Turbulent geodynamo simulations: a leap towards Earth's core
Abstract
We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convectiondriven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earth's core regime by lowering viscosity (magnetic Prandtl number Pm = 0.1) while maintaining vigorous convection (magnetic Reynolds number Rm > 500) and rapid rotation (Ekman number E = 10^{7}) at the limit of what is feasible on today's supercomputers. A detailed and comprehensive analysis highlights several key features matching geomagnetic observations or dynamo theory predictions—all present together in the same simulation—but it also unveils interesting insights relevant for Earth's core dynamics. In this strongfield, dipoledominated dynamo simulation, the magnetic energy is one order of magnitude larger than the kinetic energy. The spatial distribution of magnetic intensity is highly heterogeneous, and a stark dynamical contrast exists between the interior and the exterior of the tangent cylinder (the cylinder parallel to the axis of rotation that circumscribes the inner core). In the interior, the magnetic field is strongest, and is associated with a vigorous twisted polar vortex, whose dynamics may occasionally lead to the formation of a reverse polar flux patch at the surface of the shell. Furthermore, the strong magnetic field also allows accumulation of light material within the tangent cylinder, leading to stable stratification there. Torsional Alfvén waves are frequently triggered in the vicinity of the tangent cylinder and propagate towards the equator. Outside the tangent cylinder, the magnetic field inhibits the growth of zonal winds and the kinetic energy is mostly nonzonal. Spatiotemporal analysis indicates that the lowfrequency, nonzonal flow is quite geostrophic (columnar) and predominantly largescale: an m = 1 eddy spontaneously emerges in our most extreme simulations, without any heterogeneous boundary forcing. Our spatiotemporal analysis further reveals that (i) the lowfrequency, largescale flow is governed by a balance between Coriolis and buoyancy forces—magnetic field and flow tend to align, minimizing the Lorentz force; (ii) the highfrequency flow obeys a balance between magnetic and Coriolis forces; (iii) the convective plumes mostly live at an intermediate scale, whose dynamics is driven by a threeterm MAC balance—involving Coriolis, Lorentz and buoyancy forces. However, smallscale (≃E^{1/3}) quasigeostrophic convection is still observed in the regions of low magnetic intensity.
 Publication:

Geophysical Journal International
 Pub Date:
 October 2017
 DOI:
 10.1093/gji/ggx265
 arXiv:
 arXiv:1701.01299
 Bibcode:
 2017GeoJI.211....1S
 Keywords:

 Dynamo: theories and simulations;
 Magnetic field variations through time;
 Rapid time variations;
 Numerical modelling;
 Planetary interiors;
 Physics  Geophysics;
 Physics  Fluid Dynamics
 EPrint:
 48 pages, 28 figures, accepted for publication in GJI