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Abstract: Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core–mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigid mantle and the underlying low viscosity fluid. The present experimental study investigates the effect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g., ). [Copyright &y& Elsevier]

Abstract: Forced longitudinal librations are oscillatory perturbations of the rotation rate of a planet resulting from a gravitational coupling with orbital partners. In the present study we report the first experimental evidence that a librating cylindrical container can viscously drive mean azimuthal flows in the liquid interior, hereafter referred to as zonal flows. Using a novel laser Doppler velocimetry system, the current work extends upon the study of libration-driven flows by . We investigate the different mechanisms underlying the zonal flow generation. It is found that zonal flows in the interior result primarily from non-linearities in the Ekman boundary layer. Furthermore, the zonal flow scales as the square of the libration amplitude and is independent of the Ekman number. This scaling implies that forced longitudinal libration in an axisymmetric container (purely viscous coupling) will drive unobservably small zonal flows at planetary conditions. Thus, purely viscous librational coupling will not generate significant energy dissipation in a planetary fluid layer. It follows that any observed phase lag between the gravitational forcing and the orbital response of a planet requires non-viscous coupling mechanisms to account for the energy dissipation. [ABSTRACT FROM AUTHOR]

Abstract: Many planetary bodies undergo forced longitudinal librations [Williams, J.G., Boggs, D.H., Yoder, C.F., Ratcliff, J.T., Dickey, J.O., 2001. Lunar rotational dissipation in solid body and molten core. Journal of Geophysical Research-Planets 106 (E11), 27933–27968; Comstock, R.L., Bills, B.G., 2003. A solar system survey of forced librations in longitude. Journal of Geophysical Research-Planets 108 (E9); Margot, J.L., Peale, S.J., Jurgens, R.F., Slade, M.A., Holin, I.V., 2007. Large longitude libration of mercury reveals a molten core. Science 316 (5825), 710–714]. Yet few studies to date have investigated how longitudinal libration, the oscillatory motion of a planet around its rotation axis, couples with its interior planetary fluid dynamics [e.g., Aldridge, K.D., Toomre, A., 1969. Axisymmetric inertial oscillations of a fluid in a rotating spherical container. Journal of Fluid Mechanics 37, 307; Tilgner, A., 1999. Driven inertial oscillations in spherical shells. Physical Review E 59 (2), 1789–1794]. In this study, we investigate, via laboratory experiments, the viscously driven flow in a spherical librating fluid cavity. We focus on libration frequencies less than or equal to the planetary rotation frequency (frequency ratios ), moderate rotation rates (Ekman numbers to ) and a relatively broad range of librational amplitudes (libration amplitudes ; Rossby numbers ). In addition we model flow in three different core geometries: full sphere, and . Direct flow visualizations in the laboratory experiment allow us to identify three distinct librationally driven flow regimes. The transitions between these regimes are governed by critical values of the outer boundary layer Reynolds number, Re. For the flow is dominated by inertial modes. For the system becomes unstable to longitudinal rolls that form beneath the outer boundary. This laminar instability initiates near the equator and is qualitatively similar to Taylor-Görtler instabilities. For the flow in the vicinity of the outer boundary becomes turbulent. For several librating planets with an internal fluid layer, estimates of Re and lie in the range of values accessible in our laboratory experiment. Our results suggest that Mercury, Io, Europa and Titan may undergo boundary layer turbulence, whereas Earth’s moon, Callisto and Ganymede may become unstable to laminar longitudinal rolls. [Copyright &y& Elsevier]

The Poincaré flow (also known as the tilt-over mode) in a precessing cavity filled with water is investigated experimentally. Assuming that the flow is mainly a solid-body rotation, we have used three independent techniques to determine this rotation: introduction of light ceramic particles to materialize the fluid rotation axis, pressure measurements at the cavity wall, and ultrasonic Doppler anemometry. With the latter technique, we determine the angle between the solid body rotation vector and the cavity axis indirectly, through the secondary flow-oblique shear layers which are stationary in a frame rotating at the precession rate-that the differential rotation at the boundary induces within the fluid. Rapid changes in the direction of the axis of rotation of the fluid for critical values of the rate precession and of the rate of rotation are demonstrated. In some cases, the inclination of the fluid rotation vector with respect to the cavity axis much exceeds the inclination of the prescribed precession vector. A torque approach, which can be generalized, shows that this effect is due to a non-linear resonance between the frequencies of the Poincaré mode and of precession. As a result, we can determine the validity domain of current models of precession and nutations of planets enclosing a fluid core. [ABSTRACT FROM AUTHOR]

Fast changes of Earth's magnetic field could be explained by inviscid and diffusion‐less quasi‐geostrophic (QG) Magneto‐Coriolis modes. We present a hybrid QG model with columnar flows and three‐dimensional magnetic fields and find modes with periods of a few years at parameters relevant to Earth's core. For the simple poloidal magnetic field that we consider here they show a localization of kinetic and magnetic energy in the equatorial region. This concentration of energy near the equator and the high frequency make them a plausible mechanism to explain similar features observed in recent geomagnetic field observations. Our model potentially opens a way to probe the otherwise inaccessible magnetic field structure in the Earth's outer core. Plain Language Summary: Earth's magnetic field is evolving on many time scales. Here, we show that the changes of periods of a few years could possibly be explained by standing waves (modes) within the fluid outer core, which we model as not stratified. These modes are mostly in a balance between the magnetic and rotational forces. The numerically calculated modes show agreement with features of recent magnetic field observations through satellites, for example a stronger amplitude of the magnetic field near the equator. In a next step, our model might allow us to probe the magnetic field inside the liquid and conducting outer core. Key Points: Magneto‐Coriolis modes of periods close to torsional Alfvén modes could be present in Earth's core model without stratificationThe magnetic field changes of such modes show properties similar to geomagnetic observations, with fast changes localized near the equatorOur model could allow core‐flow inversions from geomagnetic field data to the flow and simultaneously the magnetic field within the core [ABSTRACT FROM AUTHOR]

Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos. The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate. However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies. We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence and magnetic field generation. We observe no significant effects of the inner core on the onset of the instabilities. We obtain an analytical estimate of the viscous dissipation, mostly due to boundary layer friction in our simulations. We propose theoretical onsets for hydrodynamic instabilities, and document the intensity of turbulent fluctuations. We extend previous precession dynamo studies towards lower viscosities, at the limits of today's computers. In the low viscosity regime, precession dynamos rely on the presence of large-scale vortices, and the surface magnetic fields are dominated by small scales. Interestingly, intermittent and self-killing dynamos are observed. Our results suggest that large-scale planetary magnetic fields are unlikely to be produced by a precession-driven dynamo in a spherical core. But this question remains open as planetary cores are not exactly spherical, and thus the coupling between the fluid and the boundary does not vanish in the relevant limit of small viscosity. Moreover, the fully turbulent dissipation regime has not yet been reached in simulations. Our results suggest that the melted lunar core has been in a turbulent state throughout its history. Furthermore, in the view of recent experimental results, we propose updated formulas predicting the fluid mean rotation vector and the associated dissipation in both the laminar and the turbulent regimes. [ABSTRACT FROM AUTHOR]

The elliptical instability is a generic instability which takes place in any rotating flow whose streamlines are elliptically deformed. Up to now, it has been widely studied in the case of a constant, non-zero differential rotation between the fluid and the elliptical distortion with applications in turbulence, aeronautics, planetology, and astrophysics. In this letter, we extend previous analytical studies and report the first numerical and experimental evidence that elliptical instability can also be driven by libration, i.e., periodic oscillations of the differential rotation between the fluid and the elliptical distortion, with a zero mean value. Our results suggest that intermittent, space-filling turbulence due to this instability can exist in the liquid cores and subsurface oceans of so-called synchronized planets and moons. [ABSTRACT FROM AUTHOR]