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The cause for the damping of the Earth's free core nutation (FCN) and the free inner core nutation eigenmodes has been a matter of debate since the earliest reliable estimations from nutation observations were made available. Numerical studies are difficult given the extreme values of some of the parameters associated with the Earth's fluid outer core, where important energy dissipation mechanisms can take place. We present a fully 3D numerical model for the FCN capable of describing accurately viscous and Ohmic dissipation processes taking place in the bulk of the fluid core as well as in the boundary layers. We find an asymptotic regime, appropriate for Earth's parameters, where viscous and Ohmic processes contribute to the total damping, with the dissipation taking place almost exclusively in the boundary layers. By matching the observed nutational damping, we infer an enhanced effective viscosity matching and validating methods from previous studies. We suggest that turbulence caused by the Earth's precession can be a source for the enhanced viscosity.

nutations, Very Long Baseline Interferometry

We compute the inertial modes of a freely rotating two-layer planetary model with an ellipsoidal inviscid fluid core and a perfectly rigid mantle. We present a method to derive analytical formulae for the frequencies of the free core nutation (FCN) and Chandler wobble (CW) that are valid to all orders of the dynamical flattening of the core and mantle, and we show how the FCN and CW are the direct generalization of the purely fluid spin-over mode and of the Eulerian wobble to the case where the mantle can oscillate freely around a state of steady rotation. Through a numerical computation for an axisymmetric (oblate spheroidal) planet, we demonstrate that all other inertial modes of the steadily rotating fluid core are also free modes of the freely rotating two-layer planet.

The year 2017 saw Cassini plunge to its demise into Saturn's atmosphere, putting an end to a twenty-year odyssey that challenged our beliefs on the possible presence of water and life elsewhere in the Universe. The Cassini-Huygens mission left a rich legacy of observations of Saturn and its ever-evolving world of rings and moons. The intense geological activity discovered throughout Enceladus's south-polar terrain is a puzzle in itself: where are the geysers' water supplies? how abundant is water? has it always remained unfrozen, and if so, how? The purpose of this thesis is to address some of these questions using Cassini's measurements of Enceladus's gravity field, surface topography, and diurnal libration. The latter, a subtle modulation of the moon's spin rate over its eccentric orbit around Saturn, induces slight offsets in images taken by Cassini's cameras. To correctly interpret the observations, we develop new, mutually consistent isostasy and libration models, correct to the second order in the flattenings associated with the moon's triaxial shape. We then show that the liquid water reservoir must be a global ocean as opposed to a regional sea, and obtain the best post-Cassini constraints on the thickness of the icy crust, the ocean, and the core. To alleviate the mathematical burden, we present a systematic method to handle equations in near-spherical geometries based on series expansions in powers of the flattenings, and prove their convergence. By sharing our code TenGSHui, we hope to entice the community into more reproducible and intuitive modelling, and reconnect global geodynamics with its most fundamental principles., (SC - Sciences) -- UCL, 2019

The Earth is a rapidly rotating body. The centrifugal pull makes its shape resemblea flattened ellipsoid and Coriolis forces support waves in its fluid core, known asinertial waves. These waves can lead to global oscillations, or modes, of the fluid.Periodic variations of the Earth’s rotation axis (nutations) can lead to an exchange ofangular momentum between the mantle and the fluid core and excite these inertialmodes. In addition to viscous torques that exist regardless of the shape of theboundaries, the small flattening of the core-mantle boundary (CMB) allows inertialmodes to exert pressure torques on the mantle. These torques effectively couple therigid-body dynamics of the Earth with the fluid dynamics of the fluid core. Herewe present the first high resolution numerical model that solves simultaneously therigid body dynamics of the mantle and the Navier-Stokes equation for the liquidcore. This method takes naturally into account dissipative processes in the fluidthat are ignored in current nutation models. We find that the Free Core Nutation(FCN) mode, mostly a toroidal fluid flow if the mantle has a large moment of inertia,enters into resonance with nearby modes if the mantle’s moment of inertia is reduced.These mode interactions seem to be completely analogous to the ones discovered bySchmitt (2006) in a uniformly rotating ellipsoid with varying flattening

We determine constraints on the ice shell and ocean of Enceladus from the observed libration at orbital period by assessing the effects of uncertainties in the size, density, rigidity, and viscosity of the internal layers and of the non-hydrostatic structure on the libration. The observed libration amplitude implies that the average thickness of the ice shell is between 14 km and 26 km and that the ocean is 21 km to 67 km thick.

Phobos and Deimos, the two small satellites of Mars, are thought either to be asteroids captured by the planet or to have formed in a disc of debris surrounding Mars following a giant impact. Both scenarios, however, have been unable to account for the current Mars system. Here we use numerical simulations to suggest that Phobos and Deimos accreted from the outer portion of a debris disc formed after a giant impact on Mars. In our simulations, larger moons form from material in the denser inner disc and migrate outwards due to gravitational interactions with the disc. The resulting orbital resonances spread outwards and gather dispersed outer disc debris, facilitating accretion into two satellites of sizes similar to Phobos and Deimos. The larger inner moons fall back to Mars after about 5 million years due to the tidal pull of the planet, after which the two outer satellites evolve into Phobos- and Deimos-like orbits. The proposed scenario can explain why Mars has two small satellites instead of one large moon. Our model predicts that Phobos and Deimos are composed of a mixture of material from Mars and the impactor., SCOPUS: ar.j, info:eu-repo/semantics/published

The rotation rate of Titan, the largest satellite of Sat- urn, and of Enceladus, the most geologically active satellite of Saturn, is on average equal to their or- bital mean motion. Here we discuss small deviations from the average rotation synchronous with their or- bital motion. We examine different causes at various time scales and assess possible consequences and the potential of using librations as a probe of the interior structure of the satellites.

Titan, the largest satellite of Saturn, rotates synchronously with its orbital motion. As a result of Titan's non-spherically symmetric mass distribution, the 1:1 spin-orbit resonance is stable, but small variations in the rotation rate around the equilibrium state are possible and measurements of these librations have been reported several times (Lorenz et al. 2008, Stiles et al 2008, Stiles et al. 2010, Meriggiola et al. 2012). The librations contain information on the interior of Titan, and in particular can be used to constrain several properties of the ice shell of Titan (Van Hoolst et al. 2013). The measurements of the rotation variations are based on determinations of the shift in position of Cassini SAR radar images taken during different flybys. The results, however, do not agree and the spin variations are smaller for the latest studies. Theoretical estimates show that variations in the rotation rate can occur for several reasons (Van Hoolst et al. 2013, Richard et al. 2014). First, Titan's rotation changes with a period equal to Titan's orbital period as a result of the gravitational torque exerted by Saturn. Second, dynamic variations in the atmosphere of Titan induce changes in Titan's rotation with a main period equal to half the orbital period of Saturn. Third, free librations with periods of the order of a year might be excited, and fourth, deviations from a Keplerian orbit perturb the rotation at additional frequencies. Here, we report on different theoretical aspects of the librations and compare theoretical predictions with observational results. We consider the influence of the rheology of the ice shell and take into account Cassini measurements of the external gravitational field and of the topography of Titan. We also evaluate the librations induced by Titan's hydrocarbon seas and use the most recent results of Titan's atmosphere dynamics.