Full sphere hydrodynamic and dynamo benchmarks

Marti, Philippe; Schaeffer, Nathanaël; Hollerbach, Rainer; Cébron, David; Nore, Caroline; Luddens, Francky; Guermond, Jean‐Luc; Aubert, Julien; Takehiro, Shin‐ichi; Sasaki, Youhei; Hayashi, Yoshiyuki; Simitev, Radostin D.; Busse, Friedrich H.; Vantieghem, Stijn; Jackson, Andrew

doi:10.1093/gji/ggt518

Cited by 48 publications

(49 citation statements)

References 35 publications

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“…This Poisson equation is solved with the algebraic multigrid method BoomerAMG (Henson & Yang 2002). Discussions regarding the performance of this code can be found in Marti et al (2014) and Cébron et al (2014).…”

Section: Numerical Validation and Discussionmentioning

confidence: 99%

Latitudinal libration driven flows in triaxial ellipsoids

2015

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Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a resonance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir & Cébron 2013). This theoretical approach is consistent with the results of Chan et al. (2011) andZhang et al. (2012) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear stability analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz & Hameiri 1991;Gledzer & Ponomarev 1977) that allow to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.

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Section: Numerical Validation and Discussionmentioning

confidence: 99%

Latitudinal libration driven flows in triaxial ellipsoids

2015

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“…In the XSHELLS code, these instabilities are suppressed by truncating the spherical harmonic degree at l tr (r) = 1 + r/r s l max with r s = 0.5. The XSHELLS code passes benchmarks designed to highlight issues arising at the origin (Marti et al, 2014).…”

Section: Numerics In Spheresmentioning

confidence: 99%

Rotating double-diffusive convection in stably stratified planetary cores

Monville

Vidal

Cébron

et al. 2019

Geophysical Journal International

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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 ∼ Ek −1 , where Ek is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which Ra ∼ 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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“…The numerical code has been widely benchmarked in several contexts including that of precession driven flows 32,38 . We use a typical truncation of the spectral expansion up to N = 63, L = M = 127 at moderate Ekman numbers (E 3 × 10 −5 ).…”

Section: B Numerical Solvermentioning

confidence: 99%

Shear-driven parametric instability in a precessing sphere

2015

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The present numerical study aims at shedding light on the mechanism underlying the precessional instability in a sphere. Precessional instabilities in the form of parametric resonance due to topographic coupling have been reported in a spheroidal geometry both analytically and numerically. We show that such parametric resonances can also develop in spherical geometry due to the conical shear layers driven by the Ekman pumping singularities at the critical latitudes. Scaling considerations lead to a stability criterion of the form, |P o | > O(E 4/5 ), where P o represents the Poincaré number and E the Ekman number. The predicted threshold is consistent with our numerical simulations as well as previous experimental results. When the precessional forcing is supercriticial, our simulations show evidence of an inverse cascade, i.e. small scale flows merging into large scale cyclones with a retrograde drift. Finally, it is shown that this instability mechanism may be relevant to precessing celestial bodies such as the Earth and Earth's moon.

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Full sphere hydrodynamic and dynamo benchmarks

Cited by 48 publications

References 35 publications

Latitudinal libration driven flows in triaxial ellipsoids

Latitudinal libration driven flows in triaxial ellipsoids

Rotating double-diffusive convection in stably stratified planetary cores

Shear-driven parametric instability in a precessing sphere

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