Magnetostrophic MRI in the Earth's Outer Core

We show that a simple, modified version of the Magnetorotational Instability (MRI) can develop in the outer liquid core of the Earth, in the presence of a background shear. It requires either thermal wind, or a primary instability, such as convection, to drive a weak differential rotation within the core. The force balance in the Earth's core is very unlike classical astrophysical applications of the MRI (such as gaseous disks around stars). Here, the weak differential rotation in the Earth core yields an instability by its constructive interaction with the planet's much larger rotation rate. The resulting destabilising mechanism is just strong enough to counteract stabilizing resistive effects, and produce growth on geophysically interesting timescales. We give a simple physical explanation of the instability, and show that it relies on a force balance appropriate to the Earth's core, known as magnetostrophic balance

Core-mantle boundary deformations and J2 variations resulting from the 2004 Sumatra earthquake

The deformation at the core-mantle boundary produced by the 2004 Sumatra earthquake is investigated by means of a semi-analytic theoretical model of global coseismic and postseismic deformation, predicting a millimetric coseismic perturbation over a large portion of the core-mantle boundary. Spectral features of such deformations are analysed and discussed. The time-dependent postseismic evolution of the elliptical part of the gravity field (J2) is also computed for different asthenosphere viscosity models. Our results show that, for asthenospheric viscosities smaller than 10^18 Pa s, the postseismic J2 variation in the next years is expected to leave a detectable signal in geodetic observations.Comment: 14 pages, 8 figures, 1 table. It will appear in Geophysical Journal Internationa

The Legal Standing of Shareholders Before Arbitral Tribunals: Has Any Rule of Customary International Law Crystallised?

Article published in the Michigan State International Law Review

Short Timescale Core Dynamics: TheoryandObservations

Fluid motions in the Earth's core produce changes in the geomagnetic field (secular variation) and are also an important ingredient in the planet's rotational dynamics. In this article we review current understanding of core dynamics focusing on short timescales of years to centuries. We describe both theoretical models and what may be inferred from geomagnetic and geodetic observations. The kinematic concepts of frozen flux and magnetic diffusion are discussed along with relevant dynamical regimes of magnetostrophic balance, tangential geostrophy, and quasi-geostrophy. An introduction is given to free modes and waves that are expected to be present in Earth's core including axisymmetric torsional oscillations and non-axisymmetric Magnetic-Coriolis waves. We focus on important recent developments and promising directions for future investigation

The strength of gravitational core-mantle coupling

Gravitational coupling between Earth's 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 Earth's 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

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