pizza: an open-source pseudo-spectral code for spherical quasi-geostrophic convection

Gastine, T.

doi:10.1093/gji/ggz103

Cited by 10 publications

(14 citation statements)

References 80 publications

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“…CNAB2 has been commonly used in geodynamo models since the pioneering work of Glatzmaier (1984). IMEX Runge-Kutta schemes have been rarely employed in the context of geodynamo models (Glatzmaier & Roberts 1996), rapidly-rotating convection in spherical shells (Marti et al 2016) or quasi-geostrophic models of 2-D convection (Gastine 2019). For IMEX Runge-Kutta schemes, s substages are solved to time-advance Eq.…”

Section: Numerical Approachmentioning

confidence: 99%

Geomagnetic semblance and dipolar–multipolar transition in top-heavy double-diffusive geodynamo models

Tassin

Gastine

Fournier

2021

Geophysical Journal International

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Summary Convection in the liquid outer core of the Earth is driven by thermal and chemical perturbations. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of three-dimensional global geodynamo models, in the so-called “top-heavy” regime of double-diffusive convection, when both thermal and compositional background gradients are destabilizing. Using a linear eigensolver, we begin by confirming that, compared to the standard single-diffusive configuration, the onset of convection is facilitated by the addition of a second buoyancy source. We next carry out a systematic parameter survey by performing 79 numerical dynamo simulations. We show that a good agreement between simulated magnetic fields and the geomagnetic field can be attained for any partitioning of the convective input power between its thermal and chemical components. On the contrary, the transition between dipole-dominated and multipolar dynamos is found to strongly depend on the nature of the buoyancy forcing. Classical parameters expected to govern this transition, such as the local Rossby number -a proxy of the ratio of inertial to Coriolis forces- or the degree of equatorial symmetry of the flow, fail to capture the dipole breakdown. A scale-dependent analysis of the force balance instead reveals that the transition occurs when the ratio of inertial to Lorentz forces at the dominant length scale reaches 0.5, regardless of the partitioning of the buoyancy power. The ratio of integrated kinetic to magnetic energy Ek/Em provides a reasonable proxy of this force ratio. Given that Ek/Em ≈ 10−4 − 10−3 in the Earth’s core, the geodynamo is expected to operate far from the dipole-multipole transition. It hence appears that the occurrence of geomagnetic reversals is unlikely related to dramatic and punctual changes of the amplitude of inertial forces in the Earth’s core, and that another mechanism must be sought.

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Section: Numerical Approachmentioning

confidence: 99%

Geomagnetic semblance and dipolar–multipolar transition in top-heavy double-diffusive geodynamo models

Tassin

Gastine

Fournier

2021

Geophysical Journal International

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“…More advanced extensions of the QG framework have recently been proposed where the full velocity field is better accounted for by projecting onto a QG basis (Labbé et al 2015;Maffei et al 2017;Gerick et al 2020) or by z-averaging before taking the curl (Jackson & Maffei 2020). In this work, we follow Gastine (2019) and use the QG formulation proposed by Schaeffer & Cardin (2006) that was expanded in a hybrid approach by Guervilly & Cardin (2016 to also include a 3-D temperature field. Our numerical implementation of this hybrid QG-3D method (or simply hybrid) is an extension of the pizza code by Gastine (2019) to include a 3-D temperature field in a spherical shell geometry.…”

Section: Introductionmentioning

confidence: 99%

Comparison of quasi-geostrophic, hybrid and 3-D models of planetary core convection

Barrois

Gastine

Finlay

2022

Geophysical Journal International

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Summary We present investigations of rapidly-rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from Quasi-Geostrophic (QG), 3D and hybrid QG-3D models. The 170 reported calculations span Ekman numbers, Ek, between 10−4 and 10−10, Rayleigh numbers, Ra, between 2 and 150 times supercritical, and Prandtl numbers, Pr, between 10 and 10−2. The default boundary conditions are no-slip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peak-to-peak amplitude of the pattern divided by its mean, taking values up to 5. The Quasi-Geostrophic (QG) model is based on the open-source pizza code. We extend this in a hybrid approach to include the temperature field on a 3D grid. In general, we find convection is dominated by zonal jets at mid-depths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, Ra ≤ 10 Rac when Pr = 1, and departs from the 3D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatorially anti-symmetric and z-correlations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two datasets at Pr ≥ 0.1, although the QG model is effectively more strongly driven than the hybrid case due to its cylindrically-averaged thermal boundary conditions. When Pr is decreased, the range of agreement between the Hybrid and 3D models expands, e.g. up to Ra ≤ 15 Rac at Pr = 0.1, indicating the hybrid method may be better suited to study convection in the regime Pr ≪ 1. We effectively observe two regimes: (i) at Pr ≥ 0.1 the QG and 3D models agree in the studied range of Ra/Rac while the hybrid model fails when Ra > 10 Rac; (ii) at Pr = 0.01 the QG and 3D disagree above Ra/Rac = 10 while the hybrid and 3D models agree fairly well up to Ra ∼ 20 Rac. Models that include laterally-varying heat flux at the outer boundary reproduce regional convection patterns that compare well with those found in similarly forced 3D models. Previously proposed scaling laws for rapidly-rotating convection are tested; our simulations are overall well described by a triple balance between Coriolis, inertia and Archimedean (CIA) forces with the length-scale of the convection following the diffusion-free Rhines-scaling. The Prandtl number, Pr, affects the number and the size of the jets with larger structures obtained at lower Pr; higher velocities and lower heat transport are also seen on decreasing Pr. The scaling behaviour of the convective velocity shows a strong dependence on Pr. This study is an intermediate step towards a hybrid model of core convection also including 3D magnetic effects.

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“…Since ∂T/∂z ≈ 0 in the experiment, the second term on the right-hand side of (3.4) is small. Furthermore, the small Ekman number E and large rotational Froude number Fr that result from rapid rotation ensure ∂ω z /∂z ≈ 0, which is the quasi-geostrophic approximation (Busse 1986;Gillet & Jones 2006), often used to model rotating convection in spherical shells outside the tangent cylinder (Calkins 2018;Gastine 2019).…”

Section: Supercritical Convection With Laterally Varying Boundary Heamentioning

confidence: 99%

Convection in a rapidly rotating cylindrical annulus with laterally varying boundary heat flux

Sahoo

Sreenivasan

2019

J. Fluid Mech.

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pizza: an open-source pseudo-spectral code for spherical quasi-geostrophic convection

Cited by 10 publications

References 80 publications

Geomagnetic semblance and dipolar–multipolar transition in top-heavy double-diffusive geodynamo models

Geomagnetic semblance and dipolar–multipolar transition in top-heavy double-diffusive geodynamo models

Comparison of quasi-geostrophic, hybrid and 3-D models of planetary core convection

Convection in a rapidly rotating cylindrical annulus with laterally varying boundary heat flux

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