Internal energy dissipation in Enceladus's ocean from tides and libration and the role of inertial waves

Enceladus is characterised by a south polar hot spot associated with a large outflow of heat, the source of which remains unclear. We compute the viscous dissipation resulting from tidal and libration forcing in the moon's subsurface ocean using the linearised Navier-Stokes equation in a 3-dimensional spherical model. We conclude that libration is the dominant cause of dissipation at the linear order, providing up to about 0.001 GW of heat to the ocean, which remains insufficient to explain the (about) 10 GW observed by Cassini. We also illustrate how resonances with inertial modes can significantly augment the dissipation. Our work is an extension to Rovira-Navarro et al. [2019] to include the effects of libration. The model developed here is readily applicable to the study of other moons and planets

Spherically Symmetric solutions on a cosmological dynamical background with BSSN equations

International audienceWe give a summary of the work presented in [1]. We expose a numerical method for the study of cosmological problems in spherical symmetry in full General Relativity. The stability of the code close to the origin is made possible through the use of the Partially Implicit Runge-Kutta (PIRK) algorithm described in [2]. We demonstrate the stability and convergence properties and give a simple application to the evolution of the Lemaître-Tolman-Bondi spacetime. This work is a generalisation of the study given in [3] performed on an asymptotically flat background

Inertial modes in near-spherical geometries

We propose a numerical method to compute the inertial modes of a container with nearspherical geometry based on the fully spectral discretization of the angular and radial directions using spherical harmonics and Gegenbauer polynomial expansion, respectively. This allows to solve simultaneously the Poincar´e equation and the no penetration condition as an algebraic polynomial eigenvalue problem. The inertial modes of an exact oblate spheroid are recovered to machine precision using an appropriate set of spheroidal coordinates. We show how other boundaries that deviate slightly from a sphere can be accommodated for with the technique of equivalent spherical boundary andwe demonstrate the convergence properties of this approach for the triaxial ellipsoid

Effects of topographic coupling at core-mantle boundary in rotation and orientation changes of the Earth

We study coupling mechanisms at the topographic core-mantle boundary (CMB) of the Earth in the frame of nutations and Length-of-Day (LOD) variations. The CMB topography is usually considered to have a smooth spherical or elliptical shape, however, in reality it is bumpy and there are mountains and valleys representing local height differences of the order of a kilometer. The existence of a topography induces inertial waves that need to be considered in the flow of the core. This is in addition to the Poincaré fluid motion when the nutations are computed and in addition to a relative rotation of the fluid opposite and of the same amplitude as that of the mantle for LOD variations. The additional pressure and the topographic torque depend on the shape of the CMB and can be related to the spherical harmonic coefficients of the CMB topography. We follow the philosophy of the computation of Wu and Wahr [Geophys. J. Int., 128(1), 18-42, 1997] and determine the coefficients of the velocity field in the core at the CMB in terms of the topography coefficients. We used an analytical approach instead of a numerical one. We confirm that some topography coefficients may enhance length-of-day variations and nutations at selected frequencies, and show that these increased rotation variations and nutations are due to resonance effects with inertial waves in the incremental core flow

The influence of a stratified core on Mercury's librations

Earth-based measurements of Mercury's libration amplitude have been used previously to establish the existence of Mercury's liquid core and to estimate its size. However these previous works have not yet taken into account the internal core flows that can be induced by rotational variations such as librations. In the present study, we use a numerical linear model to investigate the effect that these internal flows might have on Mercury's libration amplitude and other observables. In particular we find that the inclusion of a stably stratified layer at the top of the core – the existence of which has been suggested by thermal evolution and numerical dynamo models – in most cases prohibits the transmission of any motion from the top of the core to its deeper parts and vice versa