arXiv subjects

David Cébron

Publications and source records attributed to David Cébron.

At least 19 recordsLinked to original sources

arXiv2026

Magnetohydrodynamic drag on an oscillating sphere in a rotating spherical cavity

Oscillating-sphere drag is a classical fluid-mechanics problem, yet no theory simultaneously accounts for confinement, rotation, viscosity and magnetic fields. We consider a conducting sphere undergoing translational oscillations inside a spherical cavity, modelling confined magnetohydrodynamic flows relevant to planet interiors and liquid-metal experiments. Planetary applications include polar (rectilinear oscillations) and equatorial (circular trajectories) Slichter modes of solid inner cores or subsurface-ocean interiors relative to outer ice shells. Existing theories are restricted to separate asymptotic regimes, including viscous drag in bounded fluids (Stokes 1851), rotation effects in inviscid cavities (Busse 1974), and magnetic coupling through oscillatory boundary layers (Buffett and Goertz 1995). We derive a unified asymptotic framework for oscillatory drag in confined spherical shells with conductivity and permeability contrasts between the inner sphere, fluid shell and outer solid. Closed-form force laws and dissipation predictions are obtained for polar and equatorial modes, with finite-rotation corrections for the polar mode. The framework accounts for viscous and magnetic pressure contributions, magnetic tension, Alfvén-wave radiation and magnetohydrodynamic Stokes-Ekman layers. Recovering classical boundary-layer theories as limiting cases, the analysis yields a local Alfvén-wave drag law for spherical shells, analogous to bounded oscillatory Stokes drag. Beyond the thin boundary-layer approximation, complementary asymptotics yield a closed-form representation of bounded Stokes flow and extend inductionless theory to spherical shells. Direct numerical simulations validate the predictions across a broad parameter range. The framework predicts oscillatory coupling, added-mass, drag and dissipation in planetary cores, subsurface oceans and liquid-metal experiments.

physics.flu-dyn↗

arXiv2026

Semi-convection in rotating spherical shells: flows, layers and dynamos

Large regions of giant planets are thought to possess unstable thermal gradients stabilised by gradients in heavy-element composition. The fluid can then develop semi-convection, a double-diffusive instability driven by the unequal molecular diffusivities of heat and composition. While previous studies have focus mainly on local Cartesian models, we investigate semi-convection in rotating spherical shells, the geometry relevant to planetary interiors, using direct numerical simulations In a first non-linear phase, the flow spontaneously forms concentric density staircases composed of well-mixed layers separated by thin, strongly stratified interfaces. We propose scalings for both the thickness of these layers and their survival time in terms of the rotation rate and stratification. Over longer timescales, layers merge to produce statistically steady states consisting either of a fully convective shell or of a convective layer overlain by a persistent stably stratified layer (SSL), depending on the balance between stratification and rotation. Dynamo simulations show that flow within the convective region can generate a self-sustained magnetic field, which is filtered by zonal flows in the overlying SSL. This results in a strongly dipolar and axisymmetric external field, in encouraging agreement with Saturn's magnetic field. Across the explored parameter range, both the Rossby number and the thickness of the stably stratified layer are governed by a single combination of control parameters. This enables identification of a regime favourable to planetary-like dynamos.

physics.flu-dyn↗

arXiv2026

Ohmic and viscous damping of inner core translational oscillations

Large earthquakes can trigger translational oscillations of Earth's inner core (Slichter modes), yet their damping remains uncertain. Using simulations, we quantify viscous and Ohmic dissipation in the fluid outer core. Earth's rotation splits the motion into one polar and two equatorial modes. We explore all three and derive scaling laws for the quality factor with each dissipation mechanism. Viscous effects are negligible, confined to a thin layer at the inner core boundary. Ohmic dissipation dominates, with decay times of 3-16 years. Equatorial modes damp at least twice as fast as the polar mode. Our results suggest that Slichter modes can persist for years. Their continued non-detection is therefore more likely due to weak excitation than rapid damping.

physics.geo-ph↗

arXiv2026

Did lunar tides sustain the early Earth's dynamo?

Geological data show that, early in its history, the Earth had a large-scale magnetic field with an amplitude comparable to the one of the present geomagnetic field. However, its origin remains enigmatic and various mechanisms have been proposed to explain the Earth's field over geological time scales. Here, we critically evaluate whether tidal forcing could explain the ancient geodynamo, by combining constraints from geophysical models of the Earth-Moon system and predictions from turbulence studies. Our analysis shows that lunar tidal forcing could have been sufficiently strong before $-3.25$ Gy to trigger turbulence within the Earth's core, and potentially to sustain dynamo action during that interval. Then, we propose new scaling laws for the magnetic field amplitude $B$. We expect the latter to scale as $B \propto β^{4/3}$, where $β$ is the equatorial ellipticity of the liquid core, if the turbulence involves weak interactions of three-dimensional inertial waves. Alternatively, in the regime of strong tidal forcing, the expected scaling becomes $B \propto β$. When extrapolated to the Earth's core, it suggests that tidal forcing alone was too weak to possibly explain the ancient geomagnetic field. Therefore, our study indirectly favours another origin for the early Earth's dynamo on long time scales (e.g. exsolution of light elements atop the core, or thermal convection due to secular cooling).

physics.geo-ph↗

arXiv2025

Planetary dynamos driven by semiconvection in stably stratified layers

Stably stratified fluid layers are common in gaseous planets, stellar interiors, and planetary cores, and have long been considered incapable of sustaining dynamo action. Here, we show that semiconvection - driven by a destabilizing thermal gradient within an overall stably stratified medium - can, in fact, give rise to self-sustained magnetic fields. Motivated by recent models suggesting that large portions of Jupiter and Saturn may be semiconvective, we perform direct numerical simulations in spherical shells, operating in the planetary-relevant regime of low magnetic Prandtl numbers. From a primary semiconvection instability, a layered convection state spontaneously develops, consisting of a convective region beneath a stably stratified layer of comparable thickness. Fluid motions in this convective region are strong enough to produce magnetic fields with key features observed in planetary dynamos, including strong dipolarity, realistic field strengths, and spectral characteristics. These results provide the first direct evidence that semiconvection can drive dynamo action in stably stratified regions of gas giants and stellar interiors, with important implications for understanding astrophysical magnetic field generation.

astro-ph.EP↗

arXiv2025

Geophysical flows over topography, a playground for laboratory experiments

Physicists face major challenges in modelling multi-scale phenomena that are observed in geophysical flows (e.g. in the Earth's oceans and atmosphere, or liquid planetary cores). In particular, complexities arise because geophysical fluids are rotating and subject to density variations, but also because the fluid boundaries have complex geometries (e.g. the ocean floor) with wavelengths ranging from metres to thousands of kilometres. Dynamical models of planetary fluid layers are thus often constrained by observations, whose interpretation necessitates a comprehensive understanding of the underlying physics. To this end, geophysical studies often combine cutting-edge experiments across a wide range of parameters, together with theory and numerical simulations, to derive predictive scaling laws applicable for planetary settings. In this review, we discuss experimental efforts that have contributed to our understanding of geophysical flows with topography. More specifically, we focus on (i) the flow response to mechanical (orbital) forcings in the presence of a large-scale (ellipsoidal) topography, (ii) some effects of small-scale topography onto bulk flows and boundary-layer dynamics, and (iii) the interaction between convection and roughness. The geophysical context is briefly introduced for each case, and some experimental perspectives are drawn.

physics.flu-dyn↗

arXiv2021

Mean zonal flows induced by weak mechanical forcings in rotating spheroids

The generation of mean flows is a long-standing issue in rotating fluids. Motivated by planetary objects, we consider here a rapidly rotating fluid-filled spheroid, which is subject to weak perturbations of either the boundary (e.g. tides) or the rotation vector (e.g. in direction by precession, or in magnitude by longitudinal librations). Using boundary-layer theory, we determine the mean zonal flows generated by nonlinear interactions within the viscous Ekman layer. These flows are of interest because they survive in the relevant planetary regime of both vanishing forcings and viscous effects. We extend the theory to take into account (i) the combination of spatial and temporal perturbations, providing new mechanically driven zonal flows (e.g. driven by latitudinal librations), and (ii) the spheroidal geometry relevant for planetary bodies. Wherever possible, our analytical predictions are validated with direct numerical simulations. The theoretical solutions are in good quantitative agreement with the simulations, with expected discrepancies (zonal jets) in the presence of inertial waves generated at the critical latitudes (as for precession). Moreover, we find that the mean zonal flows can be strongly affected in spheroids. Guided by planetary applications, we also revisit the scaling laws for the geostrophic shear layers at the critical latitudes, and the influence of a solid inner core.

physics.flu-dyn↗

arXiv2021

Acoustic and inertial modes in planetary-like rotating ellipsoids

The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093) pioneered a method to compute them n incompressible fluid ellipsoids. Yet, taking density (and pressure) variations into account is required for accurate planetary applications, which has hitherto been largely overlooked in ellipsoidal models. To go beyond the incompressible theory, we present a Galerkin method in rigid coreless ellipsoids, based on a global polynomial description. We apply the method to investigate the normal modes of fully compressible, rotating and diffusionless fluids. We consider an idealized model, which fairly reproduces the density variations in the Earth's liquid core and Jupiter-like gaseous planets. We successfully benchmark the results against standard finite-element computations. Notably, we find that the quasi-geostrophic inertial modes can be significantly modified by compressibility, even in moderately compressible interiors. Finally, we discuss the use of the normal modes to build reduced dynamical models of planetary flows.

astro-ph.EP↗

arXiv2021

Kinematic dynamos in triaxial ellipsoids

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

astro-ph.EP↗

arXiv2021

Acoustic modes of rapidly rotating ellipsoids subject to centrifugal gravity

The acoustic modes of a rotating fluid-filled cavity can be used to determine the effective rotation rate of a fluid (since the resonant frequencies are modified by the flows). To be accurate, this method requires a prior knowledge of the acoustic modes in rotating fluids. Contrary to the Coriolis force, centrifugal gravity has received much less attention in the experimental context. Motivated by on-going experiments in rotating ellipsoids, we study how global rotation and buoyancy modify the acoustic modes of fluid-filled ellipsoids in isothermal (or isentropic) hydrostatic equilibrium. We go beyond the standard acoustic equation, which neglects solid-body rotation and gravity, by deriving an exact wave equation for the acoustic velocity. We then solve the wave problem using a polynomial spectral method in ellipsoids, which is compared with finite-element solutions of the primitive fluid-dynamic equations. We show that the centrifugal acceleration has measurable effects on the acoustic frequencies when $M_Ω\gtrsim 0.3$, where $M_Ω$ is the rotational Mach number defined as the ratio of the sonic and rotational time scales. Such a regime can be reached with experiments rotating at a few tens of Hz, by replacing air with a highly compressible gas (e.g. SF$_6$ or C$_4$F$_8$).

physics.flu-dyn↗

arXiv2020

Acoustic spectra of a gas-filled rotating spheroid

The acoustic spectrum of a gas-filled resonating cavity can be used to indirectly probe its internal velocity field. This unconventional velocimetry method is particularly interesting for opaque fluid or rapidly rotating flows, which cannot be imaged with standard methods. This requires to (i) identify a large enough number of acoustic modes, (ii) accurately measure their frequencies, and (iii) compare with theoretical synthetic spectra. Relying on a dedicated experiment, an air-filled rotating spheroid of moderate ellipticity, our study addresses these three challenges. To do so, we use a comprehensive theoretical framework, together with finite-element calculations, and consider symmetry arguments. We show that the effects of the Coriolis force can be successfully retrieved through our acoustic measurements, providing the first experimental measurements of the rotational splitting (or Ledoux) coefficients for a large collection of modes. Our results pave the way for the modal acoustic velocimetry to be a robust, versatile, and non-intrusive method for mapping large-scale flows. Pages: 1-14

physics.flu-dyn↗

arXiv2019

Fossil field decay due to nonlinear tides in massive binaries

Surface magnetic fields have been detected in 5 to 10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars) collaboration. Different physical conditions in the molecular clouds giving birth to isolated stars and binaries are commonly invoked. In addition, we propose that the observed lower magnetic incidence in close binaries may be due to nonlinear tides. Indeed, close binaries are probably prone to tidal instability, a fluid instability growing upon the equilibrium tidal flow via nonlinear effects. Yet, stratified effects have hitherto been largely overlooked. We theoretically and numerically investigate tidal instability in rapidly rotating, stably stratified fluids permeated by magnetic fields. We use the short-wavelength stability method to propose a comprehensive (local) theory of tidal instability at the linear onset, discussing damping effects. Then, we propose a mixing-length theory for the mixing generated by tidal instability in the nonlinear regime. We successfully assess our theoretical predictions against proof-of-concept, direct numerical simulations. Finally, we compare our predictions with the observations of short-period, double-lined spectroscopic binary systems. Using new analytical results, cross-validated by a direct integration of the stability equations, we show that tidal instability can be generated by nonlinear couplings of inertia-gravity waves with the equilibrium tidal flow in short-period massive binaries, even against the Joule diffusion. In the nonlinear regime, a fossil magnetic field can be dissipated by the turbulent magnetic diffusion induced by the saturated tidal flows. We predict that the turbulent Joule diffusion of fossil fields would occur in a few million years for several short-period massive binaries. Therefore, turbulent tidal flows could explain the observed dearth of some short-period magnetic binaries.

astro-ph.SR↗

arXiv2019

Rotating double-diffusive convection in stably stratified planetary cores

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.

physics.flu-dyn↗

arXiv2019

Precessing spherical shells: flows, dissipation, dynamo and the lunar core

Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos.The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate.However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies.We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence, and magnetic field generation.We observe no significant effects of the inner core on the onset of the instabilities.We obtain an analytical estimate of the viscous dissipation, mostly due to boundary layer friction in our simulations.We propose theoretical onsets for hydrodynamic instabilities, and document the intensity of turbulent fluctuations.We extend previous precession dynamo studies towards lower viscosities, at the limits of today's computers.In the low viscosity regime, precession dynamos rely on the presence of large-scale vortices, and the surface magnetic fields are dominated by small scales.Interestingly, intermittent and self-killing dynamos are observed.Our results suggest that large-scale planetary magnetic fields are unlikely to be produced by a precession-driven dynamo in a spherical core.But this question remains open as planetary cores are not exactly spherical, and thus the coupling between the fluid and the boundary does not vanish in the relevant limit of small viscosity.Moreover, the fully turbulent dissipation regime has not yet been reached in simulations.Our results suggest that the melted lunar core has been in a turbulent state throughout its history.Furthermore, in the view of recent experimental results, we propose updated formulas predicting the fluid mean rotation vector and the associated dissipation in both the laminar and the turbulent regimes.

physics.flu-dyn↗

arXiv2018

Magnetic fields driven by tidal mixing in radiative stars

Stellar magnetism plays an important role in stellar evolution theory. Approximatively 10% of observed main sequence (MS) and pre-main-sequence (PMS) radiative stars exhibit surface magnetic fields above the detection limit, raising the question of their origin. These stars host outer radiative envelopes, which are stably stratified. Therefore, they are assumed to be motionless in standard models of stellar structure and evolution. We focus on rapidly rotating, radiative stars which may be prone to the tidal instability, due to an orbital companion. Using direct numerical simulations in a sphere, we study the interplay between a stable stratification and the tidal instability, and assess its dynamo capability. We show that the tidal instability is triggered regardless of the strength of the stratification (Brunt-V{ä}is{ä}l{ä} frequency). Furthermore, the tidal instability can lead to both mixing and self-induced magnetic fields in stably stratified layers (provided that the Brunt-V{ä}is{ä}l{ä} frequency does not exceed the stellar spin rate in the simulations too much). The application to stars suggests that the resulting magnetic fields could be observable at the stellar surfaces. Indeed, we expect magnetic field strengths up to several Gauss.Consequently, tidally driven dynamos should be considered as a (complementary) dynamo mechanism, possibly operating in radiative MS and PMS stars hosting orbital companions. In particular, tidally driven dynamos may explain the observed magnetism of tidally deformed and rapidly rotating Vega-like stars.

astro-ph.SR↗

arXiv2017

Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits

We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche--Riemann ellipsoids moving on circular Kepler orbits. However, previous stability studies have to be reassessed. Indeed, they only consider global perturbations of large wavelength or local perturbations of short wavelength. Moreover many planets and stars undergo orbital motions on eccentric Kepler orbits, implying time-dependent ellipsoidal semi-axes. This time dependence has never been taken into account in hydrodynamic stability studies. In this work we overcome these stringent assumptions. We extend the hydrodynamic stability analysis of rotating ellipsoids to the case of eccentric orbits. We have developed two open-source and versatile numerical codes to perform global and local inviscid stability analyses. They give sufficient conditions for instability. The global method, based on an exact and closed Galerkin basis, handles rigorously global ellipsoidal perturbations of unprecedented complexity. Tidally driven and libration-driven elliptical instabilities are first recovered and unified within a single framework. Then we show that new global fluid instabilities can be triggered in ellipsoids by tidal effects due to eccentric Kepler orbits. Their existence is confirmed by a local analysis and direct numerical simulations of the fully nonlinear and viscous problem. Thus a non-zero orbital eccentricity may have a strong destabilising effect in celestial fluid bodies, which may lead to space-filling turbulence in most of the parameters range.

physics.class-ph↗

arXiv2017

Experimental and Theoretical Study of Magnetohydrodynamic Ship Models

Magnetohydrodynamic (MHD) ships represent a clear demonstration of the Lorentz force in fluids, which explains the number of students practicals or exercises described on the web. However, the related literature is rather specific and no complete comparison between theory and typical small scale experiments is currently available. This work provides, in a self-consistent framework, a detailed presentation of the relevant theoretical equations for small MHD ships and experimental measurements for future benchmarks. Theoretical results of the literature are adapted to these simple battery/magnets powered ships moving on salt water. Comparison between theory and experiments are performed to validate each theoretical step such as the Tafel and the Kohlrausch laws, or the predicted ship speed. A successful agreement is obtained without any adjustable parameter. Finally, based on these results, an optimal design is then deduced from the theory. Therefore this work provides a solid theoretical and experimental ground for small scale MHD ships, by presenting in detail several approximations and how they affect the boat efficiency. Moreover, the theory is general enough to be adapted to other contexts, such as large scale ships or industrial flow measurement techniques.

physics.class-ph↗

arXiv2017

Diffusionless hydromagnetic modes in rotating ellipsoids: a road to weakly nonlinear models?

We investigate free hydromagnetic eigenmodes of an incompressible, inviscid and ideal electrically conducting fluid in rotating triaxial ellipsoids. The container rotates with an angular velocity tilted from its figure. The magnetic base state is a uniform current density also tilted. Three-dimensional perturbations upon the base state are expanded onto a finite-dimensional polynomial basis. By combining symbolic and numerical computations, we are able to get the eigenmodes of high spatial complexity. Hydromagnetic modes of the sphere still exist in triaxial geometry. A plane-wave analysis is also carried on, explaining the dispersion relation observed in our model. Without magnetic field, the modes reduce to the inertial modes of the ellipsoids, which form a complete basis. We propose to use these modes to study the weakly nonlinear saturation of inertial instabilities, especially the elliptical one.

physics.flu-dyn↗