ERC project THEIA

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THEIA: how boundary relief changes planetary core dynamics

Led by David Cébron, CNRS researcher at ISTerre, ERC THEIA (2020–2026) brought together theory, numerical simulations and rotating-fluid experiments to understand how irregular boundaries change flows, dissipation and magnetic induction in planetary cores.

Liquid cores exchange angular momentum with the surrounding solid layers and can generate planetary magnetic fields. Their boundaries are neither perfectly spherical nor perfectly smooth. How do deformations and relief modify the waves inside the fluid and the forces acting on the solid? THEIA investigated these mechanisms, motivated by the Earth’s rotation and the magnetic history of the Earth–Moon system.

The project leaves published scientific results, open numerical methods and experimental apparatus built at ISTerre. David Cébron assembled a group spanning these complementary approaches; the achievements below reflect the contributions of its researchers, engineers and collaborators.

The intermediate THEIA tank, approximately one metre across, on the WEBER rotating platform at ISTerre. Experimental conception and design: David Cébron and Max Solazzo. CAD, mechanical construction and assembly: Max Solazzo.

Relief and the forces exchanged between core and mantle

Flow encountering boundary relief generates waves and pressure variations. Pressure acting on the sloping surface transfers angular momentum between fluid and solid. Calculating this coupling requires accounting for the relief geometry and the waves supported by the fluid.

Rémy Monville developed ToCCo, an open-source tool for calculating topographic stresses. With David Cébron and Dominique Jault, he extended core–mantle drag calculations to relief varying in both horizontal directions, including rotation, stratification, magnetic effects and curvature. Under particular assumptions about relief and stratification, the calculated stress can reach the order inferred from variations in the length of the day. This identifies a possible coupling mechanism; it does not determine the actual relief or stratification of Earth’s core. Monville, Cébron & Jault (2025).

A complementary study led at ETH Zürich by Vadim Giraud and Jérôme Noir, with David Cébron, Jérémie Vidal and Rémy Monville, combined theory and direct simulations to investigate inertial-wave pressure drag in rapidly rotating fluids. Its comparison with spin-up experiments uses the earlier measurements of Burmann and Noir, distinct from the PIV measurements made in THEIA’s one-metre tank.

The illustration shows idealised periodic relief and pressure-field sections in three wave regimes. Adapted from Figures 1 and 3 of Giraud et al., Topographic drag in rapidly rotating fluids (2026), CC BY 4.0.

Waves, forced flows and magnetic induction beyond the sphere

Jérémie Vidal and David Cébron developed and extended polynomial spectral methods that incorporate ellipsoidal boundaries directly into calculations of global modes, forced flows and stability. Their work examined acoustic and inertial modes, mechanically generated zonal flows and precessional instabilities.

Their kinematic dynamo benchmarks in triaxial ellipsoids (2021) test whether prescribed flows amplify a magnetic field, without magnetic feedback on the velocity. These are reference calculations for induction, rather than self-consistent nonlinear dynamos.

Their study of lunar tides and the early Earth’s dynamo (2026) also identified a useful limit: tidal forcing can produce unstable flows and sufficient induction while the field intensity predicted under the tested scaling remains too weak to explain the ancient magnetic record.

Stratified fluids and planetary magnetic fields

Paul Pružina, David Cébron and Nathanaël Schaeffer studied semi-convection, in which differences between thermal and compositional diffusion allow motion despite a stable overall density distribution. Their 2025 study showed that these motions can sustain planetary dynamos.

In some simulated regimes, a convecting interior sustains a magnetic field beneath a persistent stably stratified layer. Flows within that layer modify the external field, favouring strongly dipolar and nearly axisymmetric fields, with features reminiscent of Saturn’s magnetism. The illustration combines Saturn with a numerical visualisation; it is not a reconstruction of Saturn’s observed interior.

Graphical abstract accompanying Pružina, Schaeffer & Cébron, Semi-convection in rotating spherical shells: flows, layers and dynamos (2026). This paper was accepted during THEIA and published online after the grant ended.

Related work by Paolo Personnettaz, David Cébron, Nathanaël Schaeffer, Renaud Deguen and Mioara Mandea quantified viscous and magnetic damping of inner-core translational oscillations (2026). A complementary study by Cébron and Personnettaz (2026) treats an oscillating sphere in a rotating spherical cavity. Both studies also received ERC GRACEFUL support.

Experiments built at ISTerre: from mechanical design to flow measurements

THEIA established a dedicated rotating-fluid capability at ISTerre. The programme used mini-THEIA, approximately 50 cm across, and an intermediate tank approximately one metre across on WEBER to develop experimental procedures and investigate rotating flows over smooth and rough bottoms.

David Cébron and Max Solazzo, a permanent CNRS engineer at ISTerre, jointly conceived and designed the THEIA and mini-THEIA experiments. Max Solazzo carried out the CAD, mechanical construction and assembly. The daylight photograph above shows the assembled tank and support; the laser photograph below shows the apparatus during optical measurements.

Particle image velocimetry (PIV) calculates velocities in a plane from the displacement of illuminated tracer particles between successive images. Baptiste Penlou developed PIV acquisition and analysis procedures and spin-up protocols in the intermediate tank, following earlier experimental work, including Samuel Payen’s contribution in 2025.

Comparing the fluid’s adjustment after a change in rotation over smooth and rough bottoms helps investigate topographic coupling. These PIV measurements remained unpublished at the end of the ERC action. They are not presented as quantitative validation of a universal drag law. The photograph shows experimental illumination, not a processed velocity field.

Explore the experiments | See mini-THEIA, laser details and mechanical design in the gallery

A scientific and instrumental legacy

THEIA connected local wave theory, global models and laboratory methods. Its reusable tools include ToCCo, the ellipsoidal modelling programme and contributions to the existing XSHELLS code developed by Nathanaël Schaeffer. Collaborative work also developed modal acoustic velocimetry for libration-driven flows, complementing optical diagnostics.

Combining relief, stratification, magnetic fields and turbulence to account for planetary core dissipation remains an open problem. THEIA’s published models, software and experimental capability provide ways to investigate these mechanisms without claiming a unique explanation for all Earth–Moon observations.

Read the publications and full authorship | Meet the team and collaborators | Explore the numerical methods

Project information and funding

– Full title: Topographic effects in planetary fluid cores: application to the Earth–Moon system.
– Principal investigator: David Cébron, CNRS, ISTerre, Grenoble.
– ERC action: 1 September 2020–31 August 2026; completed.
– Grant agreement: 847433. CORDIS project record.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 847433).