arXiv subjects

Alexandre Fournier

Publications and source records attributed to Alexandre Fournier.

17 recordsLinked to original sources

arXiv2026

Motional induction in Ganymede's ocean

We investigate the magnetic signature of oceanic circulation in Ganymede's subsurface ocean using kinematic induction modeling. Our approach couples zonal jet flows from rotating thermal convection simulations with magnetic field models incorporating Ganymede's internal dynamo and external contributions from Jupiter. We solve the induction equation in spherical geometry for deep-ocean (493 km) and shallow-ocean (287 km) scenarios with varying magnetic Reynolds numbers. Ocean flows generate a predominantly toroidal magnetic field through the omega-effect, with a weaker poloidal component pervading beyond the conductive ocean layer. For some, but not all, induction configurations, analysis of the time-averaged Lowes-Mauersberger spectra reveals that ocean-induced signals dominate at spherical harmonic degrees $\ell \geq 4$. Deep ocean scenarios with magnetic Reynolds numbers above unity produce surface magnetic signals up to 9 nT. Our results demonstrate that Ganymede's intrinsic magnetic field creates favorable conditions for detecting subsurface ocean dynamics, thus emphasizing the need for low-altitude orbits for the Juice probe.

astro-ph.EP↗

arXiv2025

Online learning of subgrid-scale models for quasi-geostrophic turbulence in planetary interiors

Machine learning approaches to subgrid-scale (SGS) modelling are now well established in atmospheric and oceanic applications. Among these, online end-to-end learning, where the differentiable solver participates in the training, has shown particular promise. Yet, existing studies are largely restricted to idealised periodic domains, with no mechanical boundaries, precluding them from addressing the dynamics of bounded rotating flows relevant to planetary interiors. Here we consider two-dimensional quasi-geostrophic turbulence in a rapidly rotating annular bounded domain. We examine three configurations varying the geometry of the container and the rotation rate. The system exhibit key features such as zonal jets, Rossby waves, and, in the spherical shell geometry, a slow quasi-periodic inward drift of the jets. The spectral properties of the zonal and non-zonal flow can be understood in the framework of zonostrophic turbulence theory. We develop a differentiable solver for this system, which allows us to train SGS models online, over a time span of one turnover time, using coarse-grained data from direct numerical simulations. In all cases, a SGS model trained on a single turnover time accurately reproduce global integrated diagnostics, energy spectra as well as long-term dynamical behaviours ---such as jet migration--- occurring on timescales which exceed the training window by one order of magnitude. The online-trained model further outperforms classical hyperdiffusivity and Leith closure schemes, for which reducing the radial resolution is impractical. The resulting speed-up paves the way to further investigations of long-term geophysical fluid processes beyond the reach of direct numerical simulations.

physics.flu-dyn↗

arXiv2025

Core-surface kinematic control of polarity reversals in advanced geodynamo simulations

The geomagnetic field has undergone hundreds of polarity reversals over Earth's history, at a variable pace. In numerical models of Earth's core dynamics, reversals occur with increasing frequency when the convective forcing is increased past a critical level. This transition has previously been related to the influence of inertia in the force balance. Because this force is subdominant in Earth's core, concerns have been raised regarding the geophysical applicability of this paradigm. Reproducing the reversal rate of the past million years also requires forcing conditions that do not guarantee that the rest of the geomagnetic variation spectrum is reproduced. These issues motivate the search for alternative reversal mechanisms. Using a suite of numerical models where buoyancy is provided at the bottom of the core by inner-core freezing, we show that the magnetic dipole amplitude is controlled by the relative strength of subsurface upwellings and horizontal circulation at the core surface. A relative weakening of upwellings brings the system from a stable to a reversing dipole state. This mechanism is purely kinematic because it operates irrespectively of the interior force balance. It is therefore expected to apply at the physical conditions of Earth's core. Subsurface upwellings may be impeded by stable stratification in the outermost core. We show that with weak stratification levels corresponding to a nearly adiabatic core surface heat flow, a single model reproduces the observed geomagnetic variations ranging from decades to millions of years. \rev{In contrast with} the existing paradigm, reversals caused by this stable top core mechanism become more frequent when the level of stratification increases i.e. when the core heat flow decreases. This suggests that the link between mantle dynamics and magnetic reversal frequency needs to be reexamined.

physics.geo-ph↗

arXiv2021

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

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 3D 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 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 $E_k/E_m$ provides a reasonable proxy of this force ratio. Given that $E_k/E_m \ll 1$ 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.

physics.geo-ph↗

arXiv2020

Can one use Earth's magnetic axial dipole field intensity to predict reversals?

We study predictions of reversals of Earth's axial magnetic dipole field that are based solely on the dipole's intensity. The prediction strategy is, roughly, that once the dipole intensity drops below a threshold, then the field will continue to decrease and a reversal (or a major excursion) will occur. We first present a rigorous definition of an intensity threshold-based prediction strategy and then describe a mathematical and numerical framework to investigate its validity and robustness in view of the data being limited. We apply threshold-based predictions to a hierarchy of numerical models, ranging from simple scalar models to 3D geodynamos. We find that the skill of threshold-based predictions varies across the model hierarchy. The differences in skill can be explained by differences in how reversals occur: if the field decreases towards a reversal slowly (in a sense made precise in this paper), the skill is high, and if the field decreases quickly, the skill is low. Such a property could be used as an additional criterion to identify which models qualify as Earth-like. Applying threshold-based predictions to Virtual Axial Dipole Moment (VADM) paleomagnetic reconstructions (PADM2M and Sint-2000) covering the last two million years, reveals a moderate skill of threshold-based predictions for Earth's dynamo. Besides all of their limitations, threshold-based predictions suggest that no reversal is to be expected within the next 10 kyr. Most importantly, however, we show that considering an intensity threshold for identifying upcoming reversals is intrinsically limited by the dynamic behavior of Earth's magnetic field.

physics.geo-ph↗

arXiv2019

Dynamo-based limit to the extent of a stable layer atop Earth's core

The existence of a stably stratified layer underneath the core-mantle boundary (CMB) has been recently revived by corroborating evidences coming from seismic studies, mineral physics and thermal evolution models. Such a layer could find its physical origination either in compositional stratification due to the accumulation of light elements at the top or the core or in thermal stratification due to the heat flux becoming locally sub-adiabatic. The exact properties of this stably-stratified layer, namely its size $\mathcal{H}_S$ and the degree of its stratification characterised by the Brunt-V\"ais\"al\"a frequency $N$, are however uncertain and highly debated. A stable layer underneath the CMB can have crucial dynamical impacts on the geodynamo. Because of the inhibition of the convective motions, a stable layer is expected to primarily act as a low-pass filter on the magnetic field, smoothing out the rapidly-varying and small-scale features by skin effect. To investigate this effect more systematically, we compute 70 global geodynamo models varying the size of the stably-stratified layer from 0 to 300~km and its amplitude from $N/\Omega = 0$ to $N/\Omega \simeq 50$, $\Omega$ being the rotation rate. We show that the penetration of the convective flow in the stably-stratified layer is controlled by the typical size of the convective eddies and by the local variations of the ratio $N/\Omega$. Using quantitative measures of the degree of morphological semblance between the magnetic field obtained in numerical models and the geomagnetic field at the CMB, we establish an upper bound for the stable layer thickness $\mathcal{H}_s < (N/\Omega)^{-1} d_c$, $d_c$ being the horizontal size of the convective flow at the base of the stable layer. This defines a strong geomagnetic constraint on the properties of a stably-stratified layer beneath the CMB.

physics.geo-ph↗

arXiv2017

Estimating the deep solar meridional circulation using magnetic observations and a dynamo model: a variational approach

We show how magnetic observations of the Sun can be used in conjunction with an axisymmetric flux-transport solar dynamo model in order to estimate the large-scale meridional circulation throughout the convection zone. Our innovative approach rests on variational data assimilation, whereby the distance between predictions and observations (measured by an objective function) is iteratively minimized by means of an optimization algorithm seeking the meridional flow which best accounts for the data. The minimization is performed using a quasi-Newton technique, which requires the knowledge of the sensitivity of the objective function to the meridional flow. That sensitivity is efficiently computed via the integration of the adjoint flux-transport dynamo model. Closed-loop (also known as twin) experiments using synthetic data demonstrate the validity and accuracy of this technique, for a variety of meridional flow configurations, ranging from unicellular and equatorially symmetric to multicellular and equatorially asymmetric. In this well-controlled synthetic context, we perform a systematic study of the behavior of our variational approach under different observational configurations, by varying their spatial density, temporal density, noise level, as well as the width of the assimilation window. We find that the method is remarkably robust, leading in most cases to a recovery of the true meridional flow to within better than 1%. These encouraging results are a first step towards using this technique to i) better constrain the physical processes occurring inside the Sun and ii) better predict solar activity on decadal time scales.

astro-ph.SR↗

arXiv2017

Variational estimation of the large scale time dependent meridional circulation in the Sun: proofs of concept with a solar mean field dynamo model

We present in this work the development of a solar data assimilation method based on an axisymmetric mean field dynamo model and magnetic surface data, our mid-term goal is to predict the solar quasi cyclic activity. Here we focus on the ability of our algorithm to constrain the deep meridional circulation of the Sun based on solar magnetic observations. To that end, we develop a variational data assimilation technique. Within a given assimilation window, the assimilation procedure minimizes the differences between data and the forecast from the model, by finding an optimal meridional circulation in the convection zone, and an optimal initial magnetic field, via a quasi-Newton algorithm. We demonstrate the capability of the technique to estimate the meridional flow by a closed-loop experiment involving 40 years of synthetic, solar-like data. By assimilating the synthetic magnetic proxies annually, we are able to reconstruct a (stochastic) time-varying meridional circulation which is also slightly equatorially asymmetric. We show that the method is robust in estimating a flow whose level of fluctuation can reach 30% about the average, and that the horizon of predictive capability of the method is of the order of 1 cycle length.

astro-ph.SR↗

arXiv2017

Turbulent geodynamo simulations: a leap towards Earth's core

We present an attempt to reach realistic turbulent regime in direct numerical simulations of the geodynamo. We rely on a sequence of three convection-driven simulations in a rapidly rotating spherical shell. The most extreme case reaches towards the Earth's core regime by lowering viscosity (magnetic Prandtl number Pm=0.1) while maintaining vigorous convection (magnetic Reynolds number Rm>500) and rapid rotation (Ekman number E=1e-7), at the limit of what is feasible on today's supercomputers. A detailed and comprehensive analysis highlights several key features matching geomagnetic observations or dynamo theory predictions -- all present together in the same simulation -- but it also unveils interesting insights relevant for Earth's core dynamics.In this strong-field, dipole-dominated dynamo simulation, the magnetic energy is one order of magnitude larger than the kinetic energy. The spatial distribution of magnetic intensity is highly heterogeneous, and a stark dynamical contrast exists between the interior and the exterior of the tangent cylinder (the cylinder parallel to the axis of rotation that circumscribes the inner core).In the interior, the magnetic field is strongest, and is associated with a vigorous twisted polar vortex, whose dynamics may occasionally lead to the formation of a reverse polar flux patch at the surface of the shell. Furthermore, the strong magnetic field also allows accumulation of light material within the tangent cylinder, leading to stable stratification there. Torsional Alfv{\'e}n waves are frequently triggered in the vicinity of the tangent cylinder and propagate towards the equator.Outside the tangent cylinder, the magnetic field inhibits the growth of zonal winds and the kinetic energy is mostly non-zonal. Spatio-temporal analysis indicates that the low-frequency, non-zonal flow is quite geostrophic (columnar) and predominantly large-scale: an m=1 eddy spontaneously emerges in our most extreme simulations, without any heterogeneous boundary forcing.Our spatio-temporal analysis further reveals that (i) the low-frequency, large-scale flow is governed by a balance between Coriolis and buoyancy forces -- magnetic field and flow tend to align, minimizing the Lorentz force; (ii) the high-frequency flow obeys a balance between magnetic and Coriolis forces; (iii) the convective plumes mostly live at an intermediate scale, whose dynamics is driven by a 3-term 1 MAC balance -- involving Coriolis, Lorentz and buoyancy forces. However, small-scale (E^{1/3}) quasi-geostrophic convection is still observed in the regions of low magnetic intensity.

physics.geo-ph↗

arXiv2016

Spherical convective dynamos in the rapidly rotating asymptotic regime

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a unidimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

physics.geo-ph↗

arXiv2014

Hydromagnetic quasi-geostrophic modes in rapidly rotating planetary cores

The core of a terrestrial-type planet consists of a spherical shell of rapidly rotating, electrically conducting, fluid. Such a body supports two distinct classes of quasi-geostrophic eigenmodes: fast, primarily hydrodynamic, inertial modes with period related to the rotation time scale and slow, primarily magnetic, magnetostrophic modes with much longer periods. Here, we investigate the properties of these hydromagnetic quasi-geostrophic modes as a function of non-dimensional parameters controlling the strength of the background magnetic field, the planetary rotation rate, and the amount of magnetic dissipation. ... read full length abstract in the paper.

physics.geo-ph↗

arXiv2013

A mean-field Babcock-Leighton solar dynamo model with long-term variability

Dynamo models relying on the Babcock-Leighton mechanism are successful in reproducing most of the solar magnetic field dynamical characteristics. However, considering that such models operate only above a lower magnetic field threshold, they do not provide an appropriate magnetic field regeneration process characterizing a self-sustainable dynamo. In this work we consider the existence of an additional \alpha-effect to the Babcock-Leighton scenario in a mean-field axisymmetric kinematic numerical model. Both poloidal field regeneration mechanisms are treated with two different strength-limiting factors. Apart from the solar anti-symmetric parity behavior, the main solar features are reproduced: cyclic polarity reversals, mid-latitudinal equatorward migration of strong toroidal field, poleward migration of polar surface radial fields, and the quadrature phase shift between both. Long-term variability of the solutions exhibits lengthy periods of minimum activity followed by posterior recovery, akin to the observed Maunder Minimum. Based on the analysis of the residual activity during periods of minimum activity, we suggest that these are caused by a predominance of the \alpha-effect over the Babcock-Leighton mechanism in regenerating the poloidal field.

astro-ph.SR↗

arXiv2013

The predictability of advection-dominated flux-transport solar dynamo models

Space weather is a matter of practical importance in our modern society. Predictions of forecoming solar cycles mean amplitude and duration are currently being made based on flux-transport numerical models of the solar dynamo. Interested in the forecast horizon of such studies, we quantify the predictability window of a representative, advection-dominated, flux-transport dynamo model by investigating its sensitivity to initial conditions and control parameters through a perturbation analysis. We measure the rate associated with the exponential growth of an initial perturbation of the model trajectory, which yields a characteristic time scale known as the e-folding time $\tau_e$. The e-folding time is shown to decrease with the strength of the $\alpha$-effect, and to increase with the magnitude of the imposed meridional circulation. Comparing the e-folding time with the solar cycle periodicity, we obtain an average estimate for $\tau_e$ equal to 2.76 solar cycle durations. From a practical point of view, the perturbations analysed in this work can be interpreted as uncertainties affecting either the observations or the physical model itself. After reviewing these, we discuss their implications for solar cycle prediction.

astro-ph.SR↗

arXiv2010

Forward and adjoint quasi-geostrophic models of the geomagnetic secular variation

We introduce a quasi-geostrophic model of core dynamics, which aims at describing core processes on geomagnetic secular variation timescales. It extends the formalism of Alfv\'en torsional oscillations by incorporating non-zonal motions. Within this framework, the magnetohydrodynamics takes place in the equatorial plane; it involves quadratic magnetic quantities, which are averaged along the direction of rotation of the Earth. In addition, the equatorial flow is projected on the core-mantle boundary. It interacts with the magnetic field at the core surface, through the radial component of the magnetic induction equation. That part of the model connects the dynamics and the observed secular variation, with the radial component of the magnetic field acting as a passive tracer. We resort to variational data assimilation to construct formally the relationship between model predictions and observations. Variational data assimilation seeks to minimize an objective function, by computing its sensitivity to its control variables. The sensitivity is efficiently calculated after integration of the adjoint model. We illustrate that framework with twin experiments, performed first in the case of the kinematic core flow inverse problem, and then in the case of Alfv\'en torsional oscillations. In both cases, using the adjoint model allows us to retrieve core state variables which, while taking part in the dynamics, are not directly sampled at the core surface. We study the effect of several factors on the solution (width of the assimilation time window, amount and quality of data), and we discuss the potential of the model to deal with real geomagnetic observations.

physics.geo-ph↗

arXiv2007

A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system

Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system -- some version being currently under construction -- the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfv\'en waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.

physics.geo-ph↗

arXiv2007

Spherical Couette flow in a dipolar magnetic field

We consider numerically the flow of an electrically conducting fluid in a differentially rotating spherical shell, in a dipolar magnetic field. For infinitesimal differential rotation the flow consists of a super-rotating region, concentrated on the particular field line C just touching the outer sphere, in agreement with previous results. Finite differential rotation suppresses this super-rotation, and pushes it inward, toward the equator of the inner sphere. For sufficiently strong differential rotation the outer boundary layer becomes unstable, yielding time-dependent solutions. Adding an overall rotation suppresses these instabilities again. The results are in qualitative agreement with the DTS liquid sodium experiment.

physics.geo-ph↗

arXiv2005

End-effects in rapidly rotating cylindrical Taylor-Couette flow

We present numerical simulations of the flow in a rapidly rotating cylindrical annulus. We show that at the rotation rates relevant to the magneto-rotational instability, the flow is strongly constrained by the Taylor-Proudman theorem. As a result, it is controlled almost entirely by the end-plates. We then consider two possible options for minimizing these end-effects, namely (i) simply taking a very long cylinder, and (ii) splitting the end-plates into a series of differentially rotating rings. Regarding option (i), we show that the cylinder would have to be hundreds of times as long as it is wide before end-effects become unimportant in the interior. Since this is clearly not feasible, we turn to option (ii), and show that in order to obtain a smooth angular velocity profile, the end-plates would have to be split into around ten rings. If the end-plates are split into fewer rings, perhaps 3-5, the angular velocity profile will not be smooth, but will instead consist of a series of Stewartson layers at the boundaries from one ring to the next. We suggest therefore that the instabilities one obtains in this system will be the familiar Kelvin-Helmholtz instabilities of these Stewartson layers, rather than the magneto-rotational instability. At best, one might hope to obtain the MRI superimposed on these Kelvin-Helmholtz modes. Any subsequent interpretation of results is thus likely to be quite complicated.

astro-ph↗