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Modelling Earth’s magnetic field reversals

par Nathanaël SCHAEFFER - 11 janvier 2018

Magnetic field reversals have also been observed in both experiments and simulations.
In numerical simulations, obtaining long-enough time-series is possible only with high viscosity.
In such simulation, the mechanism seems to involve inertia or “turbulence” levels (as measured by the local Rossby number) but this is unlikely for the Earth’s core because inertia is expected to be negligible there.
However, the weak magnetic field (magnetic energy much lower than kinetic energy) in all these reversing dynamos questions their relevance.
Indeed, from observations of the geomagnetic field, deduced a very strong magnetic field with energy 10 000 times larger than the kinetic energy in the Earth’s core.
And still, reversing dynamos with strong magnetic field have not been found yet.
This short review of the state of the art shows that there has been different %and sometimes contradictory
mechanisms invoked for reversals in numerical models, none of which seems to explain satisfactorily the Earth’s polarity reversals.

The overarching goal of this project is to break the numerical deadlocks in geodynamo simulations, motivated by an outstanding scientific question : how and why does the magnetic field reverse polarity ?

To simulate and understand Earth’s reversals, we need models that can run very quickly — to span long time ranges — at low viscosity.
Lowering further the viscosity implies that smaller and smaller scales must be resolved as they are deeply influencing the large scales through non-linear interaction.
Using highly optimized and parallelized codes, the required increase in spatial resolution is possible, but only for short time-spans,
which prevent the study of reversals, a feature that intrinsically requires long time-spans.
This situation will not improve much in the foreseeable future, unless a radically different approach is used.

To avoid computing the huge range of scales required by low viscosity simulations,
we will use Large Eddy Simulations (LES), where only the largest scales are simulated, and the effects of unresolved small scales are prescribed by subgrid-scale models.
In this PhD thesis, the candidate will couple a 3D code to simulate the large-scales with a quasi-geostrophic (2D approach on the small scales).
This will allow to span long time-scales and study reversals in realistic regimes.

By comparing the simulations with published paleomagnetic data, we will test several hypotheses (influence of the solid inner-core size and conductivity, heterogeneous heat flux controlled by mantle and plate tectonics, ...).
Data-assimilation framework and/or Machine Learning may also be used to further constrain our model.

References :
Schaeffer+ 2017
Takahashi+ 2017
Davies+ 2004

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