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J. M. Aurnou - One of the best experts on this subject based on the ideXlab platform.
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Libration-driven flows in ellipsoidal shells
Journal of Geophysical Research. Planets, 2017Co-Authors: D. Lemasquerier, A. M. Grannan, J. Vidal, D. Cebron, B. Favier, M. Le Bars, J. M. AurnouAbstract: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).
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Experimental study of global-scale turbulence in a librating ellipsoid
Physics of Fluids, 2014Co-Authors: A. M. Grannan, D. Cebron, M. Le Bars, J. M. AurnouAbstract:We present laboratory experimental results demonstrating that Librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a Libration driven elliptical instability (LDEI). These Libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds Libration cycles for a fixed Ekman number, E = 2 × 10−5. In doing so, we recover the Libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir et al., “Experimental study of Libration-driven flows in nonaxisymmetric containers,” Phys. Earth Planet. Inter. 204-205, 1 (2012); Cébron et al., Phys. Fluids 24, 061703, “Libration driven elliptical instability,” (2012)]. Excitation of bulk filling turbulence by Librational forcing provides a mechanism for transferring rotational energy into turbulent fluid motion and thus can play an important role in the thermal evolution, interior dynamics, and magneto-hydrodynamics of librating bodies, as appear to be common in solar system settings [e.g., Comstock and Bills, “A solar system survey of forced Librations in longitude,” J. Geophys. Res. Planets 108, 1 (2003)].
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Experimental study of Libration-driven zonal flows in a straight cylinder
Physics of the Earth and Planetary Interiors, 2010Co-Authors: Jerome Noir, M. A. Calkins, M. Lasbleis, J. Cantwell, J. M. AurnouAbstract: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 Noir et al. (2009). 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
Tim Van Hoolst - One of the best experts on this subject based on the ideXlab platform.
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The Libration and interior structure of large icy satellites and Mercury
Proceedings of the International Astronomical Union, 2014Co-Authors: Tim Van HoolstAbstract:AbstractLongitudinal Librations are periodic changes in the rotation angle of a planet or satellite. Their observation and subsequent interpretation have profoundly increased our understanding of the interior structure of Mercury. Likewise, Libration is thought to provide important constraints on the interior structure of icy satellites. Here we study the Libration of Mercury and large icy satellites rotating synchronously with their orbital motion and explain how it depends on the interior structure.
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Influence of an inner core on the long-period forced Librations of Mercury
Icarus, 2013Co-Authors: Marie Yseboodt, Attilio Rivoldini, Tim Van Hoolst, Mathieu DumberryAbstract:Abstract The planetary perturbations on Mercury’s orbit lead to long-period forced Librations of Mercury’s mantle. These Librations have previously been studied for a planet with two layers: a mantle and a liquid core. Here, we calculate how the presence of a solid inner core in the liquid outer core influences the long-period forced Librations. Mantle–inner core coupling affects the long-period Libration dynamics mainly by changing the free Libration: first, it lengthens the period of the free Libration of the mantle, and second, it adds a second free Libration, closely related to the free gravitational oscillation between the mantle and inner core. The two free Librations have periods between 2.5 and 18y depending on the internal structure. We show that large amplitude long-period Librations of a few tens of arcsec are generated when the period of a planetary forcing approaches one of the two free Libration periods. These amplitudes are sufficiently large to be detectable by spacecraft measurements of the Libration of Mercury. The amplitudes of the angular velocity of Mercury’s mantle at planetary forcing periods are also amplified by the resonances, but remain much smaller than the current precision of Earth-based radar observations unless the period is very close to a free Libration period. The inclusion of mantle–inner core coupling in the rotation model does not significantly improve the fit to the radar observations. This implies that it is not yet possible to determine the size of the inner core of Mercury on the basis of available observations of Mercury’s rotation rate. Future observations of the long-period Librations may be used to constrain the interior structure of Mercury, including the size of its inner core.
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On the Librations and tides of large icy satellites
Icarus, 2013Co-Authors: Tim Van Hoolst, Rose-marie Baland, Antony TrinhAbstract:Abstract The gravitational force exerted by a central planet deforms its orbiting moons (tides) and periodically changes their rotation (Librations). Tides and Librations of large icy satellites rotating synchronously with their orbital motion are usually studied separately but we here show that tides strongly reduce the Libration amplitude of large icy satellites with a subsurface ocean. Moreover, Libration also slightly changes the tides. Periodic tides affect Libration in three ways: first the periodic tidal bulges modify the gravitational torque exerted by the central planet on the satellite, secondly torques between the periodic tidal bulges of a solid layer and the static shape of another solid layer couple the Libration of the ice shell and solid interior, and thirdly, the zonal tides periodically change the polar moment of the satellite, which acts as the inertia for rotational motion. We develop a formalism to include these elastic effects in the study of Librations and calculate the amplitudes of the longitudinal Librations at orbital period for the largest icy satellites in the Solar System: Europa, Ganymede, Callisto, and Titan. Without a subsurface ocean, elastic effects on Libration are of the order of a few percent. However, if a subsurface ocean exists as indicated by several observations for the satellites considered, elastic tides have a crucial effect. If the solid layers of the satellites are considered rigid, the Libration amplitude is at least one order of magnitude larger than for an entirely solid satellite. Periodic elastic tidal deformations of the layers, in particular of the ice shell, counterbalance this large increase and keep the Libration amplitude at the level of the Libration of the satellite without subsurface ocean. Besides gravitationally forced Librations, seasonal variations in the atmosphere of Titan also cause the rotation of Titan to change on a seasonal timescale. We show that tidal elastic effects can strongly increase the amplitude of these long-term variations in the rotation rate by a factor of about four with respect to a rigid shell. We predict that these variations can have an amplitude above the detection limit of the Cassini radar.
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The role of Mercury’s core density structure on its longitudinal Librations
Icarus, 2013Co-Authors: Mathieu Dumberry, Tim Van Hoolst, Attilio Rivoldini, Marie YseboodtAbstract:Abstract As Mercury orbits the Sun, gravitational torques on its ellipsoidal figure give rise to a longitudinal Libration. Earth-based radar observations indicate that the outermost part of the core is fluid and only the mantle participates in the Libration. If a solid inner core is present, it can alter the Libration of the mantle through gravitational coupling. Previous studies have shown that the influence of the inner core on Libration remains small, though not negligible if its radius is larger than 1000 km. However, these studies considered a simplified model of the Libration dynamics, where the density in both the inner core and fluid core were assumed uniform. Here, we build a model of Mercury’s Libration that takes into account the radially varying density profile within the core. Our results indicate that the amplitude of the 88-day mantle Libration is slightly larger than that predicted on the basis of the uniform density model, though the difference is well below the current error bars in observations. We also show that the period of the free Libration of the combined inner core and mantle is largely unaffected by the details of the core density structure. However, the period of the second free mode of Libration – broadly described by the gravitational oscillation between the mantle and inner core – is significantly longer when a more realistic core density profile is used. We discuss the implication of this result, and we also show how the role of the inner core can be taken into account when observations of gravity and rotation are combined to form constraints on the interior structure of Mercury.
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The effect of tides and an inner core on the forced longitudinal Libration of Mercury
Earth and Planetary Science Letters, 2012Co-Authors: Tim Van Hoolst, Attilio Rivoldini, Rose-marie Baland, Marie YseboodtAbstract:Abstract Mercury's longitudinal Libration at a period of 88 days depends on the moment of inertia of the planet's silicate outer part and as such contains information on the interior structure and composition of Mercury. Secondary effects on the Libration may affect the interpretation of Libration observations in terms of interior structure properties and may also provide further information on Mercury's interior. Here we assess the importance of the effects of tides and the existence of a solid inner core on the Librations of Mercury with particular focus on the 88 days Libration amplitude. Tides affect the Librations of Mercury by changing the gravitational torque exerted by the Sun on Mercury and by changing the polar moment of inertia. We show that they slightly decrease the 88 days Libration amplitude by about 1–2 m, which is below the current and future expected observational precision. We further demonstrate that the effect of an inner core on Mercury's 88 days Libration amplitude is also below the observational precision for small inner cores, but could be observed if Mercury's inner core is larger than at least 1000 km. An inner core also changes considerably the free Libration period by up to 25% if the inner core is very large. Besides giving information on the moment of inertia of the silicate shell, observations of Mercury's Libration can therefore also yield information on the inner core.
Michael Le Bars - One of the best experts on this subject based on the ideXlab platform.
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Fluid flows in a librating cylinder
Physics of Fluids, 2012Co-Authors: Alban Sauret, David Cébron, Michael Le Bars, Stéphane Le DizèsAbstract:The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal Librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Görtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various Libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial modes are not excited, we show that the mean flow correction in the bulk is a uniform rotation, independent of the Ekman number and cylinder aspect ratio, in perfect agreement with the analytical results of Wang [J. Fluid. Mech., 41, pp. 581 - 592, 1970]. When inertial modes are resonantly excited, the mean flow correction is found to have a more complex structure. Its amplitude still scales as the square of the Libration amplitude but now depends on the Ekman number.
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Experimental and numerical study of mean zonal flows generated by Librations of a rotating spherical cavity
Journal of Fluid Mechanics, 2010Co-Authors: Alban Sauret, David Cébron, Cyprien Morize, Michael Le BarsAbstract:We study both experimentally and numerically the steady zonal flow generated by longitudinal Librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (2010), developed in the limit of small Libration frequency - rotation rate ratio, and large Libration frequency - spin-up time product. Using PIV measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid body rotation in the fluid interior, which does not depend on the Libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.
Alban Sauret - One of the best experts on this subject based on the ideXlab platform.
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Fluid flows in a librating cylinder
Physics of Fluids, 2012Co-Authors: Alban Sauret, David Cébron, Michael Le Bars, Stéphane Le DizèsAbstract:The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal Librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Görtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various Libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial modes are not excited, we show that the mean flow correction in the bulk is a uniform rotation, independent of the Ekman number and cylinder aspect ratio, in perfect agreement with the analytical results of Wang [J. Fluid. Mech., 41, pp. 581 - 592, 1970]. When inertial modes are resonantly excited, the mean flow correction is found to have a more complex structure. Its amplitude still scales as the square of the Libration amplitude but now depends on the Ekman number.
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Experimental and numerical study of mean zonal flows generated by Librations of a rotating spherical cavity
Journal of Fluid Mechanics, 2010Co-Authors: Alban Sauret, David Cébron, Cyprien Morize, Michael Le BarsAbstract:We study both experimentally and numerically the steady zonal flow generated by longitudinal Librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (2010), developed in the limit of small Libration frequency - rotation rate ratio, and large Libration frequency - spin-up time product. Using PIV measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid body rotation in the fluid interior, which does not depend on the Libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.
Jerome Noir - One of the best experts on this subject based on the ideXlab platform.
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Experimental study of Libration-driven zonal flows in a straight cylinder
Physics of the Earth and Planetary Interiors, 2010Co-Authors: Jerome Noir, M. A. Calkins, M. Lasbleis, J. Cantwell, J. M. AurnouAbstract: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 Noir et al. (2009). 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
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an experimental and numerical study of Librationally driven flow in planetary cores and subsurface oceans
Physics of the Earth and Planetary Interiors, 2009Co-Authors: Jerome Noir, F Hemmerlin, Johannes Wicht, Serapio M Baca, Jonathan M AurnouAbstract: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 f ∗ ≤ 1 ), moderate rotation rates (Ekman numbers E = 1 0 − 4 to 1 0 − 5 ) and a relatively broad range of Librational amplitudes (Libration amplitudes 10 ° ≲ Δ ϕ ≲ 200 ° ; Rossby numbers 0.03 ≲ R o ≲ 5 ). In addition we model flow in three different core geometries: full sphere, r inner ≃ 0.6 r outer and r inner ≃ 0.9 r outer . 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 R e ≲ 20 the flow is dominated by inertial modes. For 20 ≲ R e ≲ 120 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-Gortler instabilities. For R e ≳ 120 the flow in the vicinity of the outer boundary becomes turbulent. For several librating planets with an internal fluid layer, estimates of Re and f ∗ 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.