Benjamin Favier

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

Inertial Wave Turbulence Driven by Elliptical Instability

The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.

Libration-driven flows in ellipsoidal shells†

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).

The energy flux spectrum of internal waves generated by turbulent convection

We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of convective--stably-stratified fluids. We demonstrate that in the limit of large Rayleigh number (

Some statistical properties of three-dimensional zonostrophic turbulence

Rain [4times 10^7,10^9]

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

) and large stratification (Brunt-V{a}is{a}l{a} frequencies

Tidally forced turbulence in planetary interiors

f_N gg f_c

A laboratory model for deep-seated jets on the gas giants

, where

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves

f_c

The diffusive sheet method for scalar mixing

is the convective frequency), simulations are in good agreement with a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region (Lecoanet & Quataert 2013 MNRAS 430 (3) 2363-2376). Specifically, we demonstrate that the wave energy flux spectrum scales like