ERC project THEIA

Relief and departures from spherical geometry modify flows in planetary cores, the forces they exert on the surrounding solids, and magnetic induction. THEIA investigated these effects through local wave theory, global spectral methods and direct simulations, alongside the development of rotating-fluid experiments at ISTerre.

Topographic drag at the core–mantle boundary

Core flow encountering relief on the mantle generates waves and pressure variations. Pressure acting on the sloping boundary exerts a torque, transferring angular momentum between the core and mantle. The magnitude of this coupling depends on the relief and on the waves that the fluid can support.

With Rémy Monville and Dominique Jault, we extended the calculation beyond parallel ridges in 2025, allowing relief to vary in both horizontal directions and accounting for rotation, stratification, magnetic effects and planetary curvature. The resulting wave response differs substantially from ridge models. Rossby waves play an important role, and the longest horizontal relief scales dominate the calculated pressure torque. For wavelengths of order 1,000 km or more and a stratification frequency comparable to planetary rotation, the predicted stress can reach the order required by length-of-day variations. This comparison depends on the assumed relief and core properties; it does not determine their actual values.

The ETH-led study by Giraud, Noir, Cébron, Vidal and Monville (2026) considers homogeneous, rapidly rotating fluids, where inertial waves produce pressure drag without stratification. Theory and direct numerical simulations extend the shallow-relief calculation to finite slopes when the frequency at which the flow encounters the relief is small compared with rotation. In the periodic geometry studied, finer relief does not always produce greater drag. The theory was also used to reinterpret the earlier spin-up experiments of Burmann and Noir, whose relaxation times give an indirect estimate of torque.

Flows and magnetic induction in ellipsoids

With Jérémie Vidal, we developed polynomial spectral methods that incorporate ellipsoidal boundaries directly into calculations of global modes, forced flows and stability. Building on earlier compressible-core models, this work examined centrifugal effects on acoustic modes, mean zonal flows under weak mechanical forcing, and precessional instabilities with stress-free boundaries.

The 2021 kinematic dynamo benchmarks determine whether prescribed flows amplify magnetic fields in triaxial ellipsoids, without magnetic feedback on the velocity. They supply reference solutions for subsequent dynamo calculations. Our study of lunar tides and the early Earth’s dynamo found that flow instability and induction can occur while the predicted field intensity remains insufficient under the tested scalings.

Stratification and magnetic coupling

With Paul Pružina and Nathanaël Schaeffer, we studied semi-convection in which faster diffusion of heat than composition permits motion despite a stable overall density distribution. The 2025 A&A paper and 2026 JFM paper describe layer formation and dynamo action in rotating spherical shells. A convecting interior can sustain a magnetic field beneath a stable layer; zonal flows within that layer modify the external field, favouring strongly dipolar, nearly axisymmetric fields in some regimes. This offers a possible interpretation of Saturn’s field. The JFM paper was accepted during THEIA and published online after the grant ended.

In models of inner-core translational oscillations, or Slichter modes, Personnettaz and collaborators (2026) quantified viscous and magnetic damping. Magnetic losses involve electromagnetic coupling and Alfvén-wave emission. The complementary oscillating-sphere theory, published online in October 2026, treats confinement, rotation, viscosity and magnetic effects together. Both studies also received ERC GRACEFUL support.

Numerical and experimental work

The Numerics page describes ToCCo, the ellipsoidal methods and work using XSHELLS. At ISTerre, the WEBER system, mini-THEIA and an approximately one-metre tank were used to develop rotation-control methods, PIV diagnostics and spin-up protocols, providing the basis for comparisons between smooth and rough bottoms. The Experiments page describes these developments and the subsequent BIG-THEIA programme. Collaborative work also developed modal acoustic velocimetry for libration-driven flows.

Combining relief, stratification, magnetic fields and turbulence to account for core–mantle dissipation remains open, as does the origin of the ancient lunar magnetic field. The team page and complete bibliography give the contributions and references.

Project information

• 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. CORDIS project record.
• EU contribution recorded by CORDIS: €1,448,493.

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).