is to prove the underpinnings of the inviscid approach to the dynamo. This is rather technical and involves showing that the limit of viscosity tending to zero is the same as the limit in which viscosity is exactly zero.
We have also provided underpinnings for the magnetostrophic approximation.
We remain optimistic that we will finally succeed in creating convincingly converged inviscid dynamos (as described in the opening paragraph). We are working on developing the computer programme QuICC for the calculation of thermal convection and magnetic field generation in rapidly rotating planets. QuICC is a massively-parallel application running at CSCS, the Swiss Supercomputer Centre. The code runs on Piz Daint and LUMI, currently respectively the 37th and 5th most powerful computers in the world . We have made great theoretical progress and have demonstrated statistically stationary solutions, a huge breakthrough, such that the developments are on track.
A host of new results have been published that arose through pure serendipity. The ability to build a first-class research team led to unexpected results, because of the synergies that occurred during team meetings.
We develop 3-D models of convectively driven dynamos under the magnetostrophic approximation. This has required major code development and new associated mathematics. We have developed a new Jones-World transform for the whole sphere, published as Marti & Jackson (2021). We have used the code to compute convective solutions in a whole sphere and have discovered large scale vortices, never before seen, published in Lin & Jackson (2021).
We have made a breakthrough in the theory underpinning the magnetostrophic approximation by carrying out a normal mode analysis of the small oscillations that can exist in the core.
This is published as Luo & Jackson (2022a, b).
An unforeseen opportunity arose to develop short-timescale modes of the core's dynamics. We call these Plesio-Geostrophic models and they are optimal for describing the evolution of the field over decades. Thus the prediction problem may have a new method of solution, as we aspire to contribute to the production of future International Geomagnetic Reference Field models, which are produced every 5 years by the international community. This is published as Jackson & Maffei (2020).
A general theme in our work is to prove the underpinnings of the inviscid approach to the dynamo. This is rather technical and involves showing that the limit of viscosity tending to zero is the same as the limit in which viscosity is exactly zero.
We have also provided underpinnings for the magnetostrophic approximation.
We remain optimistic that we will finally succeed in creating convincingly converged inviscid dynamos (as described in the opening paragraph). We are working on developing the computer programme QuICC for the calculation of thermal convection and magnetic field generation in rapidly rotating planets. QuICC is a massively-parallel application running at CSCS, the Swiss Supercomputer Centre. The code runs on Piz Daint and LUMI, currently respectively the 37th and 5th most powerful computers in the world . We have made great theoretical progress and have demonstrated statistically stationary solutions, a huge breakthrough, such that the developments are on track.
Our work on the inviscid dynamo exceeds the state-of-the art. No other group in the world is equipped to work on this topic. We have preliminary saturated solutions. When the final technical issues are resolved, we will have the ability to
potentially revise the scaling laws for the magnetic fields of planets. The present-day laws are defective in being applicable to dynamos whose viscosity is a billion times larger than reality.
potentially revise the scaling laws for the magnetic fields of planets. The present-day laws are defective in being applicable to dynamos whose viscosity is a billion times larger than reality.