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

Electromagnetic coupling between the fluid core and its solid neighbours

At low-frequency, the nearly geostrophic force balance in the fluid core constrains axisymmetric fluid motions to be purely azimuthal and independent of position along the rotation axis. Fluid motions can thus be described by a set of concentric rigid cylinders, which are free to rotate about their common axis. When these cylinders are coupled by a magnetic field, the associated restoring forces give rise to torsional oscillations. These waves are thought to cause the observed fluctuations in the length of day by transferring angular momentum to the mantle and the inner core. The theory of torsional oscillations assumes that the stresses at the fluid-solid boundaries, which transfer angular momentum, do not alter the rigid nature of the fluid cylinders. This assumption is probably valid at the base of the mantle where the magnetic field is not large enough to alter the geostrophic balance in the fluid near the boundary. However, it is not valid at the inner core boundary (ICB) where higher field strengths are likely to perturb the geostrophic balance. In this case, the Lorentz force has to be retained in the momentum balance. A complete analytical solution is given for the influence of Lorentz forces in the core. The model problem involves a conducting and rotating fluid between two plane conducting boundaries in the presence of a background magnetic field. The solution gives us a clear view of how boundary layers form near the solid and how the coupling to the mantle and the inner core occurs.' More importantly, we can directly see how the inclusion of Lorentz forces alters the velocity from rigid rotation and how this velocity differs from that obtained with the torsional oscillation theory. For cylinders that terminate on the inner core, it is found that the rigid rotations are perturbed for a range of background magnetic field strength and frequencies. At decade periods, there is insufficient inertia to disrupt rigid rotations. However, for annual fluctuations, departures in the fluid velocity from rigid rotations are significant, which implies that the Lorentz force can not be neglected in the dynamics of the fluid core when calculating the electromagnetic coupling at the ICB.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat

Steady and fluctuating inner core rotation in numerical geodynamo models

International audienceWe present a systematic survey of numerical geodynamo simulations where the inner core is allowed to differentially rotate in the longitudinal direction with respect to the mantle. We focus on the long-term behaviour of inner core rotation, on timescales much longer than the overturn time of the fluid outer core, including the steady component of rotation. The inner core is subject to viscous and magnetic torques exerted by the fluid outer core, and a gravitational restoring torque exerted by the mantle. We show that the rate of steady inner core rotation is limited by the differential rotation between spherical surfaces that the convective dynamics can sustain across the fluid outer core. We further show that this differential rotation is determined by a torque balance between the resistive Lorentz force and the Coriolis force on spherical surfaces within the fluid core. We derive a scaling law on the basis of this equilibrium suggesting that the ratio of the steady inner core rotation to typical angular velocity within the fluid core should be proportional to the square root of the Ekman number, in agreement with our numerical results. The addition of gravitational coupling does not alter this scaling, though it further reduces the amplitude of inner core rotation. In contrast, the long-term fluctuations in inner core rotation remain proportional to the fluid core angular velocity, with no apparent dependency on the Ekman number. If the same torque balance pertains to the Earth's core conditions, the inner core rotation then consists in a very slow super rotation of a few degrees per million years, superimposed over large fluctuations (at about a tenth of a degree per year). This suggests that the present-day seismically inferred inner core rotation is a fragment of a time-varying signal, rather than a steady super rotation. For the inner core rotation fluctuations not to cause excessive variations in the length-of-day, the strength of the gravitational coupling between the inner core and the mantle must be smaller than previously published values. We finally explore how the torque balance which we observe in our models could be altered in planetary cores, yielding possibly larger values of the steady rotation

Libration- and Precession-driven Dissipation in the Fluid Cores of the TRAPPIST-1 Planets

The seven planets orbiting TRAPPIST-1 have sizes and masses similar to Earth and mean densities that suggest that their interior structures are comprised of a fluid iron core and rocky mantle. Here we use idealized analytical models to compute estimates of the viscous dissipation in the fluid cores of the TRAPPIST-1 planets induced by mantle libration and precession. The dissipation induced by the libration at orbital periods is largest for TRAPPIST-1b, of the order of 600 MW, and decreases with orbital distance, to values of 5–500 W for TRAPPIST-1h, depending on its triaxial shape. Extrapolating these results to the larger libration amplitudes expected at longer periods, dissipation may perhaps be as high as 1 TW in TRAPPIST-1b. Orbital precession induces a misalignment between the spin axes of the fluid core and mantle of a planet, the amplitude of which depends on the resonant amplification of its free precession and free core nutation. Assuming Cassini states, we show that the dissipation from this misalignment can reach a few TW for planets e and f. Our dissipation estimates are lower bounds, as we neglect ohmic dissipation, which may dominate if the fluid cores of the TRAPPIST-1 planets sustain magnetic fields. Our results suggest that dissipation induced by precession can be of the same order as tidal dissipation for the outermost planets, may perhaps be sufficient to supply the power to a generate a magnetic field in their liquid cores, and likely played an important role in the evolution of the TRAPPIST-1 system

Gravitational Constraints on the Earth's Inner Core Differential Rotation

International audienceThe differential axial rotation of the solid inner core (IC) is suggested by seismic observations and expected from core dynamics models. A rotation of the IC by an angle α takes its degree 2, order 2 topography (peak‐to‐peak amplitude δh ) out of its gravitational alignment with the mantle. This creates a gravity variation of degree 2, order 2 proportional to δh and to α . Here, we use gravity observations from Satellite Laser Ranging, the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On to reconstruct the time‐variable S 2,2 Stokes coefficient. We show that for δh = 90 m, S2,2 provides upper bounds on α of 0.09°, 0.3°, and 0.4° at periods of ∼4, ∼6, and ∼12 years, respectively. These are overestimates, as our reconstructed S2,2 signal likely remains polluted by hydrology, although viscous relaxation of the IC can permit larger amplitudes.La rotation axial différentielle du noyau solide est suggérée par des observations sismiques et prévue par des modélisations des dynamiques du noyau. Une rotation de la graine par un angle α amène sa topographie de degré 2 et d'ordre 2 (d'amplitude pic à pic δh) en dehors de son alignement gravitationnel avec le manteau. Cela provoque une variation du champ de gravité de degré 2 et d'ordre 2 proportionnelle à α et δh. Nous utilisons ici les observations du champ de gravité du SLR et de GRACE(-FO) pour reconstruire la série temporelle du coefficient de Stokes S2,2. Nous démontrons que, en supposant δh = 90 m, S2,2 fournit une contrainte maximale pour α de 0.09°, 0.3° et 0.4°, respectivement aux périodes 4, 5 à 6 et 8 à 12 ans. Ces contraintes sont surestimés car notre estimation de S2,2 est fort probablement polluée des signaux hydrologiques. Toutefois, le comportement de relaxation visqueuse du noyau, encore mal modélisé, peut permettre des contraintes plus souples

Interannual variations of degree 2 from geodetic observations and surface processes

International audienc

Interannual variations of degree 2 from geodetic observations and surface processes

International audienc

Core Eigenmodes and their Impact on the Earth’s Rotation

Abstract Changes in the Earth’s rotation are deeply connected to fluid dynamical processes in the outer core. This connection can be explored by studying the associated Earth eigenmodes with periods ranging from nearly diurnal to multi-decadal. It is essential to understand how the rotational and fluid core eigenmodes mutually interact, as well as their dependence on a host of diverse factors, such as magnetic effects, density stratification, fluid instabilities or turbulence. It is feasible to build detailed models including many of these features, and doing so will in turn allow us to extract more (indirect) information about the Earth’s interior. In this article, we present a review of some of the current models, the numerical techniques, their advantages and limitations and the challenges on the road ahead