Planetary gyre, time-dependent eddies, torsional waves, and equatorial jets at the Earth's core surface

We report a calculation of time-dependent quasi-geostrophic core flows for 1940-2010. Inverting recursively for an ensemble of solutions, we evaluate the main source of uncertainties, namely the model errors arising from interactions between unresolved core surface motions and magnetic fields. Temporal correlations of these uncertainties are accounted for. The covariance matrix for the flow coefficients is also obtained recursively from the dispersion of an ensemble of solutions. Maps of the flow at the core surface show, upon a planetary-scale gyre, time-dependent large-scale eddies at mid-latitudes and vigorous azimuthal jets in the equatorial belt. The stationary part of the flow predominates on all the spatial scales that we can resolve. We retrieve torsional waves that explain the length-of-day changes at 4 to 9.5 years periods. These waves may be triggered by the nonlinear interaction between the magnetic field and sub-decadal non-zonal motions within the fluid outer core. Both the zonal and the more energetic non-zonal interannual motions were particularly intense close to the equator (below 10 degrees latitude) between 1995 and 2010. We revise down the amplitude of the decade fluctuations of the planetary scale circulation and find that electromagnetic core-mantle coupling is not the main mechanism for angular momentum exchanges on decadal time scales if mantle conductance is 3 10 8 S or lower

Stochastic modelling of regional archaeomagnetic series

SUMMARY We report a new method to infer continuous time series of the declination, inclination and intensity of the magnetic field from archeomagnetic data. Adopting a Bayesian perspective, we need to specify a priori knowledge about the time evolution of the magnetic field. It consists in a time correlation function that we choose to be compatible with present knowledge about the geomagnetic time spectra. The results are presented as distributions of possible values for the declination, inclination or intensity. We find that the methodology can be adapted to account for the age uncertainties of archeological artefacts and we use Markov Chain Monte Carlo to explore the possible dates of observations. We apply the method to intensity datasets from Mari, Syria and to intensity and directional datasets from Paris, France. Our reconstructions display more rapid variations than previous studies and we find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archeological artefacts

Numerical study of a rotating fluid in a spheroidal container.

The motion of an incompressible, viscous rotating fluid contained in a spheroidal conainer is studied by a direct numerical simulation in a oblate speroidal system. An appropriate formalism is first derived which allows us to expand any scalar field in spherical harmonics and to decompose any vector field into its sphero-poloidal and sphero-toroidal scalar parts

Axial invariance of rapidly varying diffusionless motions in the Earth's core interior

Geostrophic jets propagating as Alfv\'en waves are shown to arise ina rapidly rotating spherical shell permeated by a magnetic field among the transient motions set up by an impulsive rotation of the inner core. These axially invariant motions evolve on a time-scale which is short compared to the magnetic diffusion time. The numerical study is taken as illustrative of a more general point: on such a fast time-scale the dimensionless number appropriate to compare the rotation and magnetic forces is independent of the magnetic diffusivity in contrast with the often used Elsasser number. Extension of the analysis to non-axisymmetrical motions is supported by published studies of dynamo models and magnetic instabilities

Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation

International audienceWe introduce a quasi-geostrophic model of core dynamics, which aims at describ- ing core processes on geomagnetic secular variation timescales. It extends the for- malism of Alfv ́en torsional oscillations by incorporating non-zonal motions. Within this framework, the magnetohydrodynamics takes place in the equatorial plane; it involves quadratic magnetic quantities, which are averaged along the direction of ro- tation of the Earth. In addition, the equatorial flow is projected on the core-mantle boundary. It interacts with the magnetic field at the core surface, through the radial component of the magnetic induction equation. That part of the model connects the dynamics and the observed secular variation, with the radial component of the magnetic field acting as a passive tracer. We resort to variational data assimilation to construct formally the relationship between model predictions and observations. Variational data assimilation seeks to minimize an objective function, by computing its sensitivity to its control variables. The sensitivity is efficiently calculated after in- tegration of the adjoint model. We illustrate that framework with twin experiments, performed first in the case of the kinematic core flow inverse problem, and then in the case of Alfv ́en torsional oscillations. In both cases, using the adjoint model allows us to retrieve core state variables which, while taking part in the dynamics, are not directly sampled at the core surface. We study the effect of several factors on the solution (width of the assimilation time window, amount and quality of data), and we discuss the potential of the model to deal with real geomagnetic observations

ensemble inversion of time-dependent core flow models

International audienceQuasi-geostrophic core flow models are built from two secular variation models spanning the periods 1960--2002 and 1997--2008. We rely on an ensemble method to account for the contributions of the unresolved small-scale magnetic field interacting with core surface flows to the observed magnetic field changes. The different core flow members of the ensemble solution agree up to spherical harmonic degree $\ell\simeq 10$, and this resolved component varies only weakly with regularization. Taking into account the finite correlation time of the small-scale concealed magnetic field, we find that the time variations of the magnetic field occurring over short time-scales, such as the geomagnetic jerks, can be accounted for by the resolved -- large scale -- part of the flow to a large extent. Residuals from our flow models are 30 \% smaller for recent epochs, after 1995. This result is attributed to an improvement in the quality of geomagnetic data. The magnetic field models show little frozen-flux violation for the most recent epochs, within our estimate of the apparent magnetic flux changes at the core-mantle boundary arising from spatial resolution errors. We associate the more important flux changes detected at earlier epochs with uncertainties in the field models at large harmonic degrees. Our core flow models show, at all epochs, an eccentric and planetary scale anti-cyclonic gyre circling around the cylindrical surface tangent to the inner core, at approximately 30$^{\circ}$ and 60$^{\circ}$ latitude under the Indian and Pacific oceans, respectively. They account well for the changes in core angular momentum for the most recent epochs

Pressure torque of torsional Alfvén modes acting on an ellipsoidal mantle

We investigate the pressure torque between the fluid core and the solid mantle arising from magnetohydrodynamic modes in a rapidly rotating planetary core. A two-dimensional reduced model of the core fluid dynamics is developed to account for the non-spherical core-mantle boundary. The simplification of such a quasi-geostrophic model rests on the assumption of invariance of the equatorial components of the fluid velocity along the rotation axis. We use this model to investigate and quantify the axial torques of linear modes, focusing on the torsional Alfvén modes (TM) in an ellipsoid. We verify that the periods of these modes do not depend on the rotation frequency. Furthermore, they possess angular momentum resulting in a net pressure torque acting on the mantle. This torque scales linearly with the equatorial ellipticity. We estimate that for the TM calculated here topographic coupling to the mantle is too weak to account for the variations in the Earth’s length-of-day

On the reflection of Alfvén waves and its implication for Earth's core modelling

Alfvén waves propagate in electrically conducting fluids in the presence of a magnetic field. Their reflection properties depend on the ratio between the kinematic viscosity and the magnetic diffusivity of the fluid, also known as the magnetic Prandtl number Pm. In the special case, Pm = 1, there is no reflection on an insulating, no-slip boundary, and the incoming wave energy is entirely dissipated in the boundary layer. We investigate the consequences of this remarkable behaviour for the numerical modelling of torsional Alfvén waves (also known as torsional oscillations), which represent a special class of Alfvén waves, in rapidly rotating spherical shells. They consist of geostrophic motions and are thought to exist in the fluid cores of planets with internal magnetic field. In the geophysical limit Pm ≪ 1, these waves are reflected at the core equator, but they are entirely absorbed for Pm = 1. Our numerical calculations show that the reflection coefficient at the equator of these waves remains below 0.2 for Pm ≥ 0.3, which is the range of values for which geodynamo numerical models operate. As a result, geodynamo models with no-slip boundary conditions cannot exhibit torsional oscillation normal mode