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Nathanaël Schaeffer - One of the best experts on this subject based on the ideXlab platform.
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Turbulent convective length scale in Planetary Cores
Nature, 2019Co-Authors: Céline Guervilly, P. Cardin, Nathanaël SchaefferAbstract:Convection is a fundamental physical process in the fluid Cores of planets. It is the primary transport mechanism for heat and chemical species and the primary energy source for Planetary magnetic fields. Key properties of convection—such as the characteristic flow velocity and length scale—are poorly quantified in Planetary Cores owing to the strong dependence of these properties on Planetary rotation, buoyancy driving and magnetic fields, all of which are difficult to model using realistic conditions. In the absence of strong magnetic fields, the convective flows of the core are expected to be in a regime of rapidly rotating turbulence1, which remains largely unexplored. Here we use a combination of non-magnetic numerical models designed to explore this regime to show that the convective length scale becomes independent of the viscosity when realistic parameter values are approached and is entirely determined by the flow velocity and the Planetary rotation. The velocity decreases very rapidly at smaller scales, so this turbulent convective length scale is a lower limit for the energy-carrying length scales in the flow. Using this approach, we can model realistically the dynamics of small non-magnetic Cores such as the Moon. Although modelling the conditions of larger Planetary Cores remains out of reach, the fact that the turbulent convective length scale is independent of the viscosity allows a reliable extrapolation to these objects. For the Earth’s core conditions, we find that the turbulent convective length scale in the absence of magnetic fields would be about 30 kilometres, which is orders of magnitude larger than the ten-metre viscous length scale. The need to resolve the numerically inaccessible viscous scale could therefore be relaxed in future more realistic geodynamo simulations, at least in weakly magnetized regions. Numerical modelling of rotating turbulent convective flows shows that the length scale of convection in Planetary Cores is set by the flow speed and not by the fluid viscosity.
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Rotating convection in stably-stratified Planetary Cores
arXiv: Fluid Dynamics, 2019Co-Authors: R Monville, Jérémie Vidal, David Cébron, Nathanaël SchaefferAbstract:In Planetary fluid Cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection. We investigate rotating double-diffusive convection (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilising whereas the compositional one is destabilising. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably-stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic Planetary regimes. In particular , we show that in stably-stratified spheres, the Rayleigh numbers Ra at the onset evolve like $Ra $\sim$ Ek^{-1}$ , where Ek is the Ekman number. This differs from rotating convection in unstably-stratified spheres, for which $Ra $\sim$ Ek^{-4/3}$. The domain of existence of inviscid convection thus increases as $Ek^{-1/3}$. Second, we perform nonlinear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially anti-symmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the nonlinear flow at saturation. For even stronger stable straficiation, the flow becomes mainly equatorially-symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.
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Rotating double-diffusive convection in stably stratified Planetary Cores
Geophysical Journal International, 2019Co-Authors: R Monville, Jérémie Vidal, David Cébron, Nathanaël SchaefferAbstract:In Planetary fluid Cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection. We investigate rotating double-diffusive convection (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilising whereas the compositional one is destabilising. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic Planetary regimes. In particular, we show that in stably stratified spheres, the Rayleigh numbers $Ra$ at the onset evolve like $Ra \sim Ek^{-1}$, where $Ek$ is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which $Ra \sim Ek^{-4/3}$. The domain of existence of inviscid convection thus increases as $Ek^{-1/3}$. Second, we perform nonlinear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially anti-symmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the nonlinear flow at saturation. For even stronger stable stratification, the flow becomes mainly equatorially-symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.
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convective lengthscale in Planetary Cores
arXiv: Geophysics, 2018Co-Authors: Céline Guervilly, P. Cardin, Nathanaël SchaefferAbstract:Convection is a fundamental physical process in the fluid Cores of planets because it is the primary transport mechanism for heat and chemical species and the primary energy source for Planetary magnetic fields. Key properties of convection, such as the characteristic flow velocity and lengthscale, are poorly quantified in Planetary Cores due to their strong dependence on Planetary rotation, buoyancy driving and magnetic fields, which are all difficult to model under realistic conditions. In the absence of strong magnetic fields, the core convective flows are expected to be in a regime of rapidly-rotating turbulence, which remains largely unexplored to date. Here we use a combination of numerical models designed to explore this low-viscosity regime to show that the convective lengthscale becomes independent of the viscosity and is entirely determined by the flow velocity and Planetary rotation. For the Earth's core, we find that the characteristic con-vective lengthscale is approximately 30km and below this scale, motions are very weak. The 30-km cutoff scale rules out small-scale dynamo action and supports large-eddy simulations of core dynamics. Furthermore, it implies that our understanding of magnetic reversals from numerical geodynamo models does not relate to the Earth, because they require too intense flows. Our results also indicate that the liquid core of the Moon might still be in an active convective state despite the absence of a present-day dynamo.
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subcritical thermal convection of liquid metals in a rapidly rotating sphere
Physical Review Letters, 2017Co-Authors: E J Kaplan, Jérémie Vidal, Nathanaël Schaeffer, P. CardinAbstract:Planetary Cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) Planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the Planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek<10^{-6}. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection (Ra=0.7Ra_{crit} in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Peclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for Planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.
Yingwei Fei - One of the best experts on this subject based on the ideXlab platform.
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High-pressure behavior of Fe3P and the role of phosphorus in Planetary Cores
Earth and Planetary Science Letters, 2014Co-Authors: Yingwei Fei, Shan QinAbstract:Abstract Fe3P is a candidate component in Planetary Cores. We have investigated high-pressure behavior of Fe3P by first-principles calculations and synchrotron X-ray diffraction. Theoretical calculations reveal a magnetic collapse at 40–65 GPa, accompanied by a structural transition. The possible high-pressure polymorph is either a distorted cementite structure (Pnma) or a P4/mnc structure. By combining synchrotron X-ray diffraction and laser-heating diamond anvil cell techniques, we have collected in situ diffraction patterns of Fe3P up to 64 GPa and 1650 K. The high-pressure phase transition from I 4 ¯ to P4/mnc structure predicted by the first-principles calculations was confirmed. Discontinuous variations of lattice constants and thermal expansion coefficients with pressure were observed around 17 and 40 GPa, indicating a possible magnetic transition developed in this range, which are in agreement with the calculated results.
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High pressure and temperature electrical resistivity of iron and implications for Planetary Cores
Geophysical Research Letters, 2013Co-Authors: Liwei Deng, Yingwei Fei, Christopher T Seagle, Anat ShaharAbstract:[1] Electrical resistivity measurements of polycrystalline iron have been performed at 5, 7, and 15 GPa and in the temperature range 293–2200 K by employing a four-wired method. The kinks in electrical resistivity associated with solid iron phase transitions and the solid to liquid transition were clearly observed upon increasing temperature. Geometry corrections due to volume variations with pressure and temperature were applied to the entire data set. High pressure and temperature thermal conductivity were calculated by fitting resistivity data through the Wiedemann-Franz law. The temperature dependences of electrical resistivity and thermal conductivity for α, γ, and e solid iron have been determined at high-pressure conditions. Our study provides the first experimental constraint on the heat flux conducted at Mercury's outmost core, estimated to be 0.29–0.36 TW, assuming an adiabatic core. Extrapolations of our data to Martian outer core conditions yield a series of heat transport parameters (e.g., electrical resistivity, thermal conductivity, and heat flux), which are in reasonable comparison with various geophysical estimates.
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Magnetic transition and sound velocities of Fe3S at high pressure: implications for Earth and Planetary Cores
Earth and Planetary Science Letters, 2004Co-Authors: Jung-fu Lin, Yingwei Fei, Wolfgang Sturhahn, Jiyong Zhao, Ho-kwang Mao, Russell J. HemleyAbstract:Magnetic, elastic, thermodynamic, and vibrational properties of the most iron-rich sulfide, Fe3S, known to date have been studied with synchrotron Mossbauer spectroscopy (SMS) and nuclear resonant inelastic X-ray scattering (NRIXS) up to 57 GPa at room temperature. The magnetic hyperfine fields derived from the time spectra of the synchrotron Mossbauer spectroscopy show that the low-pressure magnetic phase displays two magnetic hyperfine field sites and that a magnetic collapse occurs at 21 GPa. The magnetic to non-magnetic transition significantly affects the elastic, thermodynamic, and vibrational properties of Fe3S. The magnetic collapse of Fe3S may also affect the phase relations in the iron–sulfur system, changing the solubility of sulfur in iron under higher pressures. Determination of the physical properties of the non-magnetic Fe3S phase is important for the interpretation of the amount and properties of sulfur present in the Planetary Cores. Sound velocities of Fe3S obtained from the measured partial phonon density of states (PDOS) for 57Fe incorporated in the alloy show that Fe3S has higher compressional and shear wave velocity than those of hcp-Fe and hcp-Fe0.92Ni0.08 alloy under high pressures, making sulfur a potential light element in the Earth's core based on geophysical arguments. The VP and VS of the non-magnetic Fe3S follow a Birch's law trend whereas the slopes decrease in the magnetic phase, indicating that the decrease of the magnetic moment significantly affects the sound velocities. If the Martian core is in the solid state containing 14.2 wt.% sulfur, it is likely that the non-magnetic Fe3S phase is a dominant component and that our measured sound velocities of Fe3S can be used to construct the corresponding velocity profile of the Martian core. It is also conceivable that Fe3P and Fe3C undergo similar magnetic phase transitions under high pressures.
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Experimental evidence that potassium is a substantial radioactive heat source in Planetary Cores.
Nature, 2003Co-Authors: V. Rama Murthy, Wim Van Westrenen, Yingwei FeiAbstract:The hypothesis that 40K may be a significant radioactive heat source in the Earth's core was proposed on theoretical grounds1,2 over three decades ago, but experiments3,4,5,6,7,8 have provided only ambiguous and contradictory evidence for the solubility of potassium in iron-rich alloys. The existence of such radioactive heat in the core would have important implications for our understanding of the thermal evolution of the Earth and global processes such as the generation of the geomagnetic field, the core–mantle boundary heat flux and the time of formation of the inner core9,10,11,12. Here we provide experimental evidence to show that the ambiguous results obtained from earlier experiments are probably due to previously unrecognized experimental and analytical difficulties. The high-pressure, high-temperature data presented here show conclusively that potassium enters iron sulphide melts in a strongly temperature-dependent fashion and that 40K can serve as a substantial heat source in the Cores of the Earth and Mars.
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physical properties of liquid fe alloys at high pressure and their bearings on the nature of metallic Planetary Cores
Journal of Geophysical Research, 2002Co-Authors: Chrystele Sanloup, François Guyot, Philippe Gillet, Yingwei FeiAbstract:[1] Sulfur and silicon are among the expected alloying light elements in Planetary liquid iron Cores. Structural properties of Fe-27 wt % S and Fe-17 wt % Si liquid alloys at high pressure and high temperature (0-5 GPa/1400-2300 K) are measured by synchrotron X-ray diffraction. Sulfur strongly modifies the local structure of liquid iron whereas silicon has only small structural effects. Fe-27 wt % S melts are indeed poorly ordered which explains a higher compressibility compared to pure liquid Fe. These results point out the necessity to consider the strong effect of S on liquid Fe properties while modeling Planetary interiors. They imply a low S content in the Earth's outer core, leaving Si as a strong candidate, and argue for a present-day Martian solid core when combined with previous global chemical models.
Jonathan M Aurnou - One of the best experts on this subject based on the ideXlab platform.
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laboratory numerical models of rapidly rotating convection in Planetary Cores
Geophysical Journal International, 2015Co-Authors: Jonathan S. Cheng, Stephan Stellmach, E. M. King, Adolfo Ribeiro, A M Grannan, Jonathan M AurnouAbstract:Author(s): Cheng, JS; Stellmach, S; Ribeiro, A; Grannan, A; King, EM; Aurnou, JM | Abstract: We present laboratory and numerical models investigating the behavioural regimes of rapidly rotating convection in high-latitude Planetary core-style settings. Our combined laboratorynumerical approach, utilizing simplified geometries, can access more extreme parameters (e.g. Rayleigh numbers Ra ≲ 1013; Nusselt numbers Nu ≲ 103; Ekman numbers E ≳ 3 × 10-8) than current global-scale dynamo simulations. Using flow visualizations and heat transfer measurements, we study the axialized flows that exist near the onset of rotating convection, as well as the 3-D flows that develop with stronger forcing. With water as the working fluid (Prandtl number Pr ≲ 7), we find a steep scaling trend for rapidly rotating convective heat transfer, Nu~(Ra/RaC)3.6, that is associated with the existence of coherent, axialized columns. This rapidly rotating trend is steeper than the trends found at moderate values of the Ekman number, and continues a trend of ever-steepening scalings as the rotation rate of the system is increased. In contrast, in more strongly forced or lower rotation rate cases, the heat transfer scaling consistently follows a shallower slope equivalent to that of non-rotating convection systems. The steep heat transfer scaling in the columnar convection regime, corroborated by our laboratory flow visualizations, imply that coherent, axial columns have a relatively narrow range of stability. Thus, we hypothesize that coherent convection columns are not stable in Planetary core settings,where the Ekman number is estimated to be~10-15. As a consequence, convective motions in the core may not be related to the columnar motions found in presentday global-scale models. Instead, we hypothesize that turbulent rotating convection cascades energy upwards from 3-D motions to large-scale quasi-2-D flow structures that are capable of efficiently generating Planetary-scale magnetic fields. We argue that the turbulent regimes of rapidly rotating convection are essential aspects of core dynamics and will be necessary components of robust, next-generation and multiscale dynamo models.
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Rotating convective turbulence in Earth and Planetary Cores
Physics of the Earth and Planetary Interiors, 2015Co-Authors: Jonathan M Aurnou, E. M. King, Michael A. Calkins, Jonathan S. Cheng, Keith Julien, David Nieves, Krista M. Soderlund, Stephan StellmachAbstract:Abstract An accurate description of turbulent core convection is necessary in order to build robust models of Planetary core processes. Towards this end, we focus here on the physics of rapidly rotating convection. In particular, we present a closely coupled suite of advanced asymptotically-reduced theoretical models, efficient Cartesian direct numerical simulations (DNS) and laboratory experiments. Good convergence is demonstrated between these three approaches, showing that a comprehensive understanding of the dynamics appears to be within reach in our simplified rotating convection system. The goal of this paper is to review these findings, and to discuss their possible implications for Planetary Cores dynamics.
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Libration-driven flow in Planetary Cores and subsurface oceans.
2011Co-Authors: Jerome Noir, David Cébron, M. Calkins, M. Le Bars, Jonathan M AurnouAbstract:In the present study, we investigate the flow driven by longitudinal libration in the liquid layer of Planetary bodies via a coupled experimental-numerical approach. Extending the work of [7], we consider the case of a non-axisymmetric container to account for the topographic coupling between the fluid and the solid shell that arises naturally in planets in low order spin-orbit resonance such as Mercury, Io, Titan, Europa, the Earth’s moon or Ganymede. We show that depending on the libration frequency, laminar or turbulent flows can develop in the system as the result of growth and collapse of an elliptical instability. An analytical expression of the growth rate of the instability is obtained using a WKB analysis further validated by series of numerical simulations. Extrapolation of our findings to Planetary conditions suggest that some librating planets may be subject to elliptical instabilities, therefore to turbulence in the liquid layer leading to significant energy dissipation [5].
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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.
Jérémie Vidal - One of the best experts on this subject based on the ideXlab platform.
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Rotating convection in stably-stratified Planetary Cores
arXiv: Fluid Dynamics, 2019Co-Authors: R Monville, Jérémie Vidal, David Cébron, Nathanaël SchaefferAbstract:In Planetary fluid Cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection. We investigate rotating double-diffusive convection (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilising whereas the compositional one is destabilising. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably-stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic Planetary regimes. In particular , we show that in stably-stratified spheres, the Rayleigh numbers Ra at the onset evolve like $Ra $\sim$ Ek^{-1}$ , where Ek is the Ekman number. This differs from rotating convection in unstably-stratified spheres, for which $Ra $\sim$ Ek^{-4/3}$. The domain of existence of inviscid convection thus increases as $Ek^{-1/3}$. Second, we perform nonlinear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially anti-symmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the nonlinear flow at saturation. For even stronger stable straficiation, the flow becomes mainly equatorially-symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.
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Rotating double-diffusive convection in stably stratified Planetary Cores
Geophysical Journal International, 2019Co-Authors: R Monville, Jérémie Vidal, David Cébron, Nathanaël SchaefferAbstract:In Planetary fluid Cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection. We investigate rotating double-diffusive convection (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilising whereas the compositional one is destabilising. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic Planetary regimes. In particular, we show that in stably stratified spheres, the Rayleigh numbers $Ra$ at the onset evolve like $Ra \sim Ek^{-1}$, where $Ek$ is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which $Ra \sim Ek^{-4/3}$. The domain of existence of inviscid convection thus increases as $Ek^{-1/3}$. Second, we perform nonlinear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially anti-symmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the nonlinear flow at saturation. For even stronger stable stratification, the flow becomes mainly equatorially-symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.
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subcritical thermal convection of liquid metals in a rapidly rotating sphere
Physical Review Letters, 2017Co-Authors: E J Kaplan, Jérémie Vidal, Nathanaël Schaeffer, P. CardinAbstract:Planetary Cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) Planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the Planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek<10^{-6}. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection (Ra=0.7Ra_{crit} in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Peclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for Planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.
Shan Qin - One of the best experts on this subject based on the ideXlab platform.
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High-pressure behavior of Fe3P and the role of phosphorus in Planetary Cores
Earth and Planetary Science Letters, 2014Co-Authors: Yingwei Fei, Shan QinAbstract:Abstract Fe3P is a candidate component in Planetary Cores. We have investigated high-pressure behavior of Fe3P by first-principles calculations and synchrotron X-ray diffraction. Theoretical calculations reveal a magnetic collapse at 40–65 GPa, accompanied by a structural transition. The possible high-pressure polymorph is either a distorted cementite structure (Pnma) or a P4/mnc structure. By combining synchrotron X-ray diffraction and laser-heating diamond anvil cell techniques, we have collected in situ diffraction patterns of Fe3P up to 64 GPa and 1650 K. The high-pressure phase transition from I 4 ¯ to P4/mnc structure predicted by the first-principles calculations was confirmed. Discontinuous variations of lattice constants and thermal expansion coefficients with pressure were observed around 17 and 40 GPa, indicating a possible magnetic transition developed in this range, which are in agreement with the calculated results.
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In situ high-pressure study of FeP: Implications for Planetary Cores
Physics of the Earth and Planetary Interiors, 2010Co-Authors: Shan Qin, Leonid DubrovinskyAbstract:Abstract FeP with MnP-type structure is isostructural with high-pressure FeS polymorphs (both post-troilite FeS and FeS VI), which are believed to exist in Planetary Cores. Due to similar PTX phase diagrams of binary Fe–P and Fe–S, phosphorus can incorporate with iron–sulfur at Planetary core conditions. To understand such substitution and the high-pressure behavior of FeP, we investigate the structural stability of FeP up to 15.6 GPa and 1800 ± 200 K by combined in situ powder X-ray diffraction and Mossbauer spectroscopy. Our experimental results show that FeP remains the MnP-type structure throughout the PT range covered. Isothermal equation of state of FeP is obtained with V0 of 92.91(8) A3, B0 of 205(7) GPa, and B ′ 0 of 4. The shortest axis of the MnP-type FeP cell, the b-axis, is the most compressible, due to the soft edge-sharing octahedra along the b-axis. Mossbauer results show that no electronic structure changes occur up to 15.6 GPa, but indicate decreasing distortion of FeP6 octahedron with pressure increasing. The behavior of FeP is quite different from that of FeS under high pressure and high temperature, suggesting that phosphorus will have a significant impact on stability and electronic properties of FeS within terrestrial planet Cores.