Libration-driven flows in ellipsoidal shells

D. Lemasquerier , A. M. Grannan (1) , J. Vidal (2) , D. Cebron (2) , B. Favier (3) , M. Le Bars (3) , J. M. Aurnou (1)

1 Department of Earth and Space Sciences [Los Angeles]
2 ISTerre - Institut des Sciences de la Terre
3 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

Planets and satellites can undergo physical librations, which consist of forced periodic variations in their rotation rate induced by gravitational interactions with nearby bodies. This mechanical forcing may drive turbulence in interior fluid layers such as subsurface oceans and metallic liquid cores through a libration-driven elliptical instability (LDEI) that refers to the resonance of two inertial modes with the libration-induced base flow. LDEI has been studied in the case of a full ellipsoid. Here we address for the first time the question of the persistence of LDEI in the more geophysically relevant ellipsoidal shell geometries. In the experimental setup, an ellipsoidal container with spherical inner cores of different sizes is filled with water. Direct side view flow visualizations are made in the librating frame using Kalliroscope particles. A Fourier analysis of the light intensity fluctuations extracted from recorded movies shows that the presence of an inner core leads to spatial heterogeneities but does not prevent LDEI. Particle image velocimetry and direct numerical simulations are performed on selected cases to confirm our results. Additionally, our survey at a fixed forcing frequency and variable rotation period (i.e., variable Ekman number, E) shows that the libration amplitude at the instability threshold varies as similar to E-0.65. This scaling is explained by a competition between surface and bulk dissipation. When extrapolating to planetary interior conditions, this leads to the E-1/2 scaling commonly considered. We argue that Enceladus' subsurface ocean and the core of the exoplanet 55 CnC e should both be unstable to LDEI. Plain Language Summary Because of their gravitational interactions with other bodies, planets and moons are subjected to mechanical forcings that perturb their spin rate. The motivation of this study is to determine whether one of these forcings, called libration, can drive global-scale flows in interior fluid layers, like the subsurface ocean of Europa or the liquid inner core of Io. Turbulent flows in these layers are of interest because they can be linked to the generation of magnetic fields, planetary heat fluxes, and energy dissipation rates. Furthermore, since it has been proposed that life may be harbored within these subsurface oceans, their internal structure and dynamics are of broad interest to the planetary science community and beyond. To model libration experimentally, containers of a given geometry are filled with water and are made to librate. Previous studies have shown that the flow can become unstable for precise oscillation frequencies. By combining laboratory experiments, numerical simulations, and a theoretical analysis, we show for the first time that this instability persists in an ellipsoidal shell geometry, i.e., an ellipsoid inside of which is suspended a spherical inner core. This result is of primary importance since most liquid cores and subsurface oceans are expected to have this geometry. Furthermore, our results show that the generated turbulence can be latitudinally inhomogeneous. By performing a survey, we extrapolate our results to planetary interior conditions and show that libration is capable of driving turbulence in planetary cores (e.g., the exoplanet 55 CnC e) and subsurface oceans (e.g., Enceladus).

Domaines: Géophysique [physics.geo-ph]

D. Lemasquerier, A. M. Grannan, J. Vidal, D. Cebron, B. Favier, et al.. Libration-driven flows in ellipsoidal shells. Journal of Geophysical Research. Planets, 2017, 122 (9), pp.1926-1950. ⟨10.1002/2017JE005340⟩. ⟨hal-01764691⟩