Mathieu Dumberry

The origin of geomagnetic jerks

Geomagnetic jerks, which in the second half of the twentieth century occurred in 1969 (refs 1, 2), 1978 (refs 3, 4), 1991 (ref. 5) and 1999 (ref. 6), are abrupt changes in the second time-derivative (secular acceleration) of the Earths magnetic field. Jerks separate periods of almost steady secular acceleration, so that the first time-derivative (secular variation) appears as a series of straight-line segments separated by geomagnetic jerks. The fact that they represent a reorganization of the secular variation implies that they are of internal origin (as has been established through spherical harmonic analysis), and their short timescale implies that they are due to a change in the fluid flow at the surface of the Earths core (as has also been established through mapping the time-varying flow at the core surface). However, little is understood of their physical origin. Here we show that geomagnetic jerks can be explained by the combination of a steady flow and a simple time-varying, axisymmetric, equatorially symmetric, toroidal zonal flow. Such a flow is consistent with torsional oscillations in the Earths core, which are simple oscillatory flows in the core that are expected on theoretical grounds, and observed in both core flow models and numerical dynamo models.

CARRE: a quasi-orthogonal mesh generator for 2D edge plasma modelling

A computer code is described which automatically generates a structured curvilinear quasi-orthogonal mesh of the type used in several models of transport for the edge and divertor regions in tokamak fusion experiments. The method considered works from numerically generated equilibria and from digitized parametrisations of structures and boundaries in the simulation domain. It therefore produces realistic computational meshes which allow comparisons between simulation results and experiments. The method is well adapted to the generation of meshes for a number of interesting magnetic field topologies, such as single null, connected and disconnected double null divertor geometries.

Constraints on core‐mantle electromagnetic coupling from torsional oscillation normal modes

[1] Decadal axial angular momentum variations in the Earth’s core are believed to be carried by the normal modes of torsional oscillations. Coupling with the mantle transfers angular momentum to the latter, leading to changes in length of day (LOD). Electromagnetic stresses at the core-mantle boundary (CMB) may be an important coupling mechanism as well as a source of dissipation for torsional oscillations. In this work, we investigate whether the observed spectra of fluid core velocities and LOD variations can be both explained in terms of the normal modes of torsional oscillations when the only coupling with the mantle is through electromagnetic stresses. We show that this explanation may be true when the magnetic field at the CMB is based on a downward continuation of surface observations, provided the conductance at the bottom of the mantle does not greatly exceed 10 8 S and small wavelength field features do not contribute more than approximately 25% of the total radial field at the CMB. A larger conductance or a higher amplitude radial magnetic field results in a damping of the normal modes of torsional oscillation that is sufficiently large that they should not be detectable. In particular, we show that this is the case for the conductance and radial magnetic field that are inferred from the Earth’s forced nutations. If these constraints are correct, the decadal periodicities in the fluid velocity and LOD must then represent the preferred frequencies of the excitation mechanism of torsional oscillations rather than the signature of the free modes. Citation: Dumberry, M., and J. E. Mound (2008), Constraints on core-mantle electromagnetic coupling from torsional oscillation normal modes, J. Geophys. Res., 113, B03102, doi:10.1029/2007JB005135.

Reconciling past changes in Earth’s rotation with 20th century global sea-level rise: Resolving Munk’s enigma

Reanalysis of Earth rotation observations reconciles them with globally averaged sea-level change in the 20th century. In 2002, Munk defined an important enigma of 20th century global mean sea-level (GMSL) rise that has yet to be resolved. First, he listed three canonical observations related to Earth’s rotation [(i) the slowing of Earth’s rotation rate over the last three millennia inferred from ancient eclipse observations, and changes in the (ii) amplitude and (iii) orientation of Earth’s rotation vector over the last century estimated from geodetic and astronomic measurements] and argued that they could all be fit by a model of ongoing glacial isostatic adjustment (GIA) associated with the last ice age. Second, he demonstrated that prevailing estimates of the 20th century GMSL rise (~1.5 to 2.0 mm/year), after correction for the maximum signal from ocean thermal expansion, implied mass flux from ice sheets and glaciers at a level that would grossly misfit the residual GIA-corrected observations of Earth’s rotation. We demonstrate that the combination of lower estimates of the 20th century GMSL rise (up to 1990) improved modeling of the GIA process and that the correction of the eclipse record for a signal due to angular momentum exchange between the fluid outer core and the mantle reconciles all three Earth rotation observations. This resolution adds confidence to recent estimates of individual contributions to 20th century sea-level change and to projections of GMSL rise to the end of the 21st century based on them.

The strength of gravitational core-mantle coupling

Gravitational coupling between Earths core and mantle has been proposed as an explanation for a 6 year variation in the length-of-day (ΔLOD) signal and plays a key role in the possible superrotation of the inner core. Explaining the observations requires that the strength of the coupling, Γ, falls within fairly restrictive bounds; however, the value of Γ is highly uncertain because it depends on the distribution of mass anomalies in the mantle. We estimate Γ from a broad range of viscous mantle flow models with density anomalies inferred from seismic tomography. Requiring models to give a correlation larger than 70% to the surface geoid and match the dynamic core-mantle boundary ellipticity inferred from Earths nutations, we find that 3 × 10 19 < Γ < 2 × 10 20 N m, too small to explain the 6 year ΔLOD signal. This new constraint on Γ has important implications for core-mantle angular momentum transfer and on the preferred mode of inner core convection.

Influence of an inner core on the long-period forced librations of Mercury

Abstract The planetary perturbations on Mercury’s orbit lead to long-period forced librations of Mercury’s mantle. These librations have previously been studied for a planet with two layers: a mantle and a liquid core. Here, we calculate how the presence of a solid inner core in the liquid outer core influences the long-period forced librations. Mantle–inner core coupling affects the long-period libration dynamics mainly by changing the free libration: first, it lengthens the period of the free libration of the mantle, and second, it adds a second free libration, closely related to the free gravitational oscillation between the mantle and inner core. The two free librations have periods between 2.5 and 18y depending on the internal structure. We show that large amplitude long-period librations of a few tens of arcsec are generated when the period of a planetary forcing approaches one of the two free libration periods. These amplitudes are sufficiently large to be detectable by spacecraft measurements of the libration of Mercury. The amplitudes of the angular velocity of Mercury’s mantle at planetary forcing periods are also amplified by the resonances, but remain much smaller than the current precision of Earth-based radar observations unless the period is very close to a free libration period. The inclusion of mantle–inner core coupling in the rotation model does not significantly improve the fit to the radar observations. This implies that it is not yet possible to determine the size of the inner core of Mercury on the basis of available observations of Mercury’s rotation rate. Future observations of the long-period librations may be used to constrain the interior structure of Mercury, including the size of its inner core.

On the validity of the geostrophic approximation for calculating the changes in the angular momentum of the core

Abstract The changes in the length of day at decade periods are attributable to exchanges of angular momentum between the core and the mantle. It is commonly assumed that the changes in angular momentum in the fluid are carried by geostrophic flows which are characterized by the rotation of rigid cylindrical shells aligned with the Earths rotation axis. In this work, we explore the validity of this assumption using the simple geometry of a plane fluid layer between two solid boundaries. Coupling at the boundaries is done by electromagnetic interactions. We quantify the conditions under which the motion of the fluid that results from this coupling is accurately described by geostrophic flows. We find that for the region outside the so-called tangent cylinder, the geostrophic approximation is valid for all periods of oscillation longer than a few days. For the region inside the tangent cylinder, the geostrophic nature of the flow is broken at annual and shorter periods by the propagation of MC waves.

Up-down symmetry in double null divertor experiments and magnetic field topology

The effect of up-down asymmetries is considered for transport in a double null divertor geometry. Particular attention is paid to the type of asymmetries associated with a disconnection of the two X points, which cause differences in the flows to the top and bottom diverters. Examples are given of the conditions under which such asymmetries arise, and quantitative estimates of transport are made. The sensitivity to these asymmetries is such that they seriously complicate the quantitative interpretation of transport experiments conducted in double null geometry

ARANEA, a program for generating unstructured triangular meshes with a JAVA Graphics User Interface

ARANEA is a program that automatically generates unstructured triangular meshes on two-dimensional planar domains. The program implements a Graphics User Interface (GUI) that enables the user to read, edit and save a number of components required in the construction of a mesh. The program is written in JAVA, version 1.1. It is useful for constructing meshes of the type required to solve partial differential equations with finite elements over complex two-dimensional domains.

Comment on “Could the Mw = 9.3 Sumatra earthquake trigger a geomagnetic jerk?”

In a recent issue of Eos, Florindo et al. [2005] suggest that large seismic events, such as the magnitude 9.3 Sumatra earthquake of 26 December 2004, may cause changes in topography at the core-mantle boundary (CMB), thereby affecting flow in the core. They hypothesize that this effect may trigger a geomagnetic jerk, which would be observed at Earths surface after a time delay to allow for the signal to propagate through the weakly conducting mantle. However, they do not provide any estimates of the amplitude or form of the CMB topography changes that are required, or of the actual CMB deformation that may have occurred as a result of the Sumatra event. Here, I argue that it is unlikely that large earthquakes can lead to geomagnetic jerks.