The magnetic field inside the Earth's fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core-mantle boundary is 0.3 mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth's core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2 mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n

We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convection-driven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earth's core regime by lowering viscosity (magnetic Prandtl number P m = 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 strong-field, dipole-dominated 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 non-zonal. Spatio-temporal analysis indicates that the low-frequency, non-zonal flow is quite geostrophic (columnar) and predominantly large-scale: an m=1 eddy spontaneously emerges in our most extreme simulations, without any heterogeneous boundary forcing.Our spatio-temporal analysis further reveals that (i) the low-frequency, 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 high-frequency 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 3-term 1 arXiv:1701.01299v3 [physics.geo-ph] 15 Jun 2017 MAC balance -involving Coriolis, Lorentz and buoyancy forces. However, smallscale ( E 1/3 ) quasi-geostrophic convection is still observed in the regions of low magnetic intensity.

International audienceWe present core flows constructed from high resolution secular variation (SV) models for the epochs 2001, 2002.5 and 2004, assuming that these flows are quasi-geostrophic in the core interior and that they do not cross the axial cylindrical surface tangent to the inner core. A large jet encircling the inner core and carrying a significant part of the core angular momentum and axial vortices of ∼700 km diameter mainly clustering around the cylinder tangent to the solid inner core, are inferred from geomagnetic SV. New regularizations are suggested from dynamic considerations. It is found that medium and small-scale velocity fields contribute significantly to the large-scale SV. Accordingly, final models of core flows are calculated after an iterative process, whereby the magnetic field variation produced by small-scale stochastic magnetic fields and medium to small-scale computed velocity fields are incorporated into the inversion itself as modelling errors. This study represents a significant step in an effort to join geomagnetic observations and the fluid core dynamics on short timescales